%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE038+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 : n004.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 12:58:42 PM UTC 2026
% Result : Theorem 0.15s 0.67s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 46 ( 42 unt; 0 def)
% Number of atoms : 52 ( 36 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 : 71 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',right_distributivity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).
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_left,axiom,
! [X1] : leq(addition(one,multiplication(star(X1),X1)),star(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_unfold_left) ).
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(goals,conjecture,
! [X4] : leq(X4,star(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',left_distributivity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_left_identity) ).
fof(c_0_11,plain,
! [X18,X19,X20] : addition(X20,addition(X19,X18)) = addition(addition(X20,X19),X18),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_12,plain,
! [X21] : addition(X21,X21) = X21,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_13,plain,
! [X22,X23,X24] : multiplication(X22,addition(X23,X24)) = addition(multiplication(X22,X23),multiplication(X22,X24)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_14,plain,
! [X31] : multiplication(X31,one) = X31,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_15,plain,
! [X16,X17] : addition(X16,X17) = addition(X17,X16),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_16,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,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_19,plain,
! [X9] : leq(addition(one,multiplication(star(X9),X9)),star(X9)),
inference(variable_rename,[status(thm)],[star_unfold_left]) ).
cnf(c_0_20,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_23,plain,
! [X8] : leq(addition(one,multiplication(X8,star(X8))),star(X8)),
inference(variable_rename,[status(thm)],[star_unfold_right]) ).
fof(c_0_24,negated_conjecture,
~ ! [X4] : leq(X4,star(X4)),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_25,plain,
! [X25,X26,X27] : multiplication(addition(X25,X26),X27) = addition(multiplication(X25,X27),multiplication(X26,X27)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_26,plain,
! [X32] : multiplication(one,X32) = X32,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_27,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_28,plain,
( ~ leq(X1,X2)
| addition(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,plain,
leq(addition(one,multiplication(star(X1),X1)),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_31,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_32,negated_conjecture,
~ leq(esk1_0,star(esk1_0)),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
cnf(c_0_33,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_27,c_0_22]) ).
cnf(c_0_36,plain,
addition(one,multiplication(star(X1),addition(X1,one))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_16]),c_0_22]),c_0_30]) ).
cnf(c_0_37,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_28,c_0_31]),c_0_16]),c_0_22]) ).
cnf(c_0_38,negated_conjecture,
~ leq(esk1_0,star(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_40,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_22]) ).
cnf(c_0_41,plain,
multiplication(star(X1),addition(X1,one)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_22]),c_0_30]),c_0_16]),c_0_17]) ).
cnf(c_0_42,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_27,c_0_37]) ).
cnf(c_0_43,negated_conjecture,
addition(esk1_0,star(esk1_0)) != star(esk1_0),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
addition(X1,star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_16]),c_0_42]),c_0_22]),c_0_42]),c_0_41]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE038+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.58 % Computer : n004.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Sun Sep 20 22:40:21 UTC 2026
% 0.10/0.59 % CPUTime :
% 0.10/0.59 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.63 Running first-order theorem proving
% 0.15/0.63 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
% 0.15/0.67 % Version: 3.5.1
% 0.15/0.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.67 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.67 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.67 % Starting sh5l with 300s (1) cores
% 0.15/0.67 % new_bool_3 with pid 1647981 completed with status 0
% 0.15/0.67 % Result found by new_bool_3
% 0.15/0.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.67 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.67 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.67 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.67 % Search class: FHUSM-FFSF21-MFFFFFNN
% 0.15/0.67 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.67 % Starting SubtermCWHack with 28s (1) cores
% 0.15/0.67 % SubtermCWHack with pid 1647984 completed with status 0
% 0.15/0.67 % Result found by SubtermCWHack
% 0.15/0.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.67 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.67 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.67 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.67 % Search class: FHUSM-FFSF21-MFFFFFNN
% 0.15/0.67 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.67 % Starting SubtermCWHack with 28s (1) cores
% 0.15/0.67 % Preprocessing time : 0.001 s
% 0.15/0.67
% 0.15/0.67 % Proof found!
% 0.15/0.67 % SZS status Theorem
% 0.15/0.67 % SZS output start CNFRefutation
% See solution above
% 0.15/0.67 % Parsed axioms : 17
% 0.15/0.67 % Removed by relevancy pruning/SinE : 3
% 0.15/0.67 % Initial clauses : 15
% 0.15/0.67 % Removed in clause preprocessing : 0
% 0.15/0.67 % Initial clauses in saturation : 15
% 0.15/0.67 % Processed clauses : 347
% 0.15/0.67 % ...of these trivial : 43
% 0.15/0.67 % ...subsumed : 210
% 0.15/0.67 % ...remaining for further processing : 94
% 0.15/0.67 % Other redundant clauses eliminated : 0
% 0.15/0.67 % Clauses deleted for lack of memory : 0
% 0.15/0.67 % Backward-subsumed : 2
% 0.15/0.67 % Backward-rewritten : 20
% 0.15/0.67 % Generated clauses : 1543
% 0.15/0.67 % ...of the previous two non-redundant : 1066
% 0.15/0.67 % ...aggressively subsumed : 0
% 0.15/0.67 % Contextual simplify-reflections : 0
% 0.15/0.67 % Paramodulations : 1543
% 0.15/0.67 % Factorizations : 0
% 0.15/0.67 % NegExts : 0
% 0.15/0.67 % Equation resolutions : 0
% 0.15/0.67 % Disequality decompositions : 0
% 0.15/0.67 % Total rewrite steps : 1499
% 0.15/0.67 % ...of those cached : 1144
% 0.15/0.67 % Propositional unsat checks : 0
% 0.15/0.67 % Propositional check models : 0
% 0.15/0.67 % Propositional check unsatisfiable : 0
% 0.15/0.67 % Propositional clauses : 0
% 0.15/0.67 % Propositional clauses after purity: 0
% 0.15/0.67 % Propositional unsat core size : 0
% 0.15/0.67 % Propositional preprocessing time : 0.000
% 0.15/0.67 % Propositional encoding time : 0.000
% 0.15/0.67 % Propositional solver time : 0.000
% 0.15/0.67 % Success case prop preproc time : 0.000
% 0.15/0.67 % Success case prop encoding time : 0.000
% 0.15/0.67 % Success case prop solver time : 0.000
% 0.15/0.67 % Current number of processed clauses : 72
% 0.15/0.67 % Positive orientable unit clauses : 32
% 0.15/0.67 % Positive unorientable unit clauses: 4
% 0.15/0.67 % Negative unit clauses : 2
% 0.15/0.67 % Non-unit-clauses : 34
% 0.15/0.67 % Current number of unprocessed clauses: 705
% 0.15/0.67 % ...number of literals in the above : 970
% 0.15/0.67 % Current number of archived formulas : 0
% 0.15/0.67 % Current number of archived clauses : 22
% 0.15/0.67 % Clause-clause subsumption calls (NU) : 601
% 0.15/0.67 % Rec. Clause-clause subsumption calls : 597
% 0.15/0.67 % Non-unit clause-clause subsumptions : 138
% 0.15/0.67 % Unit Clause-clause subsumption calls : 18
% 0.15/0.67 % Rewrite failures with RHS unbound : 0
% 0.15/0.67 % BW rewrite match attempts : 69
% 0.15/0.67 % BW rewrite match successes : 42
% 0.15/0.67 % Condensation attempts : 0
% 0.15/0.67 % Condensation successes : 0
% 0.15/0.67 % Termbank termtop insertions : 14666
% 0.15/0.67 % Search garbage collected termcells : 67
% 0.15/0.67
% 0.15/0.67 % -------------------------------------------------
% 0.15/0.67 % User time : 0.019 s
% 0.15/0.67 % System time : 0.003 s
% 0.15/0.67 % Total time : 0.022 s
% 0.15/0.67 % Maximum resident set size: 3648 pages
% 0.15/0.67
% 0.15/0.67 % -------------------------------------------------
% 0.15/0.67 % User time : 0.020 s
% 0.15/0.67 % System time : 0.009 s
% 0.15/0.67 % Total time : 0.029 s
% 0.15/0.67 % Maximum resident set size: 4864 pages
% 0.15/0.67 % E exiting
%------------------------------------------------------------------------------