%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL490+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 : n010.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 01:12:54 PM UTC 2026
% Result : Theorem 1.20s 0.77s
% Output : CNFRefutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 45 ( 22 unt; 0 def)
% Number of atoms : 91 ( 4 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 80 ( 34 ~; 31 |; 8 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 62 ( 4 sgn 26 !; 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(r5,axiom,
( r5
<=> ! [X4,X5,X6] : is_a_theorem(implies(implies(X5,X6),implies(or(X4,X5),or(X4,X6)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r5) ).
fof(principia_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_modus_ponens) ).
fof(principia_r5,axiom,
r5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r5) ).
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X1,X2] : implies(X1,X2) = or(not(X1),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_or) ).
fof(hilbert_or_1,conjecture,
or_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_1) ).
fof(principia_op_implies_or,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_implies_or) ).
fof(r2,axiom,
( r2
<=> ! [X4,X5] : is_a_theorem(implies(X5,or(X4,X5))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r2) ).
fof(principia_r2,axiom,
r2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r2) ).
fof(r3,axiom,
( r3
<=> ! [X4,X5] : is_a_theorem(implies(or(X4,X5),or(X5,X4))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r3) ).
fof(or_1,axiom,
( or_1
<=> ! [X1,X2] : is_a_theorem(implies(X1,or(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_1) ).
fof(principia_r3,axiom,
r3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r3) ).
fof(c_0_12,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_13,plain,
! [X111,X112,X113] :
( ( r5
| ~ is_a_theorem(implies(implies(esk54_0,esk55_0),implies(or(esk53_0,esk54_0),or(esk53_0,esk55_0)))) )
& ( is_a_theorem(implies(implies(X112,X113),implies(or(X111,X112),or(X111,X113))))
| ~ r5 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r5])])])])]) ).
cnf(c_0_14,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| ~ modus_ponens
| is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[principia_modus_ponens]) ).
cnf(c_0_16,plain,
( ~ r5
| is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
r5,
inference(split_conjunct,[status(thm)],[principia_r5]) ).
cnf(c_0_18,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_14,c_0_15])]) ).
cnf(c_0_19,plain,
is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]) ).
fof(c_0_20,plain,
! [X123,X124] :
( implies(X123,X124) = or(not(X123),X124)
| ~ op_implies_or ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_or])])])]) ).
fof(c_0_21,negated_conjecture,
~ or_1,
inference(assume_negation,[status(cth)],[hilbert_or_1]) ).
cnf(c_0_22,plain,
( ~ is_a_theorem(implies(X2,X3))
| is_a_theorem(implies(or(X1,X2),or(X1,X3))) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( ~ op_implies_or
| implies(X1,X2) = or(not(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,plain,
op_implies_or,
inference(split_conjunct,[status(thm)],[principia_op_implies_or]) ).
fof(c_0_25,plain,
! [X97,X98] :
( ( r2
| ~ is_a_theorem(implies(esk47_0,or(esk46_0,esk47_0))) )
& ( is_a_theorem(implies(X98,or(X97,X98)))
| ~ r2 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r2])])])])]) ).
fof(c_0_26,negated_conjecture,
~ or_1,
inference(fof_simplification,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
( ~ is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(or(X1,X3))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_28,plain,
or(not(X1),X2) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]) ).
cnf(c_0_29,plain,
( ~ r2
| is_a_theorem(implies(X1,or(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
r2,
inference(split_conjunct,[status(thm)],[principia_r2]) ).
fof(c_0_31,plain,
! [X101,X102] :
( ( r3
| ~ is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0))) )
& ( is_a_theorem(implies(or(X101,X102),or(X102,X101)))
| ~ r3 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r3])])])])]) ).
fof(c_0_32,plain,
! [X45,X46] :
( ( or_1
| ~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0))) )
& ( is_a_theorem(implies(X45,or(X45,X46)))
| ~ or_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)],[or_1])])])])]) ).
fof(c_0_33,negated_conjecture,
~ or_1,
inference(fof_nnf,[status(thm)],[c_0_26]) ).
cnf(c_0_34,plain,
( ~ is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X1,X3))
| is_a_theorem(implies(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_28]) ).
cnf(c_0_35,plain,
is_a_theorem(implies(X1,or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).
cnf(c_0_36,plain,
( ~ r3
| is_a_theorem(implies(or(X1,X2),or(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,plain,
r3,
inference(split_conjunct,[status(thm)],[principia_r3]) ).
cnf(c_0_38,plain,
( ~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0)))
| or_1 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,negated_conjecture,
~ or_1,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,plain,
( ~ is_a_theorem(implies(or(X3,X1),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]) ).
cnf(c_0_42,plain,
~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0))),
inference(sr,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
is_a_theorem(implies(X1,or(X1,X2))),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL490+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.42 % Computer : n010.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 00:36:10 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.49 Running first-order theorem proving
% 0.22/0.49 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
% 1.20/0.77 % Version: 3.5.1
% 1.20/0.77 % Preprocessing class: FSMSSLSSSSSNFFN.
% 1.20/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.20/0.77 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 1.20/0.77 % Starting new_bool_3 with 300s (1) cores
% 1.20/0.77 % Starting new_bool_1 with 300s (1) cores
% 1.20/0.77 % Starting sh5l with 300s (1) cores
% 1.20/0.77 % new_bool_3 with pid 3879177 completed with status 9
% 1.20/0.77 % sh5l with pid 3879179 completed with status 9
% 1.20/0.77 % new_bool_1 with pid 3879178 completed with status 9
% 1.20/0.77 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 3879176 completed with status 0
% 1.20/0.77 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 1.20/0.77 % Preprocessing class: FSMSSLSSSSSNFFN.
% 1.20/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.20/0.77 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 1.20/0.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.20/0.77 % No SInE strategy applied
% 1.20/0.77 % Search class: FGUSF-FFMM21-MFFFFFNN
% 1.20/0.77 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.20/0.77 % Starting SubtermCWHack with 151s (1) cores
% 1.20/0.77 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 1.20/0.77 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 1.20/0.77 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 1.20/0.77 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.20/0.77 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 3879194 completed with status 0
% 1.20/0.77 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 1.20/0.77 % Preprocessing class: FSMSSLSSSSSNFFN.
% 1.20/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.20/0.77 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 1.20/0.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.20/0.77 % No SInE strategy applied
% 1.20/0.77 % Search class: FGUSF-FFMM21-MFFFFFNN
% 1.20/0.77 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.20/0.77 % Starting SubtermCWHack with 151s (1) cores
% 1.20/0.77 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 1.20/0.77 % Preprocessing time : 0.003 s
% 1.20/0.77 % Presaturation interreduction done
% 1.20/0.77
% 1.20/0.77 % Proof found!
% 1.20/0.77 % SZS status Theorem
% 1.20/0.77 % SZS output start CNFRefutation
% See solution above
% 1.20/0.77 % Parsed axioms : 45
% 1.20/0.77 % Removed by relevancy pruning/SinE : 0
% 1.20/0.77 % Initial clauses : 74
% 1.20/0.77 % Removed in clause preprocessing : 0
% 1.20/0.77 % Initial clauses in saturation : 74
% 1.20/0.77 % Processed clauses : 1970
% 1.20/0.77 % ...of these trivial : 68
% 1.20/0.77 % ...subsumed : 1289
% 1.20/0.77 % ...remaining for further processing : 613
% 1.20/0.77 % Other redundant clauses eliminated : 0
% 1.20/0.77 % Clauses deleted for lack of memory : 0
% 1.20/0.77 % Backward-subsumed : 47
% 1.20/0.77 % Backward-rewritten : 126
% 1.20/0.77 % Generated clauses : 7501
% 1.20/0.77 % ...of the previous two non-redundant : 6727
% 1.20/0.77 % ...aggressively subsumed : 0
% 1.20/0.77 % Contextual simplify-reflections : 0
% 1.20/0.77 % Paramodulations : 7501
% 1.20/0.77 % Factorizations : 0
% 1.20/0.78 % NegExts : 0
% 1.20/0.78 % Equation resolutions : 0
% 1.20/0.78 % Disequality decompositions : 0
% 1.20/0.78 % Total rewrite steps : 4180
% 1.20/0.78 % ...of those cached : 2976
% 1.20/0.78 % Propositional unsat checks : 0
% 1.20/0.78 % Propositional check models : 0
% 1.20/0.78 % Propositional check unsatisfiable : 0
% 1.20/0.78 % Propositional clauses : 0
% 1.20/0.78 % Propositional clauses after purity: 0
% 1.20/0.78 % Propositional unsat core size : 0
% 1.20/0.78 % Propositional preprocessing time : 0.000
% 1.20/0.78 % Propositional encoding time : 0.000
% 1.20/0.78 % Propositional solver time : 0.000
% 1.20/0.78 % Success case prop preproc time : 0.000
% 1.20/0.78 % Success case prop encoding time : 0.000
% 1.20/0.78 % Success case prop solver time : 0.000
% 1.20/0.78 % Current number of processed clauses : 379
% 1.20/0.78 % Positive orientable unit clauses : 89
% 1.20/0.78 % Positive unorientable unit clauses: 1
% 1.20/0.78 % Negative unit clauses : 8
% 1.20/0.78 % Non-unit-clauses : 281
% 1.20/0.78 % Current number of unprocessed clauses: 4676
% 1.20/0.78 % ...number of literals in the above : 9716
% 1.20/0.78 % Current number of archived formulas : 0
% 1.20/0.78 % Current number of archived clauses : 234
% 1.20/0.78 % Clause-clause subsumption calls (NU) : 13963
% 1.20/0.78 % Rec. Clause-clause subsumption calls : 13923
% 1.20/0.78 % Non-unit clause-clause subsumptions : 1301
% 1.20/0.78 % Unit Clause-clause subsumption calls : 1278
% 1.20/0.78 % Rewrite failures with RHS unbound : 0
% 1.20/0.78 % BW rewrite match attempts : 456
% 1.20/0.78 % BW rewrite match successes : 74
% 1.20/0.78 % Condensation attempts : 0
% 1.20/0.78 % Condensation successes : 0
% 1.20/0.78 % Termbank termtop insertions : 97262
% 1.20/0.78 % Search garbage collected termcells : 1092
% 1.20/0.78
% 1.20/0.78 % -------------------------------------------------
% 1.20/0.78 % User time : 0.243 s
% 1.20/0.78 % System time : 0.014 s
% 1.20/0.78 % Total time : 0.257 s
% 1.20/0.78 % Maximum resident set size: 3688 pages
% 1.20/0.78
% 1.20/0.78 % -------------------------------------------------
% 1.20/0.78 % User time : 1.221 s
% 1.20/0.78 % System time : 0.138 s
% 1.20/0.78 % Total time : 1.359 s
% 1.20/0.78 % Maximum resident set size: 4864 pages
% 1.20/0.78 % E exiting
%------------------------------------------------------------------------------