%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE048+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 : 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 12:58:43 PM UTC 2026
% Result : Theorem 0.09s 0.46s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 57 ( 33 unt; 0 def)
% Number of atoms : 95 ( 42 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 64 ( 26 ~; 23 |; 8 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 83 ( 2 sgn 44 !; 1 ?)
% 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(test_2,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( addition(X4,X5) = one
& multiplication(X5,X4) = zero
& multiplication(X4,X5) = zero ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(goals,conjecture,
! [X4] :
( test(X4)
=> star(X4) = one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(star_induction_right,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X1,X2),X3),X1)
=> leq(multiplication(X3,star(X2)),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_induction_right) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_left_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_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(star_induction_left,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X1,X2),X3),X2)
=> leq(multiplication(star(X1),X3),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_induction_left) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).
fof(c_0_12,plain,
! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_13,plain,
! [X12] : addition(X12,X12) = X12,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_14,plain,
! [X40,X41] :
( ( complement(X41,X40)
| addition(X40,X41) != one
| multiplication(X41,X40) != zero
| multiplication(X40,X41) != zero )
& ( ~ complement(X41,X40)
| addition(X40,X41) = one )
& ( ~ complement(X41,X40)
| multiplication(X41,X40) = zero )
& ( ~ complement(X41,X40)
| multiplication(X40,X41) = zero ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])])]) ).
fof(c_0_15,plain,
! [X36,X38,X39] :
( ( test(X38)
| ~ complement(X39,X38) )
& ( complement(esk1_1(X36),X36)
| ~ test(X36) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[test_1])])])])])]) ).
cnf(c_0_16,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( ~ complement(X2,X1)
| addition(X1,X2) = one ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( ~ test(X1)
| complement(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_20,negated_conjecture,
~ ! [X4] :
( test(X4)
=> star(X4) = one ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_21,plain,
! [X33,X34,X35] :
( leq(multiplication(X35,star(X34)),X33)
| ~ leq(addition(multiplication(X33,X34),X35),X33) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction_right])])]) ).
fof(c_0_22,plain,
! [X17] : multiplication(one,X17) = X17,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_23,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,plain,
( ~ test(X1)
| addition(X1,esk1_1(X1)) = one ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_25,negated_conjecture,
( star(esk2_0) != one
& test(esk2_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
fof(c_0_26,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_27,plain,
! [X26,X27] :
( ( leq(X26,X27)
| addition(X26,X27) != X27 )
& ( addition(X26,X27) = X27
| ~ leq(X26,X27) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])]) ).
cnf(c_0_28,plain,
( ~ leq(addition(multiplication(X1,X2),X3),X1)
| leq(multiplication(X3,star(X2)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_30,plain,
! [X28] : leq(addition(one,multiplication(X28,star(X28))),star(X28)),
inference(variable_rename,[status(thm)],[star_unfold_right]) ).
cnf(c_0_31,plain,
( ~ test(X1)
| addition(X1,one) = one ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_32,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,plain,
( ~ leq(addition(X2,X1),one)
| leq(multiplication(X1,star(X2)),one) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,plain,
( ~ leq(X1,X2)
| addition(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_38,plain,
! [X30,X31,X32] :
( leq(multiplication(star(X30),X32),X31)
| ~ leq(addition(multiplication(X30,X31),X32),X31) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction_left])])]) ).
cnf(c_0_39,negated_conjecture,
addition(one,esk2_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_40,plain,
leq(X1,X1),
inference(spm,[status(thm)],[c_0_34,c_0_17]) ).
cnf(c_0_41,plain,
( ~ leq(X1,one)
| leq(multiplication(X1,star(X1)),one) ),
inference(spm,[status(thm)],[c_0_35,c_0_17]) ).
cnf(c_0_42,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_36,c_0_37]),c_0_16]),c_0_33]) ).
cnf(c_0_43,plain,
( ~ leq(addition(multiplication(X1,X2),X3),X2)
| leq(multiplication(star(X1),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,negated_conjecture,
leq(multiplication(esk2_0,star(one)),one),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_39]),c_0_40])]) ).
fof(c_0_45,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_46,plain,
leq(star(one),one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_40]),c_0_29]) ).
cnf(c_0_47,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_23,c_0_42]) ).
cnf(c_0_48,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_34,c_0_23]) ).
cnf(c_0_49,plain,
( ~ leq(addition(X2,multiplication(X1,X3)),X3)
| leq(multiplication(star(X1),X2),X3) ),
inference(spm,[status(thm)],[c_0_43,c_0_33]) ).
cnf(c_0_50,negated_conjecture,
addition(one,multiplication(esk2_0,star(one))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_44]),c_0_33]) ).
cnf(c_0_51,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_52,plain,
star(one) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_46]),c_0_33]),c_0_47]) ).
cnf(c_0_53,plain,
leq(one,star(X1)),
inference(spm,[status(thm)],[c_0_48,c_0_42]) ).
cnf(c_0_54,negated_conjecture,
leq(star(esk2_0),one),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_52]),c_0_53])]) ).
cnf(c_0_55,negated_conjecture,
star(esk2_0) != one,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_54]),c_0_33]),c_0_47]),c_0_55]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE048+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 22:39:06 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.46 % Version: 3.5.1
% 0.09/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.46 % Starting sh5l with 300s (1) cores
% 0.09/0.46 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3739707 completed with status 0
% 0.09/0.46 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.09/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.46 % No SInE strategy applied
% 0.09/0.46 % Search class: FGUSM-FFMF21-MFFFFFNN
% 0.09/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.09/0.46 % Starting G-E--_200_B02_F1_AE_CS_SP_PI_S0S with 136s (1) cores
% 0.09/0.46 % Starting new_bool_3 with 136s (1) cores
% 0.09/0.46 % Starting new_bool_1 with 136s (1) cores
% 0.09/0.46 % new_bool_1 with pid 3739715 completed with status 0
% 0.09/0.46 % Result found by new_bool_1
% 0.09/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.46 % No SInE strategy applied
% 0.09/0.46 % Search class: FGUSM-FFMF21-MFFFFFNN
% 0.09/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.09/0.46 % Starting G-E--_200_B02_F1_AE_CS_SP_PI_S0S with 136s (1) cores
% 0.09/0.46 % Starting new_bool_3 with 136s (1) cores
% 0.09/0.46 % Starting new_bool_1 with 136s (1) cores
% 0.09/0.46 % Preprocessing time : 0.001 s
% 0.09/0.46 % Presaturation interreduction done
% 0.09/0.46
% 0.09/0.46 % Proof found!
% 0.09/0.46 % SZS status Theorem
% 0.09/0.46 % SZS output start CNFRefutation
% See solution above
% 0.09/0.46 % Parsed axioms : 21
% 0.09/0.46 % Removed by relevancy pruning/SinE : 0
% 0.09/0.46 % Initial clauses : 28
% 0.09/0.46 % Removed in clause preprocessing : 0
% 0.09/0.46 % Initial clauses in saturation : 28
% 0.09/0.46 % Processed clauses : 529
% 0.09/0.46 % ...of these trivial : 31
% 0.09/0.46 % ...subsumed : 251
% 0.09/0.46 % ...remaining for further processing : 246
% 0.09/0.46 % Other redundant clauses eliminated : 24
% 0.09/0.46 % Clauses deleted for lack of memory : 0
% 0.09/0.46 % Backward-subsumed : 12
% 0.09/0.46 % Backward-rewritten : 24
% 0.09/0.46 % Generated clauses : 2061
% 0.09/0.46 % ...of the previous two non-redundant : 1482
% 0.09/0.46 % ...aggressively subsumed : 0
% 0.09/0.46 % Contextual simplify-reflections : 0
% 0.09/0.46 % Paramodulations : 2037
% 0.09/0.46 % Factorizations : 0
% 0.09/0.46 % NegExts : 0
% 0.09/0.46 % Equation resolutions : 24
% 0.09/0.46 % Disequality decompositions : 0
% 0.09/0.46 % Total rewrite steps : 1900
% 0.09/0.46 % ...of those cached : 1467
% 0.09/0.46 % Propositional unsat checks : 0
% 0.09/0.46 % Propositional check models : 0
% 0.09/0.46 % Propositional check unsatisfiable : 0
% 0.09/0.46 % Propositional clauses : 0
% 0.09/0.46 % Propositional clauses after purity: 0
% 0.09/0.46 % Propositional unsat core size : 0
% 0.09/0.46 % Propositional preprocessing time : 0.000
% 0.09/0.46 % Propositional encoding time : 0.000
% 0.09/0.46 % Propositional solver time : 0.000
% 0.09/0.46 % Success case prop preproc time : 0.000
% 0.09/0.46 % Success case prop encoding time : 0.000
% 0.09/0.46 % Success case prop solver time : 0.000
% 0.09/0.46 % Current number of processed clauses : 181
% 0.09/0.46 % Positive orientable unit clauses : 69
% 0.09/0.46 % Positive unorientable unit clauses: 3
% 0.09/0.46 % Negative unit clauses : 1
% 0.09/0.46 % Non-unit-clauses : 108
% 0.09/0.46 % Current number of unprocessed clauses: 1002
% 0.09/0.46 % ...number of literals in the above : 1961
% 0.09/0.46 % Current number of archived formulas : 0
% 0.09/0.46 % Current number of archived clauses : 64
% 0.09/0.46 % Clause-clause subsumption calls (NU) : 2189
% 0.09/0.46 % Rec. Clause-clause subsumption calls : 1947
% 0.09/0.46 % Non-unit clause-clause subsumptions : 252
% 0.09/0.46 % Unit Clause-clause subsumption calls : 188
% 0.09/0.46 % Rewrite failures with RHS unbound : 0
% 0.09/0.46 % BW rewrite match attempts : 81
% 0.09/0.46 % BW rewrite match successes : 58
% 0.09/0.46 % Condensation attempts : 0
% 0.09/0.46 % Condensation successes : 0
% 0.09/0.46 % Termbank termtop insertions : 22101
% 0.09/0.46 % Search garbage collected termcells : 181
% 0.09/0.46
% 0.09/0.46 % -------------------------------------------------
% 0.09/0.46 % User time : 0.019 s
% 0.09/0.46 % System time : 0.004 s
% 0.09/0.46 % Total time : 0.023 s
% 0.09/0.46 % Maximum resident set size: 3656 pages
% 0.09/0.46
% 0.09/0.46 % -------------------------------------------------
% 0.09/0.46 % User time : 0.120 s
% 0.09/0.46 % System time : 0.018 s
% 0.09/0.46 % Total time : 0.138 s
% 0.09/0.46 % Maximum resident set size: 4608 pages
% 0.09/0.46 % E exiting
%------------------------------------------------------------------------------