%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL531+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 01:12:59 PM UTC 2026
% Result : Theorem 0.23s 0.47s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 49 ( 23 unt; 0 def)
% Number of atoms : 103 ( 4 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 93 ( 39 ~; 35 |; 10 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s1_0_axiom_m4,conjecture,
axiom_m4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m4) ).
fof(necessitation,axiom,
( necessitation
<=> ! [X1] :
( is_a_theorem(X1)
=> is_a_theorem(necessarily(X1)) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL007+1.ax',op_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/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(implies_2,axiom,
( implies_2
<=> ! [X1,X2] : is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_2) ).
fof(axiom_m4,axiom,
( axiom_m4
<=> ! [X1] : is_a_theorem(strict_implies(X1,and(X1,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m4) ).
fof(km5_necessitation,axiom,
necessitation,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax',km5_necessitation) ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(hilbert_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(hilbert_implies_2,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
fof(and_3,axiom,
( and_3
<=> ! [X1,X2] : is_a_theorem(implies(X1,implies(X2,and(X1,X2)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_3) ).
fof(hilbert_and_3,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).
fof(kn1,axiom,
( kn1
<=> ! [X4] : is_a_theorem(implies(X4,and(X4,X4))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn1) ).
fof(c_0_13,negated_conjecture,
~ axiom_m4,
inference(assume_negation,[status(cth)],[s1_0_axiom_m4]) ).
fof(c_0_14,negated_conjecture,
~ axiom_m4,
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_15,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_16,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_17,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])])])])])]) ).
fof(c_0_18,plain,
! [X23,X24] :
( ( implies_2
| ~ is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0))) )
& ( is_a_theorem(implies(implies(X23,implies(X23,X24)),implies(X23,X24)))
| ~ implies_2 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_2])])])])]) ).
fof(c_0_19,plain,
! [X183] :
( ( axiom_m4
| ~ is_a_theorem(strict_implies(esk84_0,and(esk84_0,esk84_0))) )
& ( is_a_theorem(strict_implies(X183,and(X183,X183)))
| ~ axiom_m4 ) ),
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_m4])])])])]) ).
fof(c_0_20,negated_conjecture,
~ axiom_m4,
inference(fof_nnf,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( ~ is_a_theorem(X1)
| ~ necessitation
| is_a_theorem(necessarily(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
necessitation,
inference(split_conjunct,[status(thm)],[km5_necessitation]) ).
cnf(c_0_23,plain,
( ~ op_strict_implies
| strict_implies(X1,X2) = necessarily(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
op_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies]) ).
cnf(c_0_25,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| ~ modus_ponens
| is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[hilbert_modus_ponens]) ).
cnf(c_0_27,plain,
( ~ implies_2
| is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,plain,
implies_2,
inference(split_conjunct,[status(thm)],[hilbert_implies_2]) ).
fof(c_0_29,plain,
! [X41,X42] :
( ( and_3
| ~ is_a_theorem(implies(esk18_0,implies(esk19_0,and(esk18_0,esk19_0)))) )
& ( is_a_theorem(implies(X41,implies(X42,and(X41,X42))))
| ~ and_3 ) ),
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_3])])])])]) ).
cnf(c_0_30,plain,
( ~ is_a_theorem(strict_implies(esk84_0,and(esk84_0,esk84_0)))
| axiom_m4 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_31,negated_conjecture,
~ axiom_m4,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(necessarily(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]) ).
cnf(c_0_33,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]) ).
cnf(c_0_34,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_25,c_0_26])]) ).
cnf(c_0_35,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
cnf(c_0_36,plain,
( ~ and_3
| is_a_theorem(implies(X1,implies(X2,and(X1,X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,plain,
and_3,
inference(split_conjunct,[status(thm)],[hilbert_and_3]) ).
cnf(c_0_38,plain,
~ is_a_theorem(strict_implies(esk84_0,and(esk84_0,esk84_0))),
inference(sr,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_39,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
fof(c_0_40,plain,
! [X71] :
( ( kn1
| ~ is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0))) )
& ( is_a_theorem(implies(X71,and(X71,X71)))
| ~ kn1 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn1])])])])]) ).
cnf(c_0_41,plain,
( ~ is_a_theorem(implies(X1,implies(X1,X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,plain,
is_a_theorem(implies(X1,implies(X2,and(X1,X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]) ).
cnf(c_0_43,plain,
~ is_a_theorem(implies(esk84_0,and(esk84_0,esk84_0))),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
( ~ kn1
| is_a_theorem(implies(X1,and(X1,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_45,plain,
( ~ is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0)))
| kn1 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_46,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,plain,
~ kn1,
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]),c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL531+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 00:42:43 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 0.23/0.47 % Version: 3.5.1
% 0.23/0.47 % Preprocessing class: FSLSSLSSSSSNFFN.
% 0.23/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.47 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 0.23/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.47 % Starting sh5l with 300s (1) cores
% 0.23/0.47 % sh5l with pid 1833056 completed with status 9
% 0.23/0.47 % new_bool_1 with pid 1833055 completed with status 9
% 0.23/0.47 % new_bool_3 with pid 1833054 completed with status 9
% 0.23/0.47 % H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with pid 1833053 completed with status 0
% 0.23/0.47 % Result found by H----_102_C18_F1_PI_AE_CS_SP_PS_S2S
% 0.23/0.47 % Preprocessing class: FSLSSLSSSSSNFFN.
% 0.23/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.47 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 0.23/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.47 % No SInE strategy applied
% 0.23/0.47 % Search class: FGUSF-FFMM21-MFFFFFNN
% 0.23/0.47 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.47 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 151s (1) cores
% 0.23/0.47 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 136s (1) cores
% 0.23/0.47 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 136s (1) cores
% 0.23/0.47 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.23/0.47 % SubtermCWHack with pid 1833070 completed with status 0
% 0.23/0.47 % Result found by SubtermCWHack
% 0.23/0.47 % Preprocessing class: FSLSSLSSSSSNFFN.
% 0.23/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.47 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 0.23/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.47 % No SInE strategy applied
% 0.23/0.47 % Search class: FGUSF-FFMM21-MFFFFFNN
% 0.23/0.47 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.47 % Preprocessing time : 0.002 s
% 0.23/0.47
% 0.23/0.47 % Proof found!
% 0.23/0.47 % SZS status Theorem
% 0.23/0.47 % SZS output start CNFRefutation
% See solution above
% 0.23/0.47 % Parsed axioms : 88
% 0.23/0.47 % Removed by relevancy pruning/SinE : 0
% 0.23/0.47 % Initial clauses : 146
% 0.23/0.47 % Removed in clause preprocessing : 0
% 0.23/0.47 % Initial clauses in saturation : 146
% 0.23/0.47 % Processed clauses : 566
% 0.23/0.47 % ...of these trivial : 37
% 0.23/0.47 % ...subsumed : 157
% 0.23/0.47 % ...remaining for further processing : 372
% 0.23/0.47 % Other redundant clauses eliminated : 0
% 0.23/0.47 % Clauses deleted for lack of memory : 0
% 0.23/0.47 % Backward-subsumed : 11
% 0.23/0.47 % Backward-rewritten : 30
% 0.23/0.47 % Generated clauses : 1891
% 0.23/0.47 % ...of the previous two non-redundant : 1777
% 0.23/0.47 % ...aggressively subsumed : 0
% 0.23/0.47 % Contextual simplify-reflections : 4
% 0.23/0.47 % Paramodulations : 1891
% 0.23/0.47 % Factorizations : 0
% 0.23/0.47 % NegExts : 0
% 0.23/0.47 % Equation resolutions : 0
% 0.23/0.47 % Disequality decompositions : 0
% 0.23/0.47 % Total rewrite steps : 367
% 0.23/0.47 % ...of those cached : 215
% 0.23/0.47 % Propositional unsat checks : 0
% 0.23/0.47 % Propositional check models : 0
% 0.23/0.47 % Propositional check unsatisfiable : 0
% 0.23/0.47 % Propositional clauses : 0
% 0.23/0.47 % Propositional clauses after purity: 0
% 0.23/0.47 % Propositional unsat core size : 0
% 0.23/0.47 % Propositional preprocessing time : 0.000
% 0.23/0.47 % Propositional encoding time : 0.000
% 0.23/0.47 % Propositional solver time : 0.000
% 0.23/0.47 % Success case prop preproc time : 0.000
% 0.23/0.47 % Success case prop encoding time : 0.000
% 0.23/0.47 % Success case prop solver time : 0.000
% 0.23/0.47 % Current number of processed clauses : 331
% 0.23/0.47 % Positive orientable unit clauses : 80
% 0.23/0.47 % Positive unorientable unit clauses: 1
% 0.23/0.47 % Negative unit clauses : 7
% 0.23/0.47 % Non-unit-clauses : 243
% 0.23/0.47 % Current number of unprocessed clauses: 1160
% 0.23/0.47 % ...number of literals in the above : 3432
% 0.23/0.47 % Current number of archived formulas : 0
% 0.23/0.47 % Current number of archived clauses : 41
% 0.23/0.47 % Clause-clause subsumption calls (NU) : 7727
% 0.23/0.47 % Rec. Clause-clause subsumption calls : 4134
% 0.23/0.47 % Non-unit clause-clause subsumptions : 166
% 0.23/0.47 % Unit Clause-clause subsumption calls : 645
% 0.23/0.47 % Rewrite failures with RHS unbound : 0
% 0.23/0.47 % BW rewrite match attempts : 138
% 0.23/0.47 % BW rewrite match successes : 16
% 0.23/0.47 % Condensation attempts : 0
% 0.23/0.47 % Condensation successes : 0
% 0.23/0.47 % Termbank termtop insertions : 30072
% 0.23/0.47 % Search garbage collected termcells : 2057
% 0.23/0.47
% 0.23/0.47 % -------------------------------------------------
% 0.23/0.47 % User time : 0.038 s
% 0.23/0.47 % System time : 0.003 s
% 0.23/0.47 % Total time : 0.041 s
% 0.23/0.47 % Maximum resident set size: 3992 pages
% 0.23/0.47
% 0.23/0.47 % -------------------------------------------------
% 0.23/0.47 % User time : 0.169 s
% 0.23/0.47 % System time : 0.082 s
% 0.23/0.47 % Total time : 0.251 s
% 0.23/0.47 % Maximum resident set size: 4864 pages
% 0.23/0.47 % E exiting
%------------------------------------------------------------------------------