%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL305-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 01:12:23 PM UTC 2026
% Result : Unsatisfiable 144.41s 21.49s
% Output : CNFRefutation 144.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of clauses : 67 ( 34 unt; 0 nHn; 34 RR)
% Number of literals : 110 ( 7 equ; 50 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 128 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(rule_2,axiom,
( ~ theorem(X2)
| ~ theorem(implies(X2,X1))
| theorem(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',rule_2) ).
cnf(implies_definition,axiom,
implies(X1,X2) = or(not(X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',implies_definition) ).
cnf(rule_1,axiom,
( ~ axiom(X1)
| theorem(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',rule_1) ).
cnf(axiom_1_6,axiom,
axiom(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',axiom_1_6) ).
cnf(axiom_1_5,axiom,
axiom(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3)))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',axiom_1_5) ).
cnf(axiom_1_3,axiom,
axiom(implies(X1,or(X2,X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',axiom_1_3) ).
cnf(axiom_1_2,axiom,
axiom(implies(or(X1,X1),X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',axiom_1_2) ).
cnf(axiom_1_4,axiom,
axiom(implies(or(X1,X2),or(X2,X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax',axiom_1_4) ).
cnf(prove_this,negated_conjecture,
~ theorem(implies(q,equivalent(p,and(p,q)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
cnf(equivalent_defn,axiom,
equivalent(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-2.ax',equivalent_defn) ).
cnf(and_defn,axiom,
and(X1,X2) = not(or(not(X1),not(X2))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-1.ax',and_defn) ).
cnf(c_0_11,plain,
( ~ theorem(X2)
| ~ theorem(implies(X2,X1))
| theorem(X1) ),
inference(fof_simplification,[status(thm)],[rule_2]) ).
cnf(c_0_12,plain,
( ~ theorem(X2)
| ~ theorem(implies(X2,X1))
| theorem(X1) ),
c_0_11 ).
cnf(c_0_13,axiom,
implies(X1,X2) = or(not(X1),X2),
implies_definition ).
cnf(c_0_14,plain,
( ~ axiom(X1)
| theorem(X1) ),
inference(fof_simplification,[status(thm)],[rule_1]) ).
cnf(c_0_15,plain,
( ~ theorem(or(not(X2),X1))
| ~ theorem(X2)
| theorem(X1) ),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
( ~ axiom(X1)
| theorem(X1) ),
c_0_14 ).
cnf(c_0_17,axiom,
axiom(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))),
axiom_1_6 ).
cnf(c_0_18,plain,
( ~ axiom(or(not(X2),X1))
| ~ theorem(X2)
| theorem(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
axiom(or(not(or(not(X1),X2)),or(not(or(X3,X1)),or(X3,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_13]),c_0_13]),c_0_13]) ).
cnf(c_0_20,axiom,
axiom(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3)))),
axiom_1_5 ).
cnf(c_0_21,plain,
( ~ theorem(or(not(X2),X3))
| theorem(or(not(or(X1,X2)),or(X1,X3))) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,axiom,
axiom(implies(X1,or(X2,X1))),
axiom_1_3 ).
cnf(c_0_23,plain,
axiom(or(not(or(X1,or(X2,X3))),or(X2,or(X1,X3)))),
inference(rw,[status(thm)],[c_0_20,c_0_13]) ).
cnf(c_0_24,plain,
( ~ theorem(or(X1,X3))
| ~ theorem(or(not(X3),X2))
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_21]) ).
cnf(c_0_25,axiom,
axiom(implies(or(X1,X1),X1)),
axiom_1_2 ).
cnf(c_0_26,plain,
axiom(or(not(X1),or(X2,X1))),
inference(rw,[status(thm)],[c_0_22,c_0_13]) ).
cnf(c_0_27,plain,
( ~ theorem(or(X2,or(X1,X3)))
| theorem(or(X1,or(X2,X3))) ),
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
cnf(c_0_28,axiom,
axiom(implies(or(X1,X2),or(X2,X1))),
axiom_1_4 ).
cnf(c_0_29,plain,
( ~ axiom(or(not(X3),X2))
| ~ theorem(or(X1,X3))
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_30,plain,
axiom(or(not(or(X1,X1)),X1)),
inference(rw,[status(thm)],[c_0_25,c_0_13]) ).
cnf(c_0_31,plain,
( ~ theorem(X2)
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_26]) ).
cnf(c_0_32,plain,
( ~ theorem(or(not(X2),X3))
| theorem(or(X1,or(not(or(X1,X2)),X3))) ),
inference(spm,[status(thm)],[c_0_27,c_0_21]) ).
cnf(c_0_33,plain,
axiom(or(not(or(X1,X2)),or(X2,X1))),
inference(rw,[status(thm)],[c_0_28,c_0_13]) ).
cnf(c_0_34,plain,
( ~ theorem(or(X1,or(X2,X2)))
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( ~ theorem(or(X1,X1))
| theorem(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_30]) ).
cnf(c_0_36,plain,
( ~ theorem(or(X1,X3))
| theorem(or(X1,or(X2,X3))) ),
inference(spm,[status(thm)],[c_0_27,c_0_31]) ).
cnf(c_0_37,negated_conjecture,
~ theorem(implies(q,equivalent(p,and(p,q)))),
inference(fof_simplification,[status(thm)],[prove_this]) ).
cnf(c_0_38,axiom,
equivalent(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
equivalent_defn ).
cnf(c_0_39,axiom,
and(X1,X2) = not(or(not(X1),not(X2))),
and_defn ).
cnf(c_0_40,plain,
( ~ theorem(or(X1,X2))
| ~ theorem(or(not(X3),X4))
| theorem(or(X1,or(not(or(not(X2),X3)),X4))) ),
inference(spm,[status(thm)],[c_0_24,c_0_32]) ).
cnf(c_0_41,plain,
( ~ theorem(or(X2,X1))
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_33]) ).
cnf(c_0_42,plain,
( ~ axiom(or(X1,or(X2,X2)))
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_34,c_0_16]) ).
cnf(c_0_43,plain,
( ~ theorem(or(or(X1,X2),X2))
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_44,plain,
( ~ axiom(or(X2,or(X1,X3)))
| theorem(or(X1,or(X2,X3))) ),
inference(spm,[status(thm)],[c_0_27,c_0_16]) ).
cnf(c_0_45,negated_conjecture,
~ theorem(implies(q,equivalent(p,and(p,q)))),
c_0_37 ).
cnf(c_0_46,plain,
equivalent(X1,X2) = not(or(not(or(not(X1),X2)),not(or(not(X2),X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_13]),c_0_13]),c_0_39]) ).
cnf(c_0_47,plain,
( ~ theorem(or(X1,X2))
| ~ theorem(or(not(X3),not(or(not(X2),X3))))
| theorem(or(X1,not(or(not(X2),X3)))) ),
inference(spm,[status(thm)],[c_0_34,c_0_40]) ).
cnf(c_0_48,plain,
( ~ theorem(X1)
| theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_41,c_0_31]) ).
cnf(c_0_49,plain,
theorem(or(not(X1),X1)),
inference(spm,[status(thm)],[c_0_42,c_0_26]) ).
cnf(c_0_50,plain,
( ~ axiom(or(X2,or(or(X1,or(X2,X3)),X3)))
| theorem(or(X1,or(X2,X3))) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_51,negated_conjecture,
~ theorem(or(not(q),not(or(not(or(not(p),not(or(not(p),not(q))))),not(or(not(not(or(not(p),not(q)))),p)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_13]),c_0_39]),c_0_46]) ).
cnf(c_0_52,plain,
( ~ theorem(not(X3))
| ~ theorem(or(X1,X2))
| theorem(or(X1,not(or(not(X2),X3)))) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,plain,
theorem(or(X1,not(X1))),
inference(spm,[status(thm)],[c_0_41,c_0_49]) ).
cnf(c_0_54,plain,
theorem(or(X1,or(not(X2),X2))),
inference(spm,[status(thm)],[c_0_50,c_0_26]) ).
cnf(c_0_55,negated_conjecture,
( ~ theorem(not(not(or(not(not(or(not(p),not(q)))),p))))
| ~ theorem(or(not(q),or(not(p),not(or(not(p),not(q)))))) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,plain,
( ~ theorem(X1)
| theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_15,c_0_53]) ).
cnf(c_0_57,plain,
( ~ theorem(or(X1,or(X3,X2)))
| theorem(or(X1,or(X2,X3))) ),
inference(spm,[status(thm)],[c_0_29,c_0_33]) ).
cnf(c_0_58,plain,
theorem(or(not(X1),or(X2,X1))),
inference(spm,[status(thm)],[c_0_27,c_0_54]) ).
cnf(c_0_59,negated_conjecture,
( ~ theorem(or(not(not(or(not(p),not(q)))),p))
| ~ theorem(or(not(q),or(not(p),not(or(not(p),not(q)))))) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_60,plain,
( ~ axiom(or(X3,or(X1,X2)))
| theorem(or(X1,or(X2,X3))) ),
inference(spm,[status(thm)],[c_0_57,c_0_44]) ).
cnf(c_0_61,plain,
( ~ theorem(or(X1,X2))
| theorem(or(X1,not(not(X2)))) ),
inference(spm,[status(thm)],[c_0_24,c_0_53]) ).
cnf(c_0_62,plain,
theorem(or(not(X1),or(X1,X2))),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,negated_conjecture,
~ theorem(or(not(not(or(not(p),not(q)))),p)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_33])]) ).
cnf(c_0_64,plain,
( ~ theorem(or(X2,X1))
| theorem(or(not(not(X1)),X2)) ),
inference(spm,[status(thm)],[c_0_41,c_0_61]) ).
cnf(c_0_65,plain,
theorem(or(X1,or(not(X1),X2))),
inference(spm,[status(thm)],[c_0_27,c_0_62]) ).
cnf(c_0_66,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL305-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n007.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 00:17:35 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 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
% 144.41/21.49 % Version: 3.5.1
% 144.41/21.49 % Preprocessing class: FSSSSMSSSSSNFFN.
% 144.41/21.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 144.41/21.49 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 144.41/21.49 % Starting new_bool_3 with 300s (1) cores
% 144.41/21.49 % Starting new_bool_1 with 300s (1) cores
% 144.41/21.49 % Starting sh5l with 300s (1) cores
% 144.41/21.49 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3950971 completed with status 0
% 144.41/21.49 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 144.41/21.49 % Preprocessing class: FSSSSMSSSSSNFFN.
% 144.41/21.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 144.41/21.49 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 144.41/21.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 144.41/21.49 % No SInE strategy applied
% 144.41/21.49 % Search class: FHUNM-FFSF21-DFFFFFNN
% 144.41/21.49 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 144.41/21.49 % Starting SubtermCWHack with 151s (1) cores
% 144.41/21.49 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 395s (1) cores
% 144.41/21.49 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 334s (1) cores
% 144.41/21.49 % Starting new_bool_3 with 329s (1) cores
% 144.41/21.49 % Starting new_bool_1 with 291s (1) cores
% 144.41/21.49 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3950976 completed with status 0
% 144.41/21.49 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 144.41/21.49 % Preprocessing class: FSSSSMSSSSSNFFN.
% 144.41/21.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 144.41/21.49 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 144.41/21.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 144.41/21.49 % No SInE strategy applied
% 144.41/21.49 % Search class: FHUNM-FFSF21-DFFFFFNN
% 144.41/21.49 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 144.41/21.49 % Starting SubtermCWHack with 151s (1) cores
% 144.41/21.49 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 395s (1) cores
% 144.41/21.49 % Preprocessing time : 0.067 s
% 144.41/21.49
% 144.41/21.49 % Proof found!
% 144.41/21.49 % SZS status Unsatisfiable
% 144.41/21.49 % SZS output start CNFRefutation
% See solution above
% 144.41/21.49 % Parsed axioms : 11
% 144.41/21.49 % Removed by relevancy pruning/SinE : 0
% 144.41/21.49 % Initial clauses : 11
% 144.41/21.49 % Removed in clause preprocessing : 3
% 144.41/21.49 % Initial clauses in saturation : 8
% 144.41/21.49 % Processed clauses : 13723
% 144.41/21.49 % ...of these trivial : 26
% 144.41/21.49 % ...subsumed : 10459
% 144.41/21.49 % ...remaining for further processing : 3238
% 144.41/21.49 % Other redundant clauses eliminated : 0
% 144.41/21.49 % Clauses deleted for lack of memory : 0
% 144.41/21.49 % Backward-subsumed : 171
% 144.41/21.49 % Backward-rewritten : 7
% 144.41/21.49 % Generated clauses : 419733
% 144.41/21.49 % ...of the previous two non-redundant : 416617
% 144.41/21.49 % ...aggressively subsumed : 0
% 144.41/21.49 % Contextual simplify-reflections : 8
% 144.41/21.49 % Paramodulations : 419733
% 144.41/21.49 % Factorizations : 0
% 144.41/21.49 % NegExts : 0
% 144.41/21.49 % Equation resolutions : 0
% 144.41/21.49 % Disequality decompositions : 0
% 144.41/21.49 % Total rewrite steps : 2600
% 144.41/21.49 % ...of those cached : 2085
% 144.41/21.49 % Propositional unsat checks : 0
% 144.41/21.49 % Propositional check models : 0
% 144.41/21.49 % Propositional check unsatisfiable : 0
% 144.41/21.49 % Propositional clauses : 0
% 144.41/21.49 % Propositional clauses after purity: 0
% 144.41/21.49 % Propositional unsat core size : 0
% 144.41/21.49 % Propositional preprocessing time : 0.000
% 144.41/21.49 % Propositional encoding time : 0.000
% 144.41/21.49 % Propositional solver time : 0.000
% 144.41/21.49 % Success case prop preproc time : 0.000
% 144.41/21.49 % Success case prop encoding time : 0.000
% 144.41/21.49 % Success case prop solver time : 0.000
% 144.41/21.49 % Current number of processed clauses : 3060
% 144.41/21.49 % Positive orientable unit clauses : 95
% 144.41/21.49 % Positive unorientable unit clauses: 0
% 144.41/21.49 % Negative unit clauses : 35
% 144.41/21.49 % Non-unit-clauses : 2930
% 144.41/21.49 % Current number of unprocessed clauses: 402676
% 144.41/21.49 % ...number of literals in the above : 1472975
% 144.41/21.49 % Current number of archived formulas : 0
% 144.41/21.49 % Current number of archived clauses : 181
% 144.41/21.49 % Clause-clause subsumption calls (NU) : 1639060
% 144.41/21.49 % Rec. Clause-clause subsumption calls : 1186594
% 144.41/21.49 % Non-unit clause-clause subsumptions : 10190
% 144.41/21.49 % Unit Clause-clause subsumption calls : 8916
% 144.41/21.49 % Rewrite failures with RHS unbound : 0
% 144.41/21.49 % BW rewrite match attempts : 12957
% 144.41/21.49 % BW rewrite match successes : 3
% 144.41/21.49 % Condensation attempts : 0
% 144.41/21.49 % Condensation successes : 0
% 144.41/21.49 % Termbank termtop insertions : 9960269
% 144.41/21.49 % Search garbage collected termcells : 11
% 144.41/21.49
% 144.41/21.49 % -------------------------------------------------
% 144.41/21.49 % User time : 19.749 s
% 144.41/21.49 % System time : 0.633 s
% 144.41/21.49 % Total time : 20.382 s
% 144.41/21.49 % Maximum resident set size: 3644 pages
% 144.41/21.49
% 144.41/21.49 % -------------------------------------------------
% 144.41/21.49 % User time : 98.921 s
% 144.41/21.49 % System time : 3.682 s
% 144.41/21.49 % Total time : 102.603 s
% 144.41/21.49 % Maximum resident set size: 4864 pages
% 144.41/21.49 % E exiting
%------------------------------------------------------------------------------