%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL542+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 01:13:00 PM UTC 2026
% Result : Theorem 0.12s 10.70s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 15 unt; 0 def)
% Number of atoms : 54 ( 4 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 45 ( 20 ~; 16 |; 4 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 26 ( 2 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s1_0_axiom_m2,conjecture,
axiom_m2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m2) ).
fof(necessitation,axiom,
( necessitation
<=> ! [X1] :
( is_a_theorem(X1)
=> is_a_theorem(necessarily(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',necessitation) ).
fof(op_strict_implies,axiom,
( op_strict_implies
=> ! [X1,X2] : strict_implies(X1,X2) = necessarily(implies(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).
fof(axiom_m2,axiom,
( axiom_m2
<=> ! [X1,X2] : is_a_theorem(strict_implies(and(X1,X2),X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m2) ).
fof(km4b_necessitation,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+3.ax',km4b_necessitation) ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(and_1,axiom,
( and_1
<=> ! [X1,X2] : is_a_theorem(implies(and(X1,X2),X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_1) ).
fof(hilbert_and_1,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_1) ).
fof(c_0_8,negated_conjecture,
~ axiom_m2,
inference(assume_negation,[status(cth)],[s1_0_axiom_m2]) ).
fof(c_0_9,negated_conjecture,
~ axiom_m2,
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_10,plain,
! [X127] :
( ( necessitation
| ~ is_a_theorem(necessarily(esk56_0)) )
& ( necessitation
| is_a_theorem(esk56_0) )
& ( is_a_theorem(necessarily(X127))
| ~ is_a_theorem(X127)
| ~ necessitation ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[necessitation])])])])])]) ).
fof(c_0_11,plain,
! [X207,X208] :
( strict_implies(X207,X208) = necessarily(implies(X207,X208))
| ~ op_strict_implies ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_implies])])])]) ).
fof(c_0_12,plain,
! [X173,X174] :
( ( axiom_m2
| ~ is_a_theorem(strict_implies(and(esk79_0,esk80_0),esk79_0)) )
& ( is_a_theorem(strict_implies(and(X173,X174),X173))
| ~ axiom_m2 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m2])])])])]) ).
fof(c_0_13,negated_conjecture,
~ axiom_m2,
inference(fof_nnf,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( ~ is_a_theorem(X1)
| ~ necessitation
| is_a_theorem(necessarily(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
necessitation,
inference(split_conjunct,[status(thm)],[km4b_necessitation]) ).
cnf(c_0_16,plain,
( ~ op_strict_implies
| strict_implies(X1,X2) = necessarily(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
op_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies]) ).
fof(c_0_18,plain,
! [X33,X34] :
( ( and_1
| ~ is_a_theorem(implies(and(esk14_0,esk15_0),esk14_0)) )
& ( is_a_theorem(implies(and(X33,X34),X33))
| ~ and_1 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_1])])])])]) ).
cnf(c_0_19,plain,
( ~ is_a_theorem(strict_implies(and(esk79_0,esk80_0),esk79_0))
| axiom_m2 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,negated_conjecture,
~ axiom_m2,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(necessarily(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]) ).
cnf(c_0_22,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]) ).
cnf(c_0_23,plain,
( ~ and_1
| is_a_theorem(implies(and(X1,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
and_1,
inference(split_conjunct,[status(thm)],[hilbert_and_1]) ).
cnf(c_0_25,plain,
~ is_a_theorem(strict_implies(and(esk79_0,esk80_0),esk79_0)),
inference(sr,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]) ).
cnf(c_0_28,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL542+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/10.60 % Computer : n013.cluster.edu
% 0.12/10.60 % Model : x86_64 x86_64
% 0.12/10.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.60 % Memory : 8046.5625MB
% 0.12/10.60 % OS : Linux 6.8.0-71-generic
% 0.12/10.60 % CPULimit : 300
% 0.12/10.60 % WCLimit : 300
% 0.12/10.60 % DateTime : Mon Sep 21 00:37:33 UTC 2026
% 0.12/10.61 % CPUTime :
% 0.12/10.61 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/10.65 Running first-order theorem proving
% 0.12/10.65 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
% 0.12/10.70 % Version: 3.5.1
% 0.12/10.70 % Preprocessing class: FSLSSLSSSSSNFFN.
% 0.12/10.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/10.70 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 0.12/10.70 % Starting new_bool_3 with 300s (1) cores
% 0.12/10.70 % Starting new_bool_1 with 300s (1) cores
% 0.12/10.70 % Starting sh5l with 300s (1) cores
% 0.12/10.70 % H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with pid 3788360 completed with status 0
% 0.12/10.70 % Result found by H----_102_C18_F1_PI_AE_CS_SP_PS_S2S
% 0.12/10.70 % Preprocessing class: FSLSSLSSSSSNFFN.
% 0.12/10.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/10.70 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 0.12/10.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/10.70 % No SInE strategy applied
% 0.12/10.70 % Search class: FGUSF-FFMM21-MFFFFFNN
% 0.12/10.70 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/10.70 % Starting SubtermCWHack with 136s (1) cores
% 0.12/10.70 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 151s (1) cores
% 0.12/10.70 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 136s (1) cores
% 0.12/10.70 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 136s (1) cores
% 0.12/10.70 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.12/10.70 % SubtermCWHack with pid 3788370 completed with status 0
% 0.12/10.70 % Result found by SubtermCWHack
% 0.12/10.70 % Preprocessing class: FSLSSLSSSSSNFFN.
% 0.12/10.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/10.70 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 0.12/10.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/10.70 % No SInE strategy applied
% 0.12/10.70 % Search class: FGUSF-FFMM21-MFFFFFNN
% 0.12/10.70 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/10.70 % Starting SubtermCWHack with 136s (1) cores
% 0.12/10.70 % Preprocessing time : 0.004 s
% 0.12/10.70
% 0.12/10.70 % Proof found!
% 0.12/10.70 % SZS status Theorem
% 0.12/10.70 % SZS output start CNFRefutation
% See solution above
% 0.16/10.70 % Parsed axioms : 89
% 0.16/10.70 % Removed by relevancy pruning/SinE : 0
% 0.16/10.70 % Initial clauses : 147
% 0.16/10.70 % Removed in clause preprocessing : 0
% 0.16/10.70 % Initial clauses in saturation : 147
% 0.16/10.70 % Processed clauses : 100
% 0.16/10.70 % ...of these trivial : 20
% 0.16/10.70 % ...subsumed : 1
% 0.16/10.70 % ...remaining for further processing : 79
% 0.16/10.70 % Other redundant clauses eliminated : 0
% 0.16/10.70 % Clauses deleted for lack of memory : 0
% 0.16/10.70 % Backward-subsumed : 0
% 0.16/10.70 % Backward-rewritten : 0
% 0.16/10.70 % Generated clauses : 39
% 0.16/10.70 % ...of the previous two non-redundant : 24
% 0.16/10.70 % ...aggressively subsumed : 0
% 0.16/10.70 % Contextual simplify-reflections : 0
% 0.16/10.70 % Paramodulations : 39
% 0.16/10.70 % Factorizations : 0
% 0.16/10.70 % NegExts : 0
% 0.16/10.70 % Equation resolutions : 0
% 0.16/10.70 % Disequality decompositions : 0
% 0.16/10.70 % Total rewrite steps : 45
% 0.16/10.70 % ...of those cached : 15
% 0.16/10.70 % Propositional unsat checks : 0
% 0.16/10.70 % Propositional check models : 0
% 0.16/10.70 % Propositional check unsatisfiable : 0
% 0.16/10.70 % Propositional clauses : 0
% 0.16/10.70 % Propositional clauses after purity: 0
% 0.16/10.70 % Propositional unsat core size : 0
% 0.16/10.70 % Propositional preprocessing time : 0.000
% 0.16/10.70 % Propositional encoding time : 0.000
% 0.16/10.70 % Propositional solver time : 0.000
% 0.16/10.70 % Success case prop preproc time : 0.000
% 0.16/10.70 % Success case prop encoding time : 0.000
% 0.16/10.70 % Success case prop solver time : 0.000
% 0.16/10.70 % Current number of processed clauses : 79
% 0.16/10.70 % Positive orientable unit clauses : 39
% 0.16/10.70 % Positive unorientable unit clauses: 0
% 0.16/10.70 % Negative unit clauses : 2
% 0.16/10.70 % Non-unit-clauses : 38
% 0.16/10.70 % Current number of unprocessed clauses: 65
% 0.16/10.70 % ...number of literals in the above : 136
% 0.16/10.70 % Current number of archived formulas : 0
% 0.16/10.70 % Current number of archived clauses : 0
% 0.16/10.70 % Clause-clause subsumption calls (NU) : 391
% 0.16/10.70 % Rec. Clause-clause subsumption calls : 161
% 0.16/10.70 % Non-unit clause-clause subsumptions : 0
% 0.16/10.70 % Unit Clause-clause subsumption calls : 23
% 0.16/10.70 % Rewrite failures with RHS unbound : 0
% 0.16/10.70 % BW rewrite match attempts : 2
% 0.16/10.70 % BW rewrite match successes : 0
% 0.16/10.70 % Condensation attempts : 0
% 0.16/10.70 % Condensation successes : 0
% 0.16/10.70 % Termbank termtop insertions : 8820
% 0.16/10.70 % Search garbage collected termcells : 2057
% 0.16/10.70
% 0.16/10.70 % -------------------------------------------------
% 0.16/10.70 % User time : 0.013 s
% 0.16/10.70 % System time : 0.010 s
% 0.16/10.70 % Total time : 0.023 s
% 0.16/10.70 % Maximum resident set size: 3992 pages
% 0.16/10.70
% 0.16/10.70 % -------------------------------------------------
% 0.16/10.70 % User time : 0.041 s
% 0.16/10.70 % System time : 0.027 s
% 0.16/10.70 % Total time : 0.068 s
% 0.16/10.70 % Maximum resident set size: 4864 pages
% 0.16/10.70 % E exiting
%------------------------------------------------------------------------------