TSTP Solution File: PUZ016-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : PUZ016-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n029.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 : Thu Aug 31 13:11:47 EDT 2023
% Result : Unsatisfiable 80.86s 81.00s
% Output : CNFRefutation 80.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 32
% Syntax : Number of formulae : 84 ( 33 unt; 17 typ; 0 def)
% Number of atoms : 101 ( 20 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 75 ( 41 ~; 34 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 5 >; 8 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 12 con; 0-8 aty)
% Number of variables : 149 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
row: $i > $i ).
tff(decl_23,type,
not_covered: $i ).
tff(decl_24,type,
squares: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_25,type,
achievable: ( $i * $i ) > $o ).
tff(decl_26,type,
covered: $i ).
tff(decl_27,type,
successor: $i > $i ).
tff(decl_28,type,
complement: $i > $i ).
tff(decl_29,type,
n1: $i ).
tff(decl_30,type,
n2: $i ).
tff(decl_31,type,
n3: $i ).
tff(decl_32,type,
n4: $i ).
tff(decl_33,type,
n5: $i ).
tff(decl_34,type,
n6: $i ).
tff(decl_35,type,
n7: $i ).
tff(decl_36,type,
n8: $i ).
tff(decl_37,type,
n9: $i ).
tff(decl_38,type,
removed: $i ).
cnf(place_vertical_pieces,axiom,
( achievable(row(successor(X1)),squares(complement(X2),complement(X3),complement(X4),complement(X5),complement(X6),complement(X7),complement(X8),complement(X9)))
| ~ achievable(row(X1),squares(X2,X3,X4,X5,X6,X7,X8,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',place_vertical_pieces) ).
cnf(complement_of_not_covered_is_covered,axiom,
complement(not_covered) = covered,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_not_covered_is_covered) ).
cnf(complement_of_covered_is_not_covered,axiom,
complement(covered) = not_covered,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_covered_is_not_covered) ).
cnf(successor_of_7_is_8,axiom,
successor(n7) = n8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_7_is_8) ).
cnf(complement_of_removed_is_not_covered,axiom,
complement(removed) = not_covered,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_removed_is_not_covered) ).
cnf(prove_row_8_can_be_covered,negated_conjecture,
~ achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_row_8_can_be_covered) ).
cnf(cover_columns_6_and_7,axiom,
( achievable(row(X1),squares(X2,X3,X4,X5,X6,covered,covered,X7))
| ~ achievable(row(X1),squares(X2,X3,X4,X5,X6,not_covered,not_covered,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cover_columns_6_and_7) ).
cnf(successor_of_1_is_2,axiom,
successor(n1) = n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_1_is_2) ).
cnf(cover_columns_2_and_3,axiom,
( achievable(row(X1),squares(X2,covered,covered,X3,X4,X5,X6,X7))
| ~ achievable(row(X1),squares(X2,not_covered,not_covered,X3,X4,X5,X6,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cover_columns_2_and_3) ).
cnf(first_row_initially,hypothesis,
achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,not_covered,not_covered,not_covered)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_row_initially) ).
cnf(successor_of_3_is_4,axiom,
successor(n3) = n4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_3_is_4) ).
cnf(successor_of_2_is_3,axiom,
successor(n2) = n3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_2_is_3) ).
cnf(successor_of_6_is_7,axiom,
successor(n6) = n7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_6_is_7) ).
cnf(successor_of_5_is_6,axiom,
successor(n5) = n6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_5_is_6) ).
cnf(successor_of_4_is_5,axiom,
successor(n4) = n5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_4_is_5) ).
cnf(c_0_15,axiom,
( achievable(row(successor(X1)),squares(complement(X2),complement(X3),complement(X4),complement(X5),complement(X6),complement(X7),complement(X8),complement(X9)))
| ~ achievable(row(X1),squares(X2,X3,X4,X5,X6,X7,X8,X9)) ),
place_vertical_pieces ).
cnf(c_0_16,axiom,
complement(not_covered) = covered,
complement_of_not_covered_is_covered ).
cnf(c_0_17,plain,
( achievable(row(successor(X1)),squares(complement(X2),complement(X3),complement(X4),complement(X5),complement(X6),complement(X7),complement(X8),covered))
| ~ achievable(row(X1),squares(X2,X3,X4,X5,X6,X7,X8,not_covered)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,axiom,
complement(covered) = not_covered,
complement_of_covered_is_not_covered ).
cnf(c_0_19,plain,
( achievable(row(successor(X1)),squares(complement(X2),complement(X3),complement(X4),complement(X5),complement(X6),complement(X7),not_covered,covered))
| ~ achievable(row(X1),squares(X2,X3,X4,X5,X6,X7,covered,not_covered)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,plain,
( achievable(row(successor(X1)),squares(complement(X2),complement(X3),complement(X4),complement(X5),complement(X6),complement(X7),complement(X8),not_covered))
| ~ achievable(row(X1),squares(X2,X3,X4,X5,X6,X7,X8,covered)) ),
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_21,plain,
( achievable(row(successor(X1)),squares(complement(X2),complement(X3),complement(X4),complement(X5),covered,complement(X6),not_covered,covered))
| ~ achievable(row(X1),squares(X2,X3,X4,X5,not_covered,X6,covered,not_covered)) ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_22,plain,
( achievable(row(successor(X1)),squares(complement(X2),complement(X3),complement(X4),complement(X5),covered,complement(X6),complement(X7),covered))
| ~ achievable(row(X1),squares(X2,X3,X4,X5,not_covered,X6,X7,not_covered)) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_23,plain,
( achievable(row(successor(X1)),squares(complement(X2),complement(X3),complement(X4),complement(X5),complement(X6),complement(X7),covered,not_covered))
| ~ achievable(row(X1),squares(X2,X3,X4,X5,X6,X7,not_covered,covered)) ),
inference(spm,[status(thm)],[c_0_20,c_0_16]) ).
cnf(c_0_24,plain,
( achievable(row(successor(X1)),squares(complement(X2),complement(X3),complement(X4),covered,covered,complement(X5),not_covered,covered))
| ~ achievable(row(X1),squares(X2,X3,X4,not_covered,not_covered,X5,covered,not_covered)) ),
inference(spm,[status(thm)],[c_0_21,c_0_16]) ).
cnf(c_0_25,plain,
( achievable(row(successor(X1)),squares(complement(X2),complement(X3),complement(X4),covered,covered,complement(X5),complement(X6),covered))
| ~ achievable(row(X1),squares(X2,X3,X4,not_covered,not_covered,X5,X6,not_covered)) ),
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_26,plain,
( achievable(row(successor(X1)),squares(complement(X2),complement(X3),complement(X4),complement(X5),complement(X6),covered,covered,not_covered))
| ~ achievable(row(X1),squares(X2,X3,X4,X5,X6,not_covered,not_covered,covered)) ),
inference(spm,[status(thm)],[c_0_23,c_0_16]) ).
cnf(c_0_27,plain,
( achievable(row(successor(X1)),squares(covered,complement(X2),complement(X3),covered,covered,complement(X4),not_covered,covered))
| ~ achievable(row(X1),squares(not_covered,X2,X3,not_covered,not_covered,X4,covered,not_covered)) ),
inference(spm,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_28,plain,
( achievable(row(successor(X1)),squares(covered,complement(X2),complement(X3),covered,covered,complement(X4),complement(X5),covered))
| ~ achievable(row(X1),squares(not_covered,X2,X3,not_covered,not_covered,X4,X5,not_covered)) ),
inference(spm,[status(thm)],[c_0_25,c_0_16]) ).
cnf(c_0_29,axiom,
successor(n7) = n8,
successor_of_7_is_8 ).
cnf(c_0_30,plain,
( achievable(row(successor(X1)),squares(complement(X2),complement(X3),covered,complement(X4),complement(X5),covered,covered,not_covered))
| ~ achievable(row(X1),squares(X2,X3,not_covered,X4,X5,not_covered,not_covered,covered)) ),
inference(spm,[status(thm)],[c_0_26,c_0_16]) ).
cnf(c_0_31,plain,
( achievable(row(successor(X1)),squares(covered,complement(X2),complement(X3),covered,covered,not_covered,not_covered,covered))
| ~ achievable(row(X1),squares(not_covered,X2,X3,not_covered,not_covered,covered,covered,not_covered)) ),
inference(spm,[status(thm)],[c_0_27,c_0_18]) ).
cnf(c_0_32,axiom,
complement(removed) = not_covered,
complement_of_removed_is_not_covered ).
cnf(c_0_33,plain,
( achievable(row(n8),squares(covered,complement(X1),complement(X2),covered,covered,complement(X3),complement(X4),covered))
| ~ achievable(row(n7),squares(not_covered,X1,X2,not_covered,not_covered,X3,X4,not_covered)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
( achievable(row(successor(X1)),squares(complement(X2),covered,covered,complement(X3),complement(X4),covered,covered,not_covered))
| ~ achievable(row(X1),squares(X2,not_covered,not_covered,X3,X4,not_covered,not_covered,covered)) ),
inference(spm,[status(thm)],[c_0_30,c_0_16]) ).
cnf(c_0_35,plain,
( achievable(row(successor(X1)),squares(covered,complement(X2),not_covered,covered,covered,not_covered,not_covered,covered))
| ~ achievable(row(X1),squares(not_covered,X2,removed,not_covered,not_covered,covered,covered,not_covered)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
( achievable(row(n8),squares(covered,complement(X1),complement(X2),covered,covered,complement(X3),not_covered,covered))
| ~ achievable(row(n7),squares(not_covered,X1,X2,not_covered,not_covered,X3,covered,not_covered)) ),
inference(spm,[status(thm)],[c_0_33,c_0_18]) ).
cnf(c_0_37,negated_conjecture,
~ achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
prove_row_8_can_be_covered ).
cnf(c_0_38,axiom,
( achievable(row(X1),squares(X2,X3,X4,X5,X6,covered,covered,X7))
| ~ achievable(row(X1),squares(X2,X3,X4,X5,X6,not_covered,not_covered,X7)) ),
cover_columns_6_and_7 ).
cnf(c_0_39,plain,
( achievable(row(successor(X1)),squares(complement(X2),covered,covered,complement(X3),not_covered,covered,covered,not_covered))
| ~ achievable(row(X1),squares(X2,not_covered,not_covered,X3,covered,not_covered,not_covered,covered)) ),
inference(spm,[status(thm)],[c_0_34,c_0_18]) ).
cnf(c_0_40,plain,
( achievable(row(successor(X1)),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered))
| ~ achievable(row(X1),squares(not_covered,removed,removed,not_covered,not_covered,covered,covered,not_covered)) ),
inference(spm,[status(thm)],[c_0_35,c_0_32]) ).
cnf(c_0_41,axiom,
successor(n1) = n2,
successor_of_1_is_2 ).
cnf(c_0_42,plain,
( achievable(row(n8),squares(covered,complement(X1),complement(X2),covered,covered,not_covered,not_covered,covered))
| ~ achievable(row(n7),squares(not_covered,X1,X2,not_covered,not_covered,covered,covered,not_covered)) ),
inference(spm,[status(thm)],[c_0_36,c_0_18]) ).
cnf(c_0_43,negated_conjecture,
~ achievable(row(n8),squares(covered,covered,covered,covered,covered,not_covered,not_covered,covered)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,axiom,
( achievable(row(X1),squares(X2,covered,covered,X3,X4,X5,X6,X7))
| ~ achievable(row(X1),squares(X2,not_covered,not_covered,X3,X4,X5,X6,X7)) ),
cover_columns_2_and_3 ).
cnf(c_0_45,plain,
( achievable(row(successor(X1)),squares(covered,complement(X2),not_covered,covered,covered,not_covered,not_covered,covered))
| ~ achievable(row(X1),squares(not_covered,X2,covered,not_covered,not_covered,covered,covered,not_covered)) ),
inference(spm,[status(thm)],[c_0_31,c_0_18]) ).
cnf(c_0_46,plain,
( achievable(row(successor(X1)),squares(complement(X2),covered,covered,not_covered,not_covered,covered,covered,not_covered))
| ~ achievable(row(X1),squares(X2,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)) ),
inference(spm,[status(thm)],[c_0_39,c_0_18]) ).
cnf(c_0_47,plain,
( achievable(row(n2),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered))
| ~ achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,covered,covered,not_covered)) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,hypothesis,
achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,not_covered,not_covered,not_covered)),
first_row_initially ).
cnf(c_0_49,plain,
( achievable(row(n8),squares(covered,complement(X1),not_covered,covered,covered,not_covered,not_covered,covered))
| ~ achievable(row(n7),squares(not_covered,X1,covered,not_covered,not_covered,covered,covered,not_covered)) ),
inference(spm,[status(thm)],[c_0_42,c_0_18]) ).
cnf(c_0_50,negated_conjecture,
~ achievable(row(n8),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_51,plain,
( achievable(row(successor(X1)),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered))
| ~ achievable(row(X1),squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)) ),
inference(spm,[status(thm)],[c_0_45,c_0_18]) ).
cnf(c_0_52,axiom,
successor(n3) = n4,
successor_of_3_is_4 ).
cnf(c_0_53,plain,
( achievable(row(successor(X1)),squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered))
| ~ achievable(row(X1),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)) ),
inference(spm,[status(thm)],[c_0_46,c_0_18]) ).
cnf(c_0_54,axiom,
successor(n2) = n3,
successor_of_2_is_3 ).
cnf(c_0_55,plain,
achievable(row(n2),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_38]),c_0_48])]) ).
cnf(c_0_56,axiom,
successor(n6) = n7,
successor_of_6_is_7 ).
cnf(c_0_57,plain,
~ achievable(row(n7),squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_18]),c_0_50]) ).
cnf(c_0_58,axiom,
successor(n5) = n6,
successor_of_5_is_6 ).
cnf(c_0_59,plain,
( achievable(row(n4),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered))
| ~ achievable(row(n3),squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_60,plain,
achievable(row(n3),squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55])]) ).
cnf(c_0_61,plain,
~ achievable(row(n6),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_56]),c_0_57]) ).
cnf(c_0_62,plain,
( achievable(row(n6),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered))
| ~ achievable(row(n5),squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)) ),
inference(spm,[status(thm)],[c_0_51,c_0_58]) ).
cnf(c_0_63,axiom,
successor(n4) = n5,
successor_of_4_is_5 ).
cnf(c_0_64,plain,
achievable(row(n4),squares(covered,not_covered,not_covered,covered,covered,not_covered,not_covered,covered)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60])]) ).
cnf(c_0_65,plain,
~ achievable(row(n5),squares(not_covered,covered,covered,not_covered,not_covered,covered,covered,not_covered)),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_66,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_63]),c_0_64])]),c_0_65]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : PUZ016-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 22:33:25 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 80.86/81.00 % Version : CSE_E---1.5
% 80.86/81.00 % Problem : theBenchmark.p
% 80.86/81.00 % Proof found
% 80.86/81.00 % SZS status Theorem for theBenchmark.p
% 80.86/81.00 % SZS output start Proof
% See solution above
% 80.86/81.01 % Total time : 80.415000 s
% 80.86/81.01 % SZS output end Proof
% 80.86/81.01 % Total time : 80.422000 s
%------------------------------------------------------------------------------