%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL456+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 : n016.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 0.21s 0.47s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 45 ( 27 unt; 0 def)
% Number of atoms : 67 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 19 ~; 14 |; 2 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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_op_implies_or,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',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/Axioms/LCL006+2.ax',hilbert_op_implies_and) ).
fof(principia_op_and,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_and) ).
fof(hilbert_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_or) ).
fof(principia_r3,conjecture,
r3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r3) ).
fof(modus_tollens,axiom,
( modus_tollens
<=> ! [X1,X2] : is_a_theorem(implies(implies(not(X2),not(X1)),implies(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).
fof(hilbert_modus_tollens,axiom,
modus_tollens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_tollens) ).
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(c_0_12,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_13,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_14,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])])])]) ).
cnf(c_0_15,plain,
( ~ op_implies_or
| implies(X1,X2) = or(not(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
op_implies_or,
inference(split_conjunct,[status(thm)],[principia_op_implies_or]) ).
fof(c_0_17,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_18,plain,
( ~ op_implies_and
| implies(X1,X2) = not(and(X1,not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
cnf(c_0_20,plain,
( ~ op_and
| and(X1,X2) = not(or(not(X1),not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
or(not(X1),X2) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]) ).
cnf(c_0_22,plain,
op_and,
inference(split_conjunct,[status(thm)],[principia_op_and]) ).
cnf(c_0_23,plain,
( ~ op_or
| or(X1,X2) = not(and(not(X1),not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]) ).
cnf(c_0_25,plain,
op_or,
inference(split_conjunct,[status(thm)],[hilbert_op_or]) ).
fof(c_0_26,negated_conjecture,
~ r3,
inference(assume_negation,[status(cth)],[principia_r3]) ).
fof(c_0_27,plain,
! [X15,X16] :
( ( modus_tollens
| ~ is_a_theorem(implies(implies(not(esk6_0),not(esk5_0)),implies(esk5_0,esk6_0))) )
& ( is_a_theorem(implies(implies(not(X16),not(X15)),implies(X15,X16)))
| ~ modus_tollens ) ),
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_tollens])])])])]) ).
cnf(c_0_28,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_29,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
fof(c_0_30,negated_conjecture,
~ r3,
inference(fof_simplification,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
( ~ modus_tollens
| is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
modus_tollens,
inference(split_conjunct,[status(thm)],[hilbert_modus_tollens]) ).
cnf(c_0_33,plain,
not(or(X1,not(X2))) = and(not(X1),X2),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_34,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_35,negated_conjecture,
~ r3,
inference(fof_nnf,[status(thm)],[c_0_30]) ).
cnf(c_0_36,plain,
is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_29]),c_0_32])]) ).
cnf(c_0_37,plain,
implies(or(X1,not(X2)),X3) = or(and(not(X1),X2),X3),
inference(spm,[status(thm)],[c_0_21,c_0_33]) ).
cnf(c_0_38,plain,
( ~ is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0)))
| r3 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,negated_conjecture,
~ r3,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,plain,
is_a_theorem(or(and(not(X1),X2),implies(X2,X1))),
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,plain,
or(and(X1,not(X2)),X3) = implies(implies(X1,X2),X3),
inference(spm,[status(thm)],[c_0_29,c_0_24]) ).
cnf(c_0_42,plain,
~ is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0))),
inference(sr,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_29]),c_0_41]),c_0_29]) ).
cnf(c_0_44,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL456+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n016.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 00:37:54 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
% 0.21/0.47 % Version: 3.5.1
% 0.21/0.47 % Preprocessing class: FSMSSLSSSSSNFFN.
% 0.21/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.47 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 0.21/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.47 % Starting sh5l with 300s (1) cores
% 0.21/0.47 % new_bool_3 with pid 1194655 completed with status 9
% 0.21/0.47 % new_bool_1 with pid 1194656 completed with status 9
% 0.21/0.47 % sh5l with pid 1194657 completed with status 9
% 0.21/0.47 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 1194654 completed with status 0
% 0.21/0.47 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 0.21/0.47 % Preprocessing class: FSMSSLSSSSSNFFN.
% 0.21/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.47 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 0.21/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.47 % No SInE strategy applied
% 0.21/0.47 % Search class: FGUSF-FFMM21-MFFFFFNN
% 0.21/0.47 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.47 % Starting SubtermCWHack with 151s (1) cores
% 0.21/0.47 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 0.21/0.47 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 0.21/0.47 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 0.21/0.47 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.21/0.47 % H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with pid 1194673 completed with status 0
% 0.21/0.47 % Result found by H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S
% 0.21/0.47 % Preprocessing class: FSMSSLSSSSSNFFN.
% 0.21/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.47 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 0.21/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.47 % No SInE strategy applied
% 0.21/0.47 % Search class: FGUSF-FFMM21-MFFFFFNN
% 0.21/0.47 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.47 % Starting SubtermCWHack with 151s (1) cores
% 0.21/0.47 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 0.21/0.47 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 0.21/0.47 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 0.21/0.47 % Preprocessing time : 0.002 s
% 0.21/0.47 % Presaturation interreduction done
% 0.21/0.47
% 0.21/0.47 % Proof found!
% 0.21/0.47 % SZS status Theorem
% 0.21/0.47 % SZS output start CNFRefutation
% See solution above
% 0.21/0.47 % Parsed axioms : 53
% 0.21/0.47 % Removed by relevancy pruning/SinE : 0
% 0.21/0.47 % Initial clauses : 82
% 0.21/0.47 % Removed in clause preprocessing : 0
% 0.21/0.47 % Initial clauses in saturation : 82
% 0.21/0.47 % Processed clauses : 191
% 0.21/0.47 % ...of these trivial : 27
% 0.21/0.47 % ...subsumed : 11
% 0.21/0.47 % ...remaining for further processing : 153
% 0.21/0.47 % Other redundant clauses eliminated : 0
% 0.21/0.47 % Clauses deleted for lack of memory : 0
% 0.21/0.47 % Backward-subsumed : 0
% 0.21/0.47 % Backward-rewritten : 4
% 0.21/0.47 % Generated clauses : 416
% 0.21/0.47 % ...of the previous two non-redundant : 333
% 0.21/0.47 % ...aggressively subsumed : 0
% 0.21/0.47 % Contextual simplify-reflections : 0
% 0.21/0.47 % Paramodulations : 416
% 0.21/0.47 % Factorizations : 0
% 0.21/0.47 % NegExts : 0
% 0.21/0.47 % Equation resolutions : 0
% 0.21/0.47 % Disequality decompositions : 0
% 0.21/0.47 % Total rewrite steps : 268
% 0.21/0.47 % ...of those cached : 87
% 0.21/0.47 % Propositional unsat checks : 0
% 0.21/0.47 % Propositional check models : 0
% 0.21/0.47 % Propositional check unsatisfiable : 0
% 0.21/0.47 % Propositional clauses : 0
% 0.21/0.47 % Propositional clauses after purity: 0
% 0.21/0.47 % Propositional unsat core size : 0
% 0.21/0.47 % Propositional preprocessing time : 0.000
% 0.21/0.47 % Propositional encoding time : 0.000
% 0.21/0.47 % Propositional solver time : 0.000
% 0.21/0.47 % Success case prop preproc time : 0.000
% 0.21/0.47 % Success case prop encoding time : 0.000
% 0.21/0.47 % Success case prop solver time : 0.000
% 0.21/0.47 % Current number of processed clauses : 91
% 0.21/0.47 % Positive orientable unit clauses : 63
% 0.21/0.47 % Positive unorientable unit clauses: 0
% 0.21/0.47 % Negative unit clauses : 4
% 0.21/0.47 % Non-unit-clauses : 24
% 0.21/0.47 % Current number of unprocessed clauses: 275
% 0.21/0.47 % ...number of literals in the above : 357
% 0.21/0.47 % Current number of archived formulas : 0
% 0.21/0.47 % Current number of archived clauses : 62
% 0.21/0.47 % Clause-clause subsumption calls (NU) : 147
% 0.21/0.47 % Rec. Clause-clause subsumption calls : 147
% 0.21/0.47 % Non-unit clause-clause subsumptions : 10
% 0.21/0.47 % Unit Clause-clause subsumption calls : 28
% 0.21/0.47 % Rewrite failures with RHS unbound : 0
% 0.21/0.47 % BW rewrite match attempts : 34
% 0.21/0.47 % BW rewrite match successes : 4
% 0.21/0.47 % Condensation attempts : 0
% 0.21/0.47 % Condensation successes : 0
% 0.21/0.47 % Termbank termtop insertions : 9058
% 0.21/0.47 % Search garbage collected termcells : 1092
% 0.21/0.47
% 0.21/0.47 % -------------------------------------------------
% 0.21/0.47 % User time : 0.020 s
% 0.21/0.47 % System time : 0.003 s
% 0.21/0.47 % Total time : 0.023 s
% 0.21/0.47 % Maximum resident set size: 3688 pages
% 0.21/0.47
% 0.21/0.47 % -------------------------------------------------
% 0.21/0.47 % User time : 0.148 s
% 0.21/0.47 % System time : 0.069 s
% 0.21/0.47 % Total time : 0.217 s
% 0.21/0.47 % Maximum resident set size: 4864 pages
% 0.21/0.47 % E exiting
%------------------------------------------------------------------------------