%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL488+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 01:12:53 PM UTC 2026
% Result : Theorem 0.13s 0.48s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of formulae : 57 ( 31 unt; 0 def)
% Number of atoms : 102 ( 17 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 77 ( 32 ~; 29 |; 7 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 71 ( 5 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(op_implies_and,axiom,
( op_implies_and
=> ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(hilbert_and_2,conjecture,
and_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_2) ).
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(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(principia_r2,axiom,
r2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r2) ).
fof(principia_op_implies_or,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_implies_or) ).
fof(op_or,axiom,
( op_or
=> ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(op_and,axiom,
( op_and
=> ! [X1,X2] : and(X1,X2) = not(or(not(X1),not(X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_and) ).
fof(principia_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_modus_ponens) ).
fof(principia_r3,axiom,
r3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r3) ).
fof(hilbert_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(principia_op_and,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_and) ).
fof(and_2,axiom,
( and_2
<=> ! [X1,X2] : is_a_theorem(implies(and(X1,X2),X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_2) ).
fof(c_0_16,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_17,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_18,plain,
! [X121,X122] :
( implies(X121,X122) = not(and(X121,not(X122)))
| ~ op_implies_and ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])])]) ).
fof(c_0_19,negated_conjecture,
~ and_2,
inference(assume_negation,[status(cth)],[hilbert_and_2]) ).
fof(c_0_20,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_21,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])])])])]) ).
cnf(c_0_22,plain,
( ~ r2
| is_a_theorem(implies(X1,or(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
r2,
inference(split_conjunct,[status(thm)],[principia_r2]) ).
cnf(c_0_24,plain,
( ~ op_implies_or
| implies(X1,X2) = or(not(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
op_implies_or,
inference(split_conjunct,[status(thm)],[principia_op_implies_or]) ).
fof(c_0_26,plain,
! [X117,X118] :
( or(X117,X118) = not(and(not(X117),not(X118)))
| ~ op_or ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])])]) ).
cnf(c_0_27,plain,
( ~ op_implies_and
| implies(X1,X2) = not(and(X1,not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
fof(c_0_29,plain,
! [X119,X120] :
( and(X119,X120) = not(or(not(X119),not(X120)))
| ~ op_and ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_and])])])]) ).
fof(c_0_30,negated_conjecture,
~ and_2,
inference(fof_simplification,[status(thm)],[c_0_19]) ).
cnf(c_0_31,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| ~ modus_ponens
| is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[principia_modus_ponens]) ).
cnf(c_0_33,plain,
( ~ r3
| is_a_theorem(implies(or(X1,X2),or(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_34,plain,
r3,
inference(split_conjunct,[status(thm)],[principia_r3]) ).
cnf(c_0_35,plain,
is_a_theorem(implies(X1,or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
cnf(c_0_36,plain,
or(not(X1),X2) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
cnf(c_0_37,plain,
( ~ op_or
| or(X1,X2) = not(and(not(X1),not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_38,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
cnf(c_0_39,plain,
op_or,
inference(split_conjunct,[status(thm)],[hilbert_op_or]) ).
cnf(c_0_40,plain,
( ~ op_and
| and(X1,X2) = not(or(not(X1),not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_41,plain,
op_and,
inference(split_conjunct,[status(thm)],[principia_op_and]) ).
fof(c_0_42,plain,
! [X37,X38] :
( ( and_2
| ~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0)) )
& ( is_a_theorem(implies(and(X37,X38),X38))
| ~ and_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)],[and_2])])])])]) ).
fof(c_0_43,negated_conjecture,
~ and_2,
inference(fof_nnf,[status(thm)],[c_0_30]) ).
cnf(c_0_44,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_31,c_0_32])]) ).
cnf(c_0_45,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).
cnf(c_0_46,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_47,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).
cnf(c_0_48,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_36]),c_0_41])]) ).
cnf(c_0_49,plain,
( ~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0))
| and_2 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_50,negated_conjecture,
~ and_2,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_51,plain,
( ~ is_a_theorem(or(X2,X1))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_52,plain,
is_a_theorem(or(X1,implies(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_53,plain,
or(implies(X1,not(X2)),X3) = implies(and(X1,X2),X3),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,plain,
~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0)),
inference(sr,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_55,plain,
is_a_theorem(implies(and(X1,X2),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
cnf(c_0_56,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL488+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n010.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 21 00:35:54 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 0.13/0.48 % Version: 3.5.1
% 0.13/0.48 % Preprocessing class: FSMSSLSSSSSNFFN.
% 0.13/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.48 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 0.13/0.48 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.48 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.48 % Starting sh5l with 300s (1) cores
% 0.13/0.48 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 3878733 completed with status 0
% 0.13/0.48 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 0.13/0.48 % Preprocessing class: FSMSSLSSSSSNFFN.
% 0.13/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.48 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 0.13/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.48 % No SInE strategy applied
% 0.13/0.48 % Search class: FGUSF-FFMM21-MFFFFFNN
% 0.13/0.48 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.48 % Starting SubtermCWHack with 151s (1) cores
% 0.13/0.48 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 0.13/0.48 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 0.13/0.48 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 0.13/0.48 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.48 % H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with pid 3878749 completed with status 0
% 0.13/0.48 % Result found by H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S
% 0.13/0.48 % Preprocessing class: FSMSSLSSSSSNFFN.
% 0.13/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.48 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 0.13/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.48 % No SInE strategy applied
% 0.13/0.48 % Search class: FGUSF-FFMM21-MFFFFFNN
% 0.13/0.48 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.48 % Starting SubtermCWHack with 151s (1) cores
% 0.13/0.48 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 0.13/0.48 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 0.13/0.48 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 0.13/0.48 % Preprocessing time : 0.002 s
% 0.13/0.48 % Presaturation interreduction done
% 0.13/0.48
% 0.13/0.48 % Proof found!
% 0.13/0.48 % SZS status Theorem
% 0.13/0.48 % SZS output start CNFRefutation
% See solution above
% 0.13/0.48 % Parsed axioms : 45
% 0.13/0.48 % Removed by relevancy pruning/SinE : 0
% 0.13/0.48 % Initial clauses : 74
% 0.13/0.48 % Removed in clause preprocessing : 0
% 0.13/0.48 % Initial clauses in saturation : 74
% 0.13/0.48 % Processed clauses : 185
% 0.13/0.48 % ...of these trivial : 20
% 0.13/0.48 % ...subsumed : 6
% 0.13/0.48 % ...remaining for further processing : 159
% 0.13/0.48 % Other redundant clauses eliminated : 0
% 0.13/0.48 % Clauses deleted for lack of memory : 0
% 0.13/0.48 % Backward-subsumed : 1
% 0.13/0.48 % Backward-rewritten : 8
% 0.13/0.48 % Generated clauses : 414
% 0.13/0.48 % ...of the previous two non-redundant : 329
% 0.13/0.48 % ...aggressively subsumed : 0
% 0.13/0.48 % Contextual simplify-reflections : 0
% 0.13/0.48 % Paramodulations : 414
% 0.13/0.48 % Factorizations : 0
% 0.13/0.48 % NegExts : 0
% 0.13/0.48 % Equation resolutions : 0
% 0.13/0.48 % Disequality decompositions : 0
% 0.13/0.48 % Total rewrite steps : 303
% 0.13/0.48 % ...of those cached : 98
% 0.13/0.48 % Propositional unsat checks : 0
% 0.13/0.48 % Propositional check models : 0
% 0.13/0.48 % Propositional check unsatisfiable : 0
% 0.13/0.48 % Propositional clauses : 0
% 0.13/0.48 % Propositional clauses after purity: 0
% 0.13/0.48 % Propositional unsat core size : 0
% 0.13/0.48 % Propositional preprocessing time : 0.000
% 0.13/0.48 % Propositional encoding time : 0.000
% 0.13/0.48 % Propositional solver time : 0.000
% 0.13/0.48 % Success case prop preproc time : 0.000
% 0.13/0.48 % Success case prop encoding time : 0.000
% 0.13/0.48 % Success case prop solver time : 0.000
% 0.13/0.48 % Current number of processed clauses : 90
% 0.13/0.48 % Positive orientable unit clauses : 49
% 0.13/0.48 % Positive unorientable unit clauses: 0
% 0.13/0.48 % Negative unit clauses : 2
% 0.13/0.48 % Non-unit-clauses : 39
% 0.13/0.48 % Current number of unprocessed clauses: 276
% 0.13/0.48 % ...number of literals in the above : 377
% 0.13/0.48 % Current number of archived formulas : 0
% 0.13/0.48 % Current number of archived clauses : 69
% 0.13/0.48 % Clause-clause subsumption calls (NU) : 278
% 0.13/0.48 % Rec. Clause-clause subsumption calls : 275
% 0.13/0.48 % Non-unit clause-clause subsumptions : 5
% 0.13/0.48 % Unit Clause-clause subsumption calls : 82
% 0.13/0.48 % Rewrite failures with RHS unbound : 0
% 0.13/0.48 % BW rewrite match attempts : 26
% 0.13/0.48 % BW rewrite match successes : 9
% 0.13/0.48 % Condensation attempts : 0
% 0.13/0.48 % Condensation successes : 0
% 0.13/0.48 % Termbank termtop insertions : 9236
% 0.13/0.48 % Search garbage collected termcells : 1092
% 0.13/0.48
% 0.13/0.48 % -------------------------------------------------
% 0.13/0.48 % User time : 0.018 s
% 0.13/0.48 % System time : 0.003 s
% 0.13/0.48 % Total time : 0.021 s
% 0.13/0.48 % Maximum resident set size: 3944 pages
% 0.13/0.48
% 0.13/0.48 % -------------------------------------------------
% 0.13/0.48 % User time : 0.063 s
% 0.13/0.48 % System time : 0.022 s
% 0.13/0.48 % Total time : 0.085 s
% 0.13/0.48 % Maximum resident set size: 4864 pages
% 0.13/0.48 % E exiting
%------------------------------------------------------------------------------