%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL454+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 : n026.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 01:12:49 PM UTC 2026
% Result : Theorem 0.18s 0.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 20 unt; 0 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 67 ( 28 ~; 25 |; 8 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 6 prp; 0-1 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 45 ( 2 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(principia_r1,conjecture,
r1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r1) ).
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(or_3,axiom,
( or_3
<=> ! [X1,X2,X3] : is_a_theorem(implies(implies(X1,X3),implies(implies(X2,X3),implies(or(X1,X2),X3)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_3) ).
fof(hilbert_or_3,axiom,
or_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_or_3) ).
fof(implies_1,axiom,
( implies_1
<=> ! [X1,X2] : is_a_theorem(implies(X1,implies(X2,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_1) ).
fof(r1,axiom,
( r1
<=> ! [X4] : is_a_theorem(implies(or(X4,X4),X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r1) ).
fof(hilbert_implies_1,axiom,
implies_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_1) ).
fof(c_0_10,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_11,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_12,negated_conjecture,
~ r1,
inference(assume_negation,[status(cth)],[principia_r1]) ).
cnf(c_0_13,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| ~ modus_ponens
| is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[hilbert_modus_ponens]) ).
cnf(c_0_15,plain,
( ~ implies_2
| is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
implies_2,
inference(split_conjunct,[status(thm)],[hilbert_implies_2]) ).
fof(c_0_17,plain,
! [X53,X54,X55] :
( ( or_3
| ~ is_a_theorem(implies(implies(esk24_0,esk26_0),implies(implies(esk25_0,esk26_0),implies(or(esk24_0,esk25_0),esk26_0)))) )
& ( is_a_theorem(implies(implies(X53,X55),implies(implies(X54,X55),implies(or(X53,X54),X55))))
| ~ or_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)],[or_3])])])])]) ).
fof(c_0_18,negated_conjecture,
~ r1,
inference(fof_simplification,[status(thm)],[c_0_12]) ).
cnf(c_0_19,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_13,c_0_14])]) ).
cnf(c_0_20,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]) ).
cnf(c_0_21,plain,
( ~ or_3
| is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X2),implies(or(X1,X3),X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
or_3,
inference(split_conjunct,[status(thm)],[hilbert_or_3]) ).
fof(c_0_23,plain,
! [X19,X20] :
( ( implies_1
| ~ is_a_theorem(implies(esk7_0,implies(esk8_0,esk7_0))) )
& ( is_a_theorem(implies(X19,implies(X20,X19)))
| ~ implies_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)],[implies_1])])])])]) ).
fof(c_0_24,plain,
! [X95] :
( ( r1
| ~ is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0)) )
& ( is_a_theorem(implies(or(X95,X95),X95))
| ~ r1 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r1])])])])]) ).
fof(c_0_25,negated_conjecture,
~ r1,
inference(fof_nnf,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( ~ is_a_theorem(implies(X1,implies(X1,X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X2),implies(or(X1,X3),X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]) ).
cnf(c_0_28,plain,
( ~ implies_1
| is_a_theorem(implies(X1,implies(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
implies_1,
inference(split_conjunct,[status(thm)],[hilbert_implies_1]) ).
cnf(c_0_30,plain,
( ~ is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0))
| r1 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
~ r1,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
is_a_theorem(implies(implies(X1,X2),implies(or(X1,X1),X2))),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).
cnf(c_0_34,plain,
~ is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0)),
inference(sr,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(or(X1,X1),X2)) ),
inference(spm,[status(thm)],[c_0_19,c_0_32]) ).
cnf(c_0_36,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_33]) ).
cnf(c_0_37,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL454+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n026.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 00:36:08 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.18/0.48 % Version: 3.5.1
% 0.18/0.48 % Preprocessing class: FSMSSLSSSSSNFFN.
% 0.18/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.48 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 0.18/0.48 % Starting new_bool_3 with 300s (1) cores
% 0.18/0.48 % Starting new_bool_1 with 300s (1) cores
% 0.18/0.48 % Starting sh5l with 300s (1) cores
% 0.18/0.48 % new_bool_3 with pid 986634 completed with status 9
% 0.18/0.48 % sh5l with pid 986636 completed with status 9
% 0.18/0.48 % new_bool_1 with pid 986635 completed with status 9
% 0.18/0.48 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 986633 completed with status 0
% 0.18/0.48 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 0.18/0.48 % Preprocessing class: FSMSSLSSSSSNFFN.
% 0.18/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.48 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 0.18/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/0.48 % No SInE strategy applied
% 0.18/0.48 % Search class: FGUSF-FFMM21-MFFFFFNN
% 0.18/0.48 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.48 % Starting SubtermCWHack with 151s (1) cores
% 0.18/0.48 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 0.18/0.48 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 0.18/0.48 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 0.18/0.48 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.18/0.48 % U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 986650 completed with status 0
% 0.18/0.48 % Result found by U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 0.18/0.48 % Preprocessing class: FSMSSLSSSSSNFFN.
% 0.18/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.48 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 0.18/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/0.48 % No SInE strategy applied
% 0.18/0.48 % Search class: FGUSF-FFMM21-MFFFFFNN
% 0.18/0.48 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.48 % Starting SubtermCWHack with 151s (1) cores
% 0.18/0.48 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 0.18/0.48 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 0.18/0.48 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 0.18/0.48 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.18/0.48 % Preprocessing time : 0.002 s
% 0.18/0.48 % Presaturation interreduction done
% 0.18/0.48
% 0.18/0.48 % Proof found!
% 0.18/0.48 % SZS status Theorem
% 0.18/0.48 % SZS output start CNFRefutation
% See solution above
% 0.18/0.48 % Parsed axioms : 53
% 0.18/0.48 % Removed by relevancy pruning/SinE : 0
% 0.18/0.48 % Initial clauses : 82
% 0.18/0.48 % Removed in clause preprocessing : 0
% 0.18/0.48 % Initial clauses in saturation : 82
% 0.18/0.48 % Processed clauses : 283
% 0.18/0.48 % ...of these trivial : 53
% 0.18/0.48 % ...subsumed : 34
% 0.18/0.48 % ...remaining for further processing : 196
% 0.18/0.48 % Other redundant clauses eliminated : 0
% 0.18/0.48 % Clauses deleted for lack of memory : 0
% 0.18/0.48 % Backward-subsumed : 0
% 0.18/0.48 % Backward-rewritten : 18
% 0.18/0.48 % Generated clauses : 770
% 0.18/0.48 % ...of the previous two non-redundant : 604
% 0.18/0.48 % ...aggressively subsumed : 0
% 0.18/0.48 % Contextual simplify-reflections : 0
% 0.18/0.48 % Paramodulations : 770
% 0.18/0.48 % Factorizations : 0
% 0.18/0.48 % NegExts : 0
% 0.18/0.48 % Equation resolutions : 0
% 0.18/0.48 % Disequality decompositions : 0
% 0.18/0.48 % Total rewrite steps : 517
% 0.18/0.48 % ...of those cached : 248
% 0.18/0.48 % Propositional unsat checks : 0
% 0.18/0.48 % Propositional check models : 0
% 0.18/0.48 % Propositional check unsatisfiable : 0
% 0.18/0.48 % Propositional clauses : 0
% 0.18/0.48 % Propositional clauses after purity: 0
% 0.18/0.48 % Propositional unsat core size : 0
% 0.18/0.48 % Propositional preprocessing time : 0.000
% 0.18/0.48 % Propositional encoding time : 0.000
% 0.18/0.48 % Propositional solver time : 0.000
% 0.18/0.48 % Success case prop preproc time : 0.000
% 0.18/0.48 % Success case prop encoding time : 0.000
% 0.18/0.48 % Success case prop solver time : 0.000
% 0.18/0.48 % Current number of processed clauses : 120
% 0.18/0.48 % Positive orientable unit clauses : 75
% 0.18/0.48 % Positive unorientable unit clauses: 2
% 0.18/0.48 % Negative unit clauses : 3
% 0.18/0.48 % Non-unit-clauses : 40
% 0.18/0.48 % Current number of unprocessed clauses: 458
% 0.18/0.48 % ...number of literals in the above : 615
% 0.18/0.48 % Current number of archived formulas : 0
% 0.18/0.48 % Current number of archived clauses : 76
% 0.18/0.48 % Clause-clause subsumption calls (NU) : 179
% 0.18/0.48 % Rec. Clause-clause subsumption calls : 179
% 0.18/0.48 % Non-unit clause-clause subsumptions : 33
% 0.18/0.48 % Unit Clause-clause subsumption calls : 63
% 0.18/0.48 % Rewrite failures with RHS unbound : 0
% 0.18/0.48 % BW rewrite match attempts : 207
% 0.18/0.48 % BW rewrite match successes : 20
% 0.18/0.48 % Condensation attempts : 0
% 0.18/0.48 % Condensation successes : 0
% 0.18/0.48 % Termbank termtop insertions : 13963
% 0.18/0.48 % Search garbage collected termcells : 1092
% 0.18/0.48
% 0.18/0.48 % -------------------------------------------------
% 0.18/0.48 % User time : 0.027 s
% 0.18/0.48 % System time : 0.004 s
% 0.18/0.48 % Total time : 0.031 s
% 0.18/0.48 % Maximum resident set size: 3688 pages
% 0.18/0.48
% 0.18/0.48 % -------------------------------------------------
% 0.18/0.48 % User time : 0.197 s
% 0.18/0.48 % System time : 0.074 s
% 0.18/0.48 % Total time : 0.271 s
% 0.18/0.48 % Maximum resident set size: 4608 pages
% 0.18/0.48 % E exiting
%------------------------------------------------------------------------------