%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE037+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 12:58:41 PM UTC 2026
% Result : Theorem 0.14s 0.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 21 unt; 0 def)
% Number of atoms : 31 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 14 ( 8 ~; 4 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4] : leq(one,star(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',order) ).
fof(star_unfold_right,axiom,
! [X1] : leq(addition(one,multiplication(X1,star(X1))),star(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_unfold_right) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).
fof(c_0_6,negated_conjecture,
~ ! [X4] : leq(one,star(X4)),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_7,plain,
! [X20,X21,X22] : addition(X22,addition(X21,X20)) = addition(addition(X22,X21),X20),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_8,plain,
! [X23] : addition(X23,X23) = X23,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_9,plain,
! [X6,X7] :
( ( leq(X6,X7)
| addition(X6,X7) != X7 )
& ( addition(X6,X7) = X7
| ~ leq(X6,X7) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])]) ).
fof(c_0_10,plain,
! [X8] : leq(addition(one,multiplication(X8,star(X8))),star(X8)),
inference(variable_rename,[status(thm)],[star_unfold_right]) ).
fof(c_0_11,plain,
! [X18,X19] : addition(X18,X19) = addition(X19,X18),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_12,negated_conjecture,
~ leq(one,star(esk1_0)),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_13,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( ~ leq(X1,X2)
| addition(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
~ leq(one,star(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_13]),c_0_17]) ).
cnf(c_0_22,negated_conjecture,
addition(one,star(esk1_0)) != star(esk1_0),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE037+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 22:39:34 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 0.14/0.46 % Version: 3.5.1
% 0.14/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.46 % Starting sh5l with 300s (1) cores
% 0.14/0.46 % new_bool_1 with pid 2515032 completed with status 0
% 0.14/0.46 % Result found by new_bool_1
% 0.14/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.46 % Search class: FHUSM-FFSF21-MFFFFFNN
% 0.14/0.46 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.14/0.46 % SubtermCWHack with pid 2515036 completed with status 0
% 0.14/0.46 % Result found by SubtermCWHack
% 0.14/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.46 % Search class: FHUSM-FFSF21-MFFFFFNN
% 0.14/0.46 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.14/0.46 % Preprocessing time : 0.001 s
% 0.14/0.46
% 0.14/0.46 % Proof found!
% 0.14/0.46 % SZS status Theorem
% 0.14/0.46 % SZS output start CNFRefutation
% See solution above
% 0.14/0.46 % Parsed axioms : 17
% 0.14/0.46 % Removed by relevancy pruning/SinE : 3
% 0.14/0.46 % Initial clauses : 15
% 0.14/0.46 % Removed in clause preprocessing : 0
% 0.14/0.46 % Initial clauses in saturation : 15
% 0.14/0.46 % Processed clauses : 67
% 0.14/0.46 % ...of these trivial : 4
% 0.14/0.46 % ...subsumed : 34
% 0.14/0.46 % ...remaining for further processing : 29
% 0.14/0.46 % Other redundant clauses eliminated : 0
% 0.14/0.46 % Clauses deleted for lack of memory : 0
% 0.14/0.46 % Backward-subsumed : 0
% 0.14/0.46 % Backward-rewritten : 3
% 0.14/0.46 % Generated clauses : 338
% 0.14/0.46 % ...of the previous two non-redundant : 258
% 0.14/0.46 % ...aggressively subsumed : 0
% 0.14/0.46 % Contextual simplify-reflections : 0
% 0.14/0.46 % Paramodulations : 338
% 0.14/0.46 % Factorizations : 0
% 0.14/0.46 % NegExts : 0
% 0.14/0.46 % Equation resolutions : 0
% 0.14/0.46 % Disequality decompositions : 0
% 0.14/0.46 % Total rewrite steps : 270
% 0.14/0.46 % ...of those cached : 152
% 0.14/0.46 % Propositional unsat checks : 0
% 0.14/0.46 % Propositional check models : 0
% 0.14/0.46 % Propositional check unsatisfiable : 0
% 0.14/0.46 % Propositional clauses : 0
% 0.14/0.46 % Propositional clauses after purity: 0
% 0.14/0.46 % Propositional unsat core size : 0
% 0.14/0.46 % Propositional preprocessing time : 0.000
% 0.14/0.46 % Propositional encoding time : 0.000
% 0.14/0.46 % Propositional solver time : 0.000
% 0.14/0.46 % Success case prop preproc time : 0.000
% 0.14/0.46 % Success case prop encoding time : 0.000
% 0.14/0.46 % Success case prop solver time : 0.000
% 0.14/0.46 % Current number of processed clauses : 26
% 0.14/0.46 % Positive orientable unit clauses : 17
% 0.14/0.46 % Positive unorientable unit clauses: 4
% 0.14/0.46 % Negative unit clauses : 1
% 0.14/0.46 % Non-unit-clauses : 4
% 0.14/0.46 % Current number of unprocessed clauses: 206
% 0.14/0.46 % ...number of literals in the above : 242
% 0.14/0.46 % Current number of archived formulas : 0
% 0.14/0.46 % Current number of archived clauses : 3
% 0.14/0.46 % Clause-clause subsumption calls (NU) : 4
% 0.14/0.46 % Rec. Clause-clause subsumption calls : 4
% 0.14/0.46 % Non-unit clause-clause subsumptions : 0
% 0.14/0.46 % Unit Clause-clause subsumption calls : 6
% 0.14/0.46 % Rewrite failures with RHS unbound : 0
% 0.14/0.46 % BW rewrite match attempts : 40
% 0.14/0.46 % BW rewrite match successes : 31
% 0.14/0.46 % Condensation attempts : 0
% 0.14/0.46 % Condensation successes : 0
% 0.14/0.46 % Termbank termtop insertions : 3270
% 0.14/0.46 % Search garbage collected termcells : 67
% 0.14/0.46
% 0.14/0.46 % -------------------------------------------------
% 0.14/0.46 % User time : 0.007 s
% 0.14/0.46 % System time : 0.003 s
% 0.14/0.46 % Total time : 0.011 s
% 0.14/0.46 % Maximum resident set size: 3648 pages
% 0.14/0.46
% 0.14/0.46 % -------------------------------------------------
% 0.14/0.46 % User time : 0.010 s
% 0.14/0.46 % System time : 0.007 s
% 0.14/0.46 % Total time : 0.017 s
% 0.14/0.46 % Maximum resident set size: 4608 pages
% 0.14/0.46 % E exiting
%------------------------------------------------------------------------------