%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : LCL365+2 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 01:19:13 PM UTC 2026
% Result : Theorem 119.81s 24.79s
% Output : CNFRefutation 119.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 51 ( 27 unt; 0 def)
% Number of atoms : 80 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 62 ( 33 ~; 27 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 196 ( 33 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(condensed_detachment,axiom,
! [X1,X2] :
( ( is_a_theorem(X1)
& is_a_theorem(implies(X1,X2)) )
=> is_a_theorem(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
fof(f2,axiom,
! [X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,X17] : is_a_theorem(implies(implies(implies(implies(implies(X3,implies(X4,X3)),implies(implies(X5,implies(X6,implies(X7,X6))),X8)),X8),implies(implies(implies(implies(implies(implies(implies(X9,X10),implies(implies(X10,X11),implies(X9,X11))),implies(implies(implies(n(X12),X12),X12),X13)),X13),implies(implies(X14,implies(n(X14),X15)),X16)),X16),X17)),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f2) ).
fof(f3,conjecture,
is_a_theorem(implies(implies(implies(x,implies(implies(y,z),z)),u),implies(implies(n(z),y),u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f3) ).
fof(c_0_3,plain,
! [X18,X19] :
( is_a_theorem(X19)
| ~ is_a_theorem(X18)
| ~ is_a_theorem(implies(X18,X19)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[condensed_detachment])])]) ).
fof(c_0_4,plain,
! [X20,X21,X22,X23,X24,X25,X26,X27,X28,X29,X30,X31,X32,X33,X34] : is_a_theorem(implies(implies(implies(implies(implies(X20,implies(X21,X20)),implies(implies(X22,implies(X23,implies(X24,X23))),X25)),X25),implies(implies(implies(implies(implies(implies(implies(X26,X27),implies(implies(X27,X28),implies(X26,X28))),implies(implies(implies(n(X29),X29),X29),X30)),X30),implies(implies(X31,implies(n(X31),X32)),X33)),X33),X34)),X34)),
inference(variable_rename,[status(thm)],[f2]) ).
cnf(c_0_5,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,plain,
is_a_theorem(implies(implies(implies(implies(implies(X1,implies(X2,X1)),implies(implies(X3,implies(X4,implies(X5,X4))),X6)),X6),implies(implies(implies(implies(implies(implies(implies(X7,X8),implies(implies(X8,X9),implies(X7,X9))),implies(implies(implies(n(X10),X10),X10),X11)),X11),implies(implies(X12,implies(n(X12),X13)),X14)),X14),X15)),X15)),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X2,implies(X3,X2)),implies(implies(X4,implies(X5,implies(X6,X5))),X7)),X7),implies(implies(implies(implies(implies(implies(implies(X8,X9),implies(implies(X9,X10),implies(X8,X10))),implies(implies(implies(n(X11),X11),X11),X12)),X12),implies(implies(X13,implies(n(X13),X14)),X15)),X15),X1)))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_9,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_10,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X2,X3),implies(implies(X3,X4),implies(X2,X4))),implies(implies(implies(n(X5),X5),X5),X6)),X6),implies(implies(X7,implies(n(X7),X8)),X9)),X9),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_9]) ).
cnf(c_0_11,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X1)),implies(implies(X3,implies(X4,implies(X5,X4))),X6)),X6)),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
is_a_theorem(implies(X1,implies(implies(n(X2),X2),X2))),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,plain,
is_a_theorem(implies(implies(n(X1),X1),X1)),
inference(spm,[status(thm)],[c_0_10,c_0_12]) ).
cnf(c_0_14,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,X2)))),
inference(spm,[status(thm)],[c_0_7,c_0_11]) ).
cnf(c_0_15,plain,
( ~ is_a_theorem(implies(n(X1),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_5,c_0_13]) ).
cnf(c_0_16,plain,
is_a_theorem(implies(X1,implies(implies(implies(implies(implies(implies(X2,X3),implies(implies(X3,X4),implies(X2,X4))),implies(implies(implies(n(X5),X5),X5),X6)),X6),implies(implies(X7,implies(n(X7),X8)),X9)),X9))),
inference(spm,[status(thm)],[c_0_7,c_0_14]) ).
cnf(c_0_17,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))),implies(implies(implies(n(X4),X4),X4),X5)),X5),implies(implies(X6,implies(n(X6),X7)),X8)),X8)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X2,X3),implies(implies(X3,X4),implies(X2,X4))),implies(implies(implies(n(X5),X5),X5),X6)),X6),implies(implies(X7,implies(n(X7),X8)),X1)))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_5,c_0_17]) ).
cnf(c_0_19,plain,
( ~ is_a_theorem(implies(implies(X2,implies(X3,X2)),implies(implies(X4,implies(X5,implies(X6,X5))),X1)))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_5,c_0_11]) ).
cnf(c_0_20,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))),implies(implies(implies(n(X4),X4),X4),X5)),X5)),
inference(spm,[status(thm)],[c_0_18,c_0_8]) ).
cnf(c_0_21,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X1)),X3),implies(X4,X3))),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,plain,
( ~ is_a_theorem(implies(implies(implies(X2,X3),implies(implies(X3,X4),implies(X2,X4))),implies(implies(implies(n(X5),X5),X5),X1)))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_5,c_0_20]) ).
cnf(c_0_23,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
inference(spm,[status(thm)],[c_0_18,c_0_21]) ).
cnf(c_0_24,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_25,plain,
( ~ is_a_theorem(implies(implies(implies(n(X2),X2),X2),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_9]) ).
cnf(c_0_26,plain,
( ~ is_a_theorem(implies(X3,X1))
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_5,c_0_23]) ).
cnf(c_0_27,plain,
( ~ is_a_theorem(implies(implies(X3,X1),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_5,c_0_24]) ).
cnf(c_0_28,plain,
( ~ is_a_theorem(implies(X1,implies(n(X2),X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),implies(X3,X2)))),
inference(spm,[status(thm)],[c_0_27,c_0_23]) ).
fof(c_0_30,negated_conjecture,
~ is_a_theorem(implies(implies(implies(x,implies(implies(y,z),z)),u),implies(implies(n(z),y),u))),
inference(assume_negation,[status(cth)],[f3]) ).
cnf(c_0_31,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X1)),X3),X3)),
inference(spm,[status(thm)],[c_0_28,c_0_21]) ).
cnf(c_0_32,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_5,c_0_29]) ).
fof(c_0_33,negated_conjecture,
~ is_a_theorem(implies(implies(implies(x,implies(implies(y,z),z)),u),implies(implies(n(z),y),u))),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
cnf(c_0_34,plain,
( ~ is_a_theorem(implies(implies(X2,implies(X3,X2)),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_5,c_0_31]) ).
cnf(c_0_35,plain,
( ~ is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(X3,X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_5,c_0_26]) ).
cnf(c_0_36,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(implies(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_28,c_0_32]) ).
fof(c_0_37,negated_conjecture,
~ is_a_theorem(implies(implies(implies(x,implies(implies(y,z),z)),u),implies(implies(n(z),y),u))),
inference(fof_nnf,[status(thm)],[c_0_33]) ).
cnf(c_0_38,plain,
( ~ is_a_theorem(implies(X1,X3))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_34,c_0_26]) ).
cnf(c_0_39,plain,
( ~ is_a_theorem(X3)
| ~ is_a_theorem(implies(X1,implies(X3,X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
is_a_theorem(implies(implies(implies(implies(n(X1),X1),X1),X2),X2)),
inference(spm,[status(thm)],[c_0_27,c_0_20]) ).
cnf(c_0_41,negated_conjecture,
~ is_a_theorem(implies(implies(implies(x,implies(implies(y,z),z)),u),implies(implies(n(z),y),u))),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,plain,
( ~ is_a_theorem(implies(implies(implies(X2,X3),implies(implies(X3,X4),implies(X2,X4))),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_38]) ).
cnf(c_0_43,plain,
( ~ is_a_theorem(implies(X2,X3))
| is_a_theorem(implies(implies(X1,X2),implies(X1,X3))) ),
inference(spm,[status(thm)],[c_0_39,c_0_23]) ).
cnf(c_0_44,plain,
( ~ is_a_theorem(implies(X1,implies(implies(implies(n(X3),X3),X3),X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_35,c_0_40]) ).
cnf(c_0_45,negated_conjecture,
~ is_a_theorem(implies(implies(n(z),y),implies(x,implies(implies(y,z),z)))),
inference(spm,[status(thm)],[c_0_41,c_0_26]) ).
cnf(c_0_46,plain,
( ~ is_a_theorem(implies(implies(implies(X2,X4),implies(X1,X4)),X3))
| is_a_theorem(implies(implies(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,plain,
is_a_theorem(implies(implies(X1,implies(n(X2),X2)),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_44,c_0_23]) ).
cnf(c_0_48,negated_conjecture,
~ is_a_theorem(implies(implies(n(z),y),implies(implies(y,z),z))),
inference(spm,[status(thm)],[c_0_45,c_0_38]) ).
cnf(c_0_49,plain,
is_a_theorem(implies(implies(n(X1),X2),implies(implies(X2,X1),X1))),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL365+2 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 21 00:23:52 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 Running first-order theorem proving
% 0.08/0.35 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
% 119.81/24.79 % Version: 3.5.1
% 119.81/24.79 % Preprocessing class: FSMSSMSSSSSNFFN.
% 119.81/24.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 119.81/24.79 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 119.81/24.79 % Starting new_bool_3 with 300s (1) cores
% 119.81/24.79 % Starting new_bool_1 with 300s (1) cores
% 119.81/24.79 % Starting sh5l with 300s (1) cores
% 119.81/24.79 % new_bool_3 with pid 1220781 completed with status 0
% 119.81/24.79 % Result found by new_bool_3
% 119.81/24.79 % Preprocessing class: FSMSSMSSSSSNFFN.
% 119.81/24.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 119.81/24.79 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 119.81/24.79 % Starting new_bool_3 with 300s (1) cores
% 119.81/24.79 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 119.81/24.79 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 119.81/24.79 % Search class: FHUNF-FFSF21-DFFFFFNN
% 119.81/24.79 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 119.81/24.79 % Starting SubtermCWHack with 31s (1) cores
% 119.81/24.79 % SubtermCWHack with pid 1220789 completed with status 0
% 119.81/24.79 % Result found by SubtermCWHack
% 119.81/24.79 % Preprocessing class: FSMSSMSSSSSNFFN.
% 119.81/24.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 119.81/24.79 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 119.81/24.79 % Starting new_bool_3 with 300s (1) cores
% 119.81/24.79 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 119.81/24.79 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 119.81/24.79 % Search class: FHUNF-FFSF21-DFFFFFNN
% 119.81/24.79 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 119.81/24.79 % Starting SubtermCWHack with 31s (1) cores
% 119.81/24.79 % Preprocessing time : 0.001 s
% 119.81/24.79
% 119.81/24.79 % Proof found!
% 119.81/24.79 % SZS status Theorem
% 119.81/24.79 % SZS output start CNFRefutation
% See solution above
% 119.81/24.79 % Parsed axioms : 3
% 119.81/24.79 % Removed by relevancy pruning/SinE : 0
% 119.81/24.79 % Initial clauses : 3
% 119.81/24.79 % Removed in clause preprocessing : 0
% 119.81/24.79 % Initial clauses in saturation : 3
% 119.81/24.79 % Processed clauses : 114516
% 119.81/24.79 % ...of these trivial : 5161
% 119.81/24.79 % ...subsumed : 103620
% 119.81/24.79 % ...remaining for further processing : 5735
% 119.81/24.79 % Other redundant clauses eliminated : 0
% 119.81/24.79 % Clauses deleted for lack of memory : 0
% 119.81/24.79 % Backward-subsumed : 22
% 119.81/24.79 % Backward-rewritten : 34
% 119.81/24.79 % Generated clauses : 2668062
% 119.81/24.79 % ...of the previous two non-redundant : 2055585
% 119.81/24.79 % ...aggressively subsumed : 0
% 119.81/24.79 % Contextual simplify-reflections : 0
% 119.81/24.79 % Paramodulations : 2668062
% 119.81/24.79 % Factorizations : 0
% 119.81/24.79 % NegExts : 0
% 119.81/24.79 % Equation resolutions : 0
% 119.81/24.79 % Disequality decompositions : 0
% 119.81/24.79 % Total rewrite steps : 621232
% 119.81/24.79 % ...of those cached : 598815
% 119.81/24.79 % Propositional unsat checks : 0
% 119.81/24.79 % Propositional check models : 0
% 119.81/24.79 % Propositional check unsatisfiable : 0
% 119.81/24.79 % Propositional clauses : 0
% 119.81/24.79 % Propositional clauses after purity: 0
% 119.81/24.79 % Propositional unsat core size : 0
% 119.81/24.79 % Propositional preprocessing time : 0.000
% 119.81/24.79 % Propositional encoding time : 0.000
% 119.81/24.79 % Propositional solver time : 0.000
% 119.81/24.79 % Success case prop preproc time : 0.000
% 119.81/24.79 % Success case prop encoding time : 0.000
% 119.81/24.79 % Success case prop solver time : 0.000
% 119.81/24.79 % Current number of processed clauses : 5679
% 119.81/24.79 % Positive orientable unit clauses : 2414
% 119.81/24.79 % Positive unorientable unit clauses: 0
% 119.81/24.79 % Negative unit clauses : 27
% 119.81/24.79 % Non-unit-clauses : 3238
% 119.81/24.79 % Current number of unprocessed clauses: 1940473
% 119.81/24.79 % ...number of literals in the above : 3600919
% 119.81/24.79 % Current number of archived formulas : 0
% 119.81/24.79 % Current number of archived clauses : 56
% 119.81/24.79 % Clause-clause subsumption calls (NU) : 2828171
% 119.81/24.79 % Rec. Clause-clause subsumption calls : 2810854
% 119.81/24.79 % Non-unit clause-clause subsumptions : 103552
% 119.81/24.79 % Unit Clause-clause subsumption calls : 151301
% 119.81/24.79 % Rewrite failures with RHS unbound : 0
% 119.81/24.79 % BW rewrite match attempts : 1700377
% 119.81/24.79 % BW rewrite match successes : 34
% 119.81/24.79 % Condensation attempts : 0
% 119.81/24.79 % Condensation successes : 0
% 119.81/24.79 % Termbank termtop insertions : 49188027
% 119.81/24.79 % Search garbage collected termcells : 19
% 119.81/24.79
% 119.81/24.79 % -------------------------------------------------
% 119.81/24.79 % User time : 23.338 s
% 119.81/24.79 % System time : 0.768 s
% 119.81/24.79 % Total time : 24.106 s
% 119.81/24.79 % Maximum resident set size: 3600 pages
% 119.81/24.79
% 119.81/24.79 % -------------------------------------------------
% 119.81/24.79 % User time : 23.339 s
% 119.81/24.79 % System time : 0.772 s
% 119.81/24.79 % Total time : 24.112 s
% 119.81/24.79 % Maximum resident set size: 4608 pages
% 119.81/24.79 % E exiting
%------------------------------------------------------------------------------