%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : PUZ016-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:01:33 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.45s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of clauses : 39 ( 33 unt; 0 nHn; 39 RR)
% Number of literals : 45 ( 20 equ; 9 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-8 aty)
% Number of variables : 48 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(place_vertical_pieces,axiom,
( ~ achievable(row(X1),squares(X2,X3,X4,X5,X6,X7,X8,X9))
| achievable(row(successor(X1)),squares(complement(X2),complement(X3),complement(X4),complement(X5),complement(X6),complement(X7),complement(X8),complement(X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',place_vertical_pieces) ).
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_1_is_2,axiom,
successor(n1) = n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_1_is_2) ).
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_removed_is_not_covered,axiom,
complement(removed) = not_covered,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_removed_is_not_covered) ).
cnf(successor_of_2_is_3,axiom,
successor(n2) = n3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_2_is_3) ).
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(cover_columns_2_and_3,axiom,
( ~ achievable(row(X1),squares(X2,not_covered,not_covered,X3,X4,X5,X6,X7))
| achievable(row(X1),squares(X2,covered,covered,X3,X4,X5,X6,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cover_columns_2_and_3) ).
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_4_is_5,axiom,
successor(n4) = n5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_4_is_5) ).
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_6_is_7,axiom,
successor(n6) = n7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_6_is_7) ).
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(successor_of_7_is_8,axiom,
successor(n7) = n8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_7_is_8) ).
cnf(c_0_14,plain,
( ~ achievable(row(X1),squares(X2,X3,X4,X5,X6,X7,X8,X9))
| achievable(row(successor(X1)),squares(complement(X2),complement(X3),complement(X4),complement(X5),complement(X6),complement(X7),complement(X8),complement(X9))) ),
inference(fof_simplification,[status(thm)],[place_vertical_pieces]) ).
cnf(c_0_15,plain,
( ~ achievable(row(X1),squares(X2,X3,X4,X5,X6,X7,X8,X9))
| achievable(row(successor(X1)),squares(complement(X2),complement(X3),complement(X4),complement(X5),complement(X6),complement(X7),complement(X8),complement(X9))) ),
c_0_14 ).
cnf(c_0_16,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_17,axiom,
successor(n1) = n2,
successor_of_1_is_2 ).
cnf(c_0_18,axiom,
complement(not_covered) = covered,
complement_of_not_covered_is_covered ).
cnf(c_0_19,axiom,
complement(removed) = not_covered,
complement_of_removed_is_not_covered ).
cnf(c_0_20,hypothesis,
achievable(row(n2),squares(covered,not_covered,not_covered,covered,covered,covered,covered,covered)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18]),c_0_19]),c_0_19]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]) ).
cnf(c_0_21,axiom,
successor(n2) = n3,
successor_of_2_is_3 ).
cnf(c_0_22,axiom,
complement(covered) = not_covered,
complement_of_covered_is_not_covered ).
cnf(c_0_23,plain,
( ~ achievable(row(X1),squares(X2,not_covered,not_covered,X3,X4,X5,X6,X7))
| achievable(row(X1),squares(X2,covered,covered,X3,X4,X5,X6,X7)) ),
inference(fof_simplification,[status(thm)],[cover_columns_2_and_3]) ).
cnf(c_0_24,hypothesis,
achievable(row(n3),squares(not_covered,covered,covered,not_covered,not_covered,not_covered,not_covered,not_covered)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_20]),c_0_21]),c_0_22]),c_0_18]),c_0_18]),c_0_22]),c_0_22]),c_0_22]),c_0_22]),c_0_22]) ).
cnf(c_0_25,axiom,
successor(n3) = n4,
successor_of_3_is_4 ).
cnf(c_0_26,plain,
( ~ achievable(row(X1),squares(X2,not_covered,not_covered,X3,X4,X5,X6,X7))
| achievable(row(X1),squares(X2,covered,covered,X3,X4,X5,X6,X7)) ),
c_0_23 ).
cnf(c_0_27,hypothesis,
achievable(row(n4),squares(covered,not_covered,not_covered,covered,covered,covered,covered,covered)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_24]),c_0_25]),c_0_18]),c_0_22]),c_0_22]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]) ).
cnf(c_0_28,hypothesis,
achievable(row(n4),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,axiom,
successor(n4) = n5,
successor_of_4_is_5 ).
cnf(c_0_30,hypothesis,
achievable(row(n5),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_28]),c_0_29]),c_0_22]),c_0_22]),c_0_22]),c_0_22]),c_0_22]),c_0_22]),c_0_22]),c_0_22]) ).
cnf(c_0_31,axiom,
successor(n5) = n6,
successor_of_5_is_6 ).
cnf(c_0_32,hypothesis,
achievable(row(n6),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_30]),c_0_31]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]) ).
cnf(c_0_33,axiom,
successor(n6) = n7,
successor_of_6_is_7 ).
cnf(c_0_34,negated_conjecture,
~ achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
inference(fof_simplification,[status(thm)],[prove_row_8_can_be_covered]) ).
cnf(c_0_35,hypothesis,
achievable(row(n7),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_32]),c_0_33]),c_0_22]),c_0_22]),c_0_22]),c_0_22]),c_0_22]),c_0_22]),c_0_22]),c_0_22]) ).
cnf(c_0_36,axiom,
successor(n7) = n8,
successor_of_7_is_8 ).
cnf(c_0_37,negated_conjecture,
~ achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
c_0_34 ).
cnf(c_0_38,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_35]),c_0_36]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 03:45:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.45 % Version: 3.5.1
% 0.10/0.45 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.10/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.45 % Starting sh5l with 300s (1) cores
% 0.10/0.45 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1616920 completed with status 0
% 0.10/0.45 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.10/0.45 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.10/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.45 % No SInE strategy applied
% 0.10/0.45 % Search class: FHUSF-FFMM32-SFFFFFNN
% 0.10/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.10/0.45 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 169s (1) cores
% 0.10/0.45 % Starting new_bool_3 with 169s (1) cores
% 0.10/0.45 % Starting new_bool_1 with 169s (1) cores
% 0.10/0.45 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1616926 completed with status 0
% 0.10/0.45 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.10/0.45 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.10/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.45 % No SInE strategy applied
% 0.10/0.45 % Search class: FHUSF-FFMM32-SFFFFFNN
% 0.10/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.10/0.45 % Preprocessing time : 0.001 s
% 0.10/0.45 % Presaturation interreduction done
% 0.10/0.45
% 0.10/0.45 % Proof found!
% 0.10/0.45 % SZS status Unsatisfiable
% 0.10/0.45 % SZS output start CNFRefutation
% See solution above
% 0.10/0.45 % Parsed axioms : 21
% 0.10/0.45 % Removed by relevancy pruning/SinE : 0
% 0.10/0.45 % Initial clauses : 21
% 0.10/0.45 % Removed in clause preprocessing : 0
% 0.10/0.45 % Initial clauses in saturation : 21
% 0.10/0.45 % Processed clauses : 171
% 0.10/0.45 % ...of these trivial : 23
% 0.10/0.45 % ...subsumed : 0
% 0.10/0.45 % ...remaining for further processing : 148
% 0.10/0.45 % Other redundant clauses eliminated : 0
% 0.10/0.45 % Clauses deleted for lack of memory : 0
% 0.10/0.45 % Backward-subsumed : 0
% 0.10/0.45 % Backward-rewritten : 0
% 0.10/0.45 % Generated clauses : 317
% 0.10/0.45 % ...of the previous two non-redundant : 228
% 0.10/0.45 % ...aggressively subsumed : 0
% 0.10/0.45 % Contextual simplify-reflections : 0
% 0.10/0.45 % Paramodulations : 317
% 0.10/0.45 % Factorizations : 0
% 0.10/0.45 % NegExts : 0
% 0.10/0.45 % Equation resolutions : 0
% 0.10/0.45 % Disequality decompositions : 0
% 0.10/0.45 % Total rewrite steps : 1072
% 0.10/0.45 % ...of those cached : 1003
% 0.10/0.45 % Propositional unsat checks : 0
% 0.10/0.45 % Propositional check models : 0
% 0.10/0.45 % Propositional check unsatisfiable : 0
% 0.10/0.45 % Propositional clauses : 0
% 0.10/0.45 % Propositional clauses after purity: 0
% 0.10/0.45 % Propositional unsat core size : 0
% 0.10/0.45 % Propositional preprocessing time : 0.000
% 0.10/0.45 % Propositional encoding time : 0.000
% 0.10/0.45 % Propositional solver time : 0.000
% 0.10/0.45 % Success case prop preproc time : 0.000
% 0.10/0.45 % Success case prop encoding time : 0.000
% 0.10/0.45 % Success case prop solver time : 0.000
% 0.10/0.45 % Current number of processed clauses : 127
% 0.10/0.45 % Positive orientable unit clauses : 118
% 0.10/0.45 % Positive unorientable unit clauses: 0
% 0.10/0.45 % Negative unit clauses : 1
% 0.10/0.45 % Non-unit-clauses : 8
% 0.10/0.45 % Current number of unprocessed clauses: 94
% 0.10/0.45 % ...number of literals in the above : 94
% 0.10/0.45 % Current number of archived formulas : 0
% 0.10/0.45 % Current number of archived clauses : 21
% 0.10/0.45 % Clause-clause subsumption calls (NU) : 84
% 0.10/0.45 % Rec. Clause-clause subsumption calls : 84
% 0.10/0.45 % Non-unit clause-clause subsumptions : 0
% 0.10/0.45 % Unit Clause-clause subsumption calls : 0
% 0.10/0.45 % Rewrite failures with RHS unbound : 0
% 0.10/0.45 % BW rewrite match attempts : 457
% 0.10/0.45 % BW rewrite match successes : 0
% 0.10/0.45 % Condensation attempts : 0
% 0.10/0.45 % Condensation successes : 0
% 0.10/0.45 % Termbank termtop insertions : 6806
% 0.10/0.45 % Search garbage collected termcells : 26
% 0.10/0.45
% 0.10/0.45 % -------------------------------------------------
% 0.10/0.45 % User time : 0.009 s
% 0.10/0.45 % System time : 0.005 s
% 0.10/0.45 % Total time : 0.014 s
% 0.10/0.45 % Maximum resident set size: 3392 pages
% 0.10/0.45
% 0.10/0.45 % -------------------------------------------------
% 0.10/0.45 % User time : 0.034 s
% 0.10/0.45 % System time : 0.023 s
% 0.10/0.45 % Total time : 0.058 s
% 0.10/0.45 % Maximum resident set size: 4608 pages
% 0.10/0.45 % E exiting
%------------------------------------------------------------------------------