%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL039-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 01:11:36 PM UTC 2026
% Result : Unsatisfiable 2.14s 0.76s
% Output : CNFRefutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of clauses : 48 ( 22 unt; 0 nHn; 28 RR)
% Number of literals : 81 ( 0 equ; 37 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 83 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
cnf(necessitation1,axiom,
is_a_theorem(implies(necessary(implies(X1,X2)),implies(necessary(X1),necessary(X2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',necessitation1) ).
cnf(axiom_of_necessitation,axiom,
( ~ is_a_theorem(X1)
| is_a_theorem(necessary(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_of_necessitation) ).
cnf(cn_35,axiom,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_35) ).
cnf(cn_18,axiom,
is_a_theorem(implies(X1,implies(X2,X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_18) ).
cnf(cn_49,axiom,
is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_49) ).
cnf(necessitation2,axiom,
is_a_theorem(implies(necessary(X1),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',necessitation2) ).
cnf(prove_this,negated_conjecture,
~ is_a_theorem(implies(necessary(a),not(necessary(not(a))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
cnf(c_0_8,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(X2) ),
inference(fof_simplification,[status(thm)],[condensed_detachment]) ).
cnf(c_0_9,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(X2) ),
c_0_8 ).
cnf(c_0_10,axiom,
is_a_theorem(implies(necessary(implies(X1,X2)),implies(necessary(X1),necessary(X2)))),
necessitation1 ).
cnf(c_0_11,plain,
( ~ is_a_theorem(necessary(implies(X1,X2)))
| is_a_theorem(implies(necessary(X1),necessary(X2))) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(necessary(X1)) ),
inference(fof_simplification,[status(thm)],[axiom_of_necessitation]) ).
cnf(c_0_13,axiom,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3)))),
cn_35 ).
cnf(c_0_14,plain,
( ~ is_a_theorem(necessary(X2))
| ~ is_a_theorem(necessary(implies(X2,X1)))
| is_a_theorem(necessary(X1)) ),
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_15,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(necessary(X1)) ),
c_0_12 ).
cnf(c_0_16,plain,
( ~ is_a_theorem(implies(X1,implies(X2,X3)))
| is_a_theorem(implies(implies(X1,X2),implies(X1,X3))) ),
inference(spm,[status(thm)],[c_0_9,c_0_13]) ).
cnf(c_0_17,axiom,
is_a_theorem(implies(X1,implies(X2,X1))),
cn_18 ).
cnf(c_0_18,plain,
( ~ is_a_theorem(necessary(X2))
| ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(necessary(X1)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,axiom,
is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1))),
cn_49 ).
cnf(c_0_20,plain,
( ~ is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(X1,implies(X3,X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_9,c_0_16]) ).
cnf(c_0_21,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_9,c_0_17]) ).
cnf(c_0_22,axiom,
is_a_theorem(implies(necessary(X1),X1)),
necessitation2 ).
cnf(c_0_23,plain,
( ~ is_a_theorem(necessary(implies(not(X2),not(X1))))
| is_a_theorem(necessary(implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X1,X1)) ),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_25,plain,
( ~ is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X1,X3))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( ~ is_a_theorem(necessary(X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_22]) ).
cnf(c_0_27,plain,
( ~ is_a_theorem(necessary(X2))
| is_a_theorem(necessary(implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_28,plain,
( ~ is_a_theorem(implies(not(X2),not(X1)))
| is_a_theorem(necessary(implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_23,c_0_15]) ).
cnf(c_0_29,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_24,c_0_17]) ).
cnf(c_0_30,plain,
( ~ is_a_theorem(implies(implies(X3,X1),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_31,plain,
( ~ is_a_theorem(necessary(X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
is_a_theorem(necessary(implies(X1,X1))),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
is_a_theorem(implies(not(X1),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_30,c_0_19]) ).
cnf(c_0_34,plain,
( ~ is_a_theorem(implies(implies(not(X1),not(X2)),X2))
| is_a_theorem(implies(implies(not(X1),not(X2)),X1)) ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_35,plain,
is_a_theorem(implies(X1,implies(X2,X2))),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
( ~ is_a_theorem(implies(implies(X1,X3),X2))
| is_a_theorem(implies(not(X1),X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_33]) ).
cnf(c_0_37,plain,
is_a_theorem(implies(implies(not(X1),not(implies(X2,X2))),X1)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
is_a_theorem(implies(not(not(X1)),X1)),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_39,negated_conjecture,
~ is_a_theorem(implies(necessary(a),not(necessary(not(a))))),
inference(fof_simplification,[status(thm)],[prove_this]) ).
cnf(c_0_40,plain,
( ~ is_a_theorem(implies(not(X2),not(X1)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_9,c_0_19]) ).
cnf(c_0_41,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(not(not(X1)),X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
~ is_a_theorem(implies(necessary(a),not(necessary(not(a))))),
c_0_39 ).
cnf(c_0_43,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(necessary(X1),X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_22]) ).
cnf(c_0_44,plain,
( ~ is_a_theorem(implies(X2,not(X1)))
| is_a_theorem(implies(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
~ is_a_theorem(implies(a,not(necessary(not(a))))),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_46,plain,
is_a_theorem(implies(X1,not(necessary(not(X1))))),
inference(spm,[status(thm)],[c_0_44,c_0_22]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 00:03:30 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 2.14/0.76 % Version: 3.5.1
% 2.14/0.76 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.14/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.14/0.76 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.14/0.76 % Starting new_bool_3 with 300s (1) cores
% 2.14/0.76 % Starting new_bool_1 with 300s (1) cores
% 2.14/0.76 % Starting sh5l with 300s (1) cores
% 2.14/0.76 % new_bool_3 with pid 538888 completed with status 0
% 2.14/0.76 % Result found by new_bool_3
% 2.14/0.76 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.14/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.14/0.76 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.14/0.76 % Starting new_bool_3 with 300s (1) cores
% 2.14/0.76 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 2.14/0.76 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.14/0.76 % Search class: FHUNM-FFSF21-MFFFFFNN
% 2.14/0.76 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 2.14/0.76 % Starting SubtermCWHack with 31s (1) cores
% 2.14/0.76 % SubtermCWHack with pid 538896 completed with status 0
% 2.14/0.76 % Result found by SubtermCWHack
% 2.14/0.76 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.14/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.14/0.76 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.14/0.76 % Starting new_bool_3 with 300s (1) cores
% 2.14/0.76 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 2.14/0.76 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.14/0.76 % Search class: FHUNM-FFSF21-MFFFFFNN
% 2.14/0.76 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 2.14/0.76 % Starting SubtermCWHack with 31s (1) cores
% 2.14/0.76 % Preprocessing time : 0.001 s
% 2.14/0.76
% 2.14/0.76 % Proof found!
% 2.14/0.76 % SZS status Unsatisfiable
% 2.14/0.76 % SZS output start CNFRefutation
% See solution above
% 2.14/0.76 % Parsed axioms : 8
% 2.14/0.76 % Removed by relevancy pruning/SinE : 0
% 2.14/0.76 % Initial clauses : 8
% 2.14/0.76 % Removed in clause preprocessing : 0
% 2.14/0.76 % Initial clauses in saturation : 8
% 2.14/0.76 % Processed clauses : 4317
% 2.14/0.76 % ...of these trivial : 141
% 2.14/0.76 % ...subsumed : 3300
% 2.14/0.76 % ...remaining for further processing : 876
% 2.14/0.76 % Other redundant clauses eliminated : 0
% 2.14/0.76 % Clauses deleted for lack of memory : 0
% 2.14/0.76 % Backward-subsumed : 59
% 2.14/0.76 % Backward-rewritten : 4
% 2.14/0.76 % Generated clauses : 29581
% 2.14/0.76 % ...of the previous two non-redundant : 24588
% 2.14/0.76 % ...aggressively subsumed : 0
% 2.14/0.76 % Contextual simplify-reflections : 0
% 2.14/0.76 % Paramodulations : 29581
% 2.14/0.76 % Factorizations : 0
% 2.14/0.76 % NegExts : 0
% 2.14/0.76 % Equation resolutions : 0
% 2.14/0.76 % Disequality decompositions : 0
% 2.14/0.76 % Total rewrite steps : 5013
% 2.14/0.76 % ...of those cached : 4633
% 2.14/0.76 % Propositional unsat checks : 0
% 2.14/0.76 % Propositional check models : 0
% 2.14/0.76 % Propositional check unsatisfiable : 0
% 2.14/0.76 % Propositional clauses : 0
% 2.14/0.76 % Propositional clauses after purity: 0
% 2.14/0.76 % Propositional unsat core size : 0
% 2.14/0.76 % Propositional preprocessing time : 0.000
% 2.14/0.76 % Propositional encoding time : 0.000
% 2.14/0.76 % Propositional solver time : 0.000
% 2.14/0.76 % Success case prop preproc time : 0.000
% 2.14/0.76 % Success case prop encoding time : 0.000
% 2.14/0.76 % Success case prop solver time : 0.000
% 2.14/0.76 % Current number of processed clauses : 813
% 2.14/0.76 % Positive orientable unit clauses : 239
% 2.14/0.76 % Positive unorientable unit clauses: 0
% 2.14/0.76 % Negative unit clauses : 3
% 2.14/0.76 % Non-unit-clauses : 571
% 2.14/0.76 % Current number of unprocessed clauses: 19876
% 2.14/0.76 % ...number of literals in the above : 45975
% 2.14/0.76 % Current number of archived formulas : 0
% 2.14/0.76 % Current number of archived clauses : 63
% 2.14/0.76 % Clause-clause subsumption calls (NU) : 52918
% 2.14/0.76 % Rec. Clause-clause subsumption calls : 52918
% 2.14/0.76 % Non-unit clause-clause subsumptions : 3358
% 2.14/0.76 % Unit Clause-clause subsumption calls : 998
% 2.14/0.76 % Rewrite failures with RHS unbound : 0
% 2.14/0.76 % BW rewrite match attempts : 8800
% 2.14/0.76 % BW rewrite match successes : 4
% 2.14/0.76 % Condensation attempts : 0
% 2.14/0.76 % Condensation successes : 0
% 2.14/0.76 % Termbank termtop insertions : 375368
% 2.14/0.76 % Search garbage collected termcells : 9
% 2.14/0.76
% 2.14/0.76 % -------------------------------------------------
% 2.14/0.76 % User time : 0.295 s
% 2.14/0.76 % System time : 0.024 s
% 2.14/0.76 % Total time : 0.319 s
% 2.14/0.76 % Maximum resident set size: 3584 pages
% 2.14/0.76
% 2.14/0.76 % -------------------------------------------------
% 2.14/0.76 % User time : 0.298 s
% 2.14/0.76 % System time : 0.027 s
% 2.14/0.76 % Total time : 0.325 s
% 2.14/0.76 % Maximum resident set size: 4864 pages
% 2.14/0.76 % E exiting
%------------------------------------------------------------------------------