%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL538+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 : n004.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 0.17s 0.48s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 19 unt; 0 def)
% Number of atoms : 76 ( 4 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 66 ( 25 ~; 26 |; 9 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_M,axiom,
( axiom_M
<=> ! [X1] : is_a_theorem(implies(necessarily(X1),X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_M) ).
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(s1_0_modus_ponens_strict_implies,conjecture,
modus_ponens_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_modus_ponens_strict_implies) ).
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X1,X2] :
( ( is_a_theorem(implies(X1,X2))
& is_a_theorem(X1) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(km4b_axiom_M,axiom,
axiom_M,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+3.ax',km4b_axiom_M) ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(hilbert_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(modus_ponens_strict_implies,axiom,
( modus_ponens_strict_implies
<=> ! [X1,X2] :
( ( is_a_theorem(strict_implies(X1,X2))
& is_a_theorem(X1) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',modus_ponens_strict_implies) ).
fof(c_0_8,plain,
! [X145] :
( ( axiom_M
| ~ is_a_theorem(implies(necessarily(esk65_0),esk65_0)) )
& ( is_a_theorem(implies(necessarily(X145),X145))
| ~ axiom_M ) ),
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_M])])])])]) ).
fof(c_0_9,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_10,negated_conjecture,
~ modus_ponens_strict_implies,
inference(assume_negation,[status(cth)],[s1_0_modus_ponens_strict_implies]) ).
fof(c_0_11,plain,
! [X7,X8] :
( ( modus_ponens
| ~ is_a_theorem(esk2_0) )
& ( modus_ponens
| is_a_theorem(implies(esk1_0,esk2_0)) )
& ( modus_ponens
| is_a_theorem(esk1_0) )
& ( is_a_theorem(X8)
| ~ is_a_theorem(implies(X7,X8))
| ~ is_a_theorem(X7)
| ~ modus_ponens ) ),
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)],[modus_ponens])])])])])]) ).
cnf(c_0_12,plain,
( ~ axiom_M
| is_a_theorem(implies(necessarily(X1),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
axiom_M,
inference(split_conjunct,[status(thm)],[km4b_axiom_M]) ).
cnf(c_0_14,plain,
( ~ op_strict_implies
| strict_implies(X1,X2) = necessarily(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
op_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies]) ).
fof(c_0_16,negated_conjecture,
~ modus_ponens_strict_implies,
inference(fof_simplification,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| ~ modus_ponens
| is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[hilbert_modus_ponens]) ).
cnf(c_0_19,plain,
is_a_theorem(implies(necessarily(X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13])]) ).
cnf(c_0_20,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]) ).
fof(c_0_21,plain,
! [X129,X130] :
( ( modus_ponens_strict_implies
| ~ is_a_theorem(esk58_0) )
& ( modus_ponens_strict_implies
| is_a_theorem(strict_implies(esk57_0,esk58_0)) )
& ( modus_ponens_strict_implies
| is_a_theorem(esk57_0) )
& ( is_a_theorem(X130)
| ~ is_a_theorem(strict_implies(X129,X130))
| ~ is_a_theorem(X129)
| ~ modus_ponens_strict_implies ) ),
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)],[modus_ponens_strict_implies])])])])])]) ).
fof(c_0_22,negated_conjecture,
~ modus_ponens_strict_implies,
inference(fof_nnf,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
cnf(c_0_24,plain,
is_a_theorem(implies(strict_implies(X1,X2),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( modus_ponens_strict_implies
| is_a_theorem(strict_implies(esk57_0,esk58_0)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,negated_conjecture,
~ modus_ponens_strict_implies,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( ~ is_a_theorem(strict_implies(X1,X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
is_a_theorem(strict_implies(esk57_0,esk58_0)),
inference(sr,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,plain,
( modus_ponens_strict_implies
| is_a_theorem(esk57_0) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,plain,
( ~ is_a_theorem(esk58_0)
| modus_ponens_strict_implies ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,plain,
is_a_theorem(implies(esk57_0,esk58_0)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
is_a_theorem(esk57_0),
inference(sr,[status(thm)],[c_0_29,c_0_26]) ).
cnf(c_0_33,plain,
~ is_a_theorem(esk58_0),
inference(sr,[status(thm)],[c_0_30,c_0_26]) ).
cnf(c_0_34,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_31]),c_0_32])]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL538+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n004.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 21 00:37:35 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 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
% 0.17/0.48 % Version: 3.5.1
% 0.17/0.48 % Preprocessing class: FSLSSLSSSSSNFFN.
% 0.17/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.48 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 0.17/0.48 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.48 % Starting new_bool_1 with 300s (1) cores
% 0.17/0.48 % Starting sh5l with 300s (1) cores
% 0.17/0.48 % H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with pid 1881980 completed with status 0
% 0.17/0.48 % Result found by H----_102_C18_F1_PI_AE_CS_SP_PS_S2S
% 0.17/0.48 % Preprocessing class: FSLSSLSSSSSNFFN.
% 0.17/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.48 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 0.17/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/0.48 % No SInE strategy applied
% 0.17/0.48 % Search class: FGUSF-FFMM21-MFFFFFNN
% 0.17/0.48 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.48 % Starting SubtermCWHack with 136s (1) cores
% 0.17/0.48 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 151s (1) cores
% 0.17/0.48 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 136s (1) cores
% 0.17/0.48 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 136s (1) cores
% 0.17/0.48 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.17/0.48 % SubtermCWHack with pid 1882000 completed with status 0
% 0.17/0.48 % Result found by SubtermCWHack
% 0.17/0.48 % Preprocessing class: FSLSSLSSSSSNFFN.
% 0.17/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.48 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 0.17/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/0.48 % No SInE strategy applied
% 0.17/0.48 % Search class: FGUSF-FFMM21-MFFFFFNN
% 0.17/0.48 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.48 % Starting SubtermCWHack with 136s (1) cores
% 0.17/0.48 % Preprocessing time : 0.003 s
% 0.17/0.48
% 0.17/0.48 % Proof found!
% 0.17/0.48 % SZS status Theorem
% 0.17/0.48 % SZS output start CNFRefutation
% See solution above
% 0.17/0.48 % Parsed axioms : 89
% 0.17/0.48 % Removed by relevancy pruning/SinE : 0
% 0.17/0.48 % Initial clauses : 147
% 0.17/0.48 % Removed in clause preprocessing : 0
% 0.17/0.48 % Initial clauses in saturation : 147
% 0.17/0.48 % Processed clauses : 168
% 0.17/0.48 % ...of these trivial : 20
% 0.17/0.48 % ...subsumed : 10
% 0.17/0.48 % ...remaining for further processing : 138
% 0.17/0.48 % Other redundant clauses eliminated : 0
% 0.17/0.48 % Clauses deleted for lack of memory : 0
% 0.17/0.48 % Backward-subsumed : 0
% 0.17/0.48 % Backward-rewritten : 7
% 0.17/0.48 % Generated clauses : 206
% 0.17/0.48 % ...of the previous two non-redundant : 173
% 0.17/0.48 % ...aggressively subsumed : 0
% 0.17/0.48 % Contextual simplify-reflections : 0
% 0.17/0.48 % Paramodulations : 206
% 0.17/0.48 % Factorizations : 0
% 0.17/0.48 % NegExts : 0
% 0.17/0.48 % Equation resolutions : 0
% 0.17/0.48 % Disequality decompositions : 0
% 0.17/0.48 % Total rewrite steps : 73
% 0.17/0.48 % ...of those cached : 27
% 0.17/0.48 % Propositional unsat checks : 0
% 0.17/0.48 % Propositional check models : 0
% 0.17/0.48 % Propositional check unsatisfiable : 0
% 0.17/0.48 % Propositional clauses : 0
% 0.17/0.48 % Propositional clauses after purity: 0
% 0.17/0.48 % Propositional unsat core size : 0
% 0.17/0.48 % Propositional preprocessing time : 0.000
% 0.17/0.48 % Propositional encoding time : 0.000
% 0.17/0.48 % Propositional solver time : 0.000
% 0.17/0.48 % Success case prop preproc time : 0.000
% 0.17/0.48 % Success case prop encoding time : 0.000
% 0.17/0.48 % Success case prop solver time : 0.000
% 0.17/0.48 % Current number of processed clauses : 131
% 0.17/0.48 % Positive orientable unit clauses : 55
% 0.17/0.48 % Positive unorientable unit clauses: 1
% 0.17/0.48 % Negative unit clauses : 2
% 0.17/0.48 % Non-unit-clauses : 73
% 0.17/0.48 % Current number of unprocessed clauses: 151
% 0.17/0.48 % ...number of literals in the above : 304
% 0.17/0.48 % Current number of archived formulas : 0
% 0.17/0.48 % Current number of archived clauses : 7
% 0.17/0.48 % Clause-clause subsumption calls (NU) : 1145
% 0.17/0.48 % Rec. Clause-clause subsumption calls : 598
% 0.17/0.48 % Non-unit clause-clause subsumptions : 9
% 0.17/0.48 % Unit Clause-clause subsumption calls : 108
% 0.17/0.48 % Rewrite failures with RHS unbound : 0
% 0.17/0.48 % BW rewrite match attempts : 9
% 0.17/0.48 % BW rewrite match successes : 5
% 0.17/0.48 % Condensation attempts : 0
% 0.17/0.48 % Condensation successes : 0
% 0.17/0.48 % Termbank termtop insertions : 10218
% 0.17/0.48 % Search garbage collected termcells : 2057
% 0.17/0.48
% 0.17/0.48 % -------------------------------------------------
% 0.17/0.48 % User time : 0.016 s
% 0.17/0.48 % System time : 0.008 s
% 0.17/0.48 % Total time : 0.024 s
% 0.17/0.48 % Maximum resident set size: 3992 pages
% 0.17/0.48
% 0.17/0.48 % -------------------------------------------------
% 0.17/0.48 % User time : 0.056 s
% 0.17/0.48 % System time : 0.023 s
% 0.17/0.48 % Total time : 0.079 s
% 0.17/0.48 % Maximum resident set size: 4608 pages
% 0.17/0.48 % E exiting
%------------------------------------------------------------------------------