%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE018+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 12:58:37 PM UTC 2026
% Result : Theorem 0.10s 0.46s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 53 ( 37 unt; 0 def)
% Number of atoms : 96 ( 53 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 67 ( 24 ~; 20 |; 15 &)
% ( 3 <=>; 5 =>; 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5,X6] :
( ( test(X6)
& test(X5)
& test(X4) )
=> ( leq(multiplication(X4,c(X5)),X6)
=> leq(X4,addition(X5,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(test_3,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(test_2,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( addition(X4,X5) = one
& multiplication(X5,X4) = zero
& multiplication(X4,X5) = zero ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(c_0_11,negated_conjecture,
~ ! [X4,X5,X6] :
( ( test(X6)
& test(X5)
& test(X4) )
=> ( leq(multiplication(X4,c(X5)),X6)
=> leq(X4,addition(X5,X6)) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_12,plain,
! [X27,X28] :
( ( leq(X27,X28)
| addition(X27,X28) != X28 )
& ( addition(X27,X28) = X28
| ~ leq(X27,X28) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])]) ).
fof(c_0_13,negated_conjecture,
( ~ leq(esk2_0,addition(esk3_0,esk4_0))
& leq(multiplication(esk2_0,c(esk3_0)),esk4_0)
& test(esk4_0)
& test(esk3_0)
& test(esk2_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
cnf(c_0_14,plain,
( ~ leq(X1,X2)
| addition(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,negated_conjecture,
leq(multiplication(esk2_0,c(esk3_0)),esk4_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_16,plain,
! [X7,X8] : addition(X7,X8) = addition(X8,X7),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_17,plain,
! [X9,X10,X11] : addition(X11,addition(X10,X9)) = addition(addition(X11,X10),X9),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_18,negated_conjecture,
addition(multiplication(esk2_0,c(esk3_0)),esk4_0) = esk4_0,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_20,plain,
! [X35,X36] :
( ( ~ test(X35)
| c(X35) = X36
| ~ complement(X35,X36) )
& ( ~ test(X35)
| complement(X35,X36)
| c(X35) != X36 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])])]) ).
cnf(c_0_21,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
addition(esk4_0,multiplication(esk2_0,c(esk3_0))) = esk4_0,
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_23,plain,
! [X33,X34] :
( ( complement(X34,X33)
| addition(X33,X34) != one
| multiplication(X34,X33) != zero
| multiplication(X33,X34) != zero )
& ( ~ complement(X34,X33)
| addition(X33,X34) = one )
& ( ~ complement(X34,X33)
| multiplication(X34,X33) = zero )
& ( ~ complement(X34,X33)
| multiplication(X33,X34) = zero ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])])]) ).
cnf(c_0_24,plain,
( ~ test(X1)
| c(X1) != X2
| complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
addition(esk4_0,addition(multiplication(esk2_0,c(esk3_0)),X1)) = addition(esk4_0,X1),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_26,plain,
! [X19,X20,X21] : multiplication(X19,addition(X20,X21)) = addition(multiplication(X19,X20),multiplication(X19,X21)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_27,plain,
( ~ complement(X2,X1)
| addition(X1,X2) = one ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
( ~ test(X1)
| complement(X1,c(X1)) ),
inference(er,[status(thm)],[c_0_24]) ).
cnf(c_0_29,negated_conjecture,
addition(esk4_0,addition(X1,multiplication(esk2_0,c(esk3_0)))) = addition(esk4_0,X1),
inference(spm,[status(thm)],[c_0_25,c_0_19]) ).
cnf(c_0_30,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
( ~ test(X1)
| addition(c(X1),X1) = one ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_32,plain,
! [X17] : multiplication(X17,one) = X17,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_33,negated_conjecture,
addition(esk4_0,multiplication(esk2_0,addition(X1,c(esk3_0)))) = addition(esk4_0,multiplication(esk2_0,X1)),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
( ~ test(X1)
| addition(X1,c(X1)) = one ),
inference(rw,[status(thm)],[c_0_31,c_0_19]) ).
cnf(c_0_35,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_37,negated_conjecture,
addition(esk4_0,multiplication(esk2_0,esk3_0)) = addition(esk2_0,esk4_0),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_36])]),c_0_19]) ).
fof(c_0_38,plain,
! [X22,X23,X24] : multiplication(addition(X22,X23),X24) = addition(multiplication(X22,X24),multiplication(X23,X24)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_39,plain,
! [X13] : addition(X13,X13) = X13,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_40,negated_conjecture,
addition(esk4_0,addition(multiplication(esk2_0,esk3_0),X1)) = addition(esk2_0,addition(esk4_0,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_37]),c_0_21]) ).
cnf(c_0_41,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_42,plain,
! [X18] : multiplication(one,X18) = X18,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_43,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_44,negated_conjecture,
addition(esk4_0,multiplication(addition(esk2_0,X1),esk3_0)) = addition(esk2_0,addition(esk4_0,multiplication(X1,esk3_0))),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_46,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_47,negated_conjecture,
~ leq(esk2_0,addition(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_48,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_49,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_43]) ).
cnf(c_0_50,negated_conjecture,
addition(esk2_0,addition(esk4_0,multiplication(c(esk2_0),esk3_0))) = addition(esk3_0,esk4_0),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_34]),c_0_45]),c_0_46])]),c_0_19]) ).
cnf(c_0_51,negated_conjecture,
addition(esk2_0,addition(esk3_0,esk4_0)) != addition(esk3_0,esk4_0),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE018+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 22:39:12 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.10/0.46 % Version: 3.5.1
% 0.10/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.46 % Starting sh5l with 300s (1) cores
% 0.10/0.46 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 202288 completed with status 0
% 0.10/0.46 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.10/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.46 % No SInE strategy applied
% 0.10/0.46 % Search class: FGUSM-FFSS21-SFFFFFNN
% 0.10/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.46 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 136s (1) cores
% 0.10/0.46 % Starting new_bool_3 with 136s (1) cores
% 0.10/0.46 % Starting new_bool_1 with 136s (1) cores
% 0.10/0.46 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 202294 completed with status 0
% 0.10/0.46 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.10/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.46 % No SInE strategy applied
% 0.10/0.46 % Search class: FGUSM-FFSS21-SFFFFFNN
% 0.10/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.46 % Preprocessing time : 0.002 s
% 0.10/0.46 % Presaturation interreduction done
% 0.10/0.46
% 0.10/0.46 % Proof found!
% 0.10/0.46 % SZS status Theorem
% 0.10/0.46 % SZS output start CNFRefutation
% See solution above
% 0.10/0.46 % Parsed axioms : 17
% 0.10/0.46 % Removed by relevancy pruning/SinE : 0
% 0.10/0.46 % Initial clauses : 27
% 0.10/0.46 % Removed in clause preprocessing : 0
% 0.10/0.46 % Initial clauses in saturation : 27
% 0.10/0.46 % Processed clauses : 247
% 0.10/0.46 % ...of these trivial : 38
% 0.10/0.46 % ...subsumed : 56
% 0.10/0.46 % ...remaining for further processing : 153
% 0.10/0.46 % Other redundant clauses eliminated : 6
% 0.10/0.46 % Clauses deleted for lack of memory : 0
% 0.10/0.46 % Backward-subsumed : 3
% 0.10/0.46 % Backward-rewritten : 25
% 0.10/0.46 % Generated clauses : 1118
% 0.10/0.46 % ...of the previous two non-redundant : 721
% 0.10/0.46 % ...aggressively subsumed : 0
% 0.10/0.46 % Contextual simplify-reflections : 3
% 0.10/0.46 % Paramodulations : 1112
% 0.10/0.46 % Factorizations : 0
% 0.10/0.46 % NegExts : 0
% 0.10/0.46 % Equation resolutions : 6
% 0.10/0.46 % Disequality decompositions : 0
% 0.10/0.46 % Total rewrite steps : 1391
% 0.10/0.46 % ...of those cached : 991
% 0.10/0.46 % Propositional unsat checks : 0
% 0.10/0.46 % Propositional check models : 0
% 0.10/0.46 % Propositional check unsatisfiable : 0
% 0.10/0.46 % Propositional clauses : 0
% 0.10/0.46 % Propositional clauses after purity: 0
% 0.10/0.46 % Propositional unsat core size : 0
% 0.10/0.46 % Propositional preprocessing time : 0.000
% 0.10/0.46 % Propositional encoding time : 0.000
% 0.10/0.46 % Propositional solver time : 0.000
% 0.10/0.46 % Success case prop preproc time : 0.000
% 0.10/0.46 % Success case prop encoding time : 0.000
% 0.10/0.46 % Success case prop solver time : 0.000
% 0.10/0.46 % Current number of processed clauses : 97
% 0.10/0.46 % Positive orientable unit clauses : 49
% 0.10/0.46 % Positive unorientable unit clauses: 3
% 0.10/0.46 % Negative unit clauses : 2
% 0.10/0.46 % Non-unit-clauses : 43
% 0.10/0.46 % Current number of unprocessed clauses: 518
% 0.10/0.46 % ...number of literals in the above : 790
% 0.10/0.46 % Current number of archived formulas : 0
% 0.10/0.46 % Current number of archived clauses : 55
% 0.10/0.46 % Clause-clause subsumption calls (NU) : 361
% 0.10/0.46 % Rec. Clause-clause subsumption calls : 297
% 0.10/0.46 % Non-unit clause-clause subsumptions : 39
% 0.10/0.46 % Unit Clause-clause subsumption calls : 36
% 0.10/0.46 % Rewrite failures with RHS unbound : 0
% 0.10/0.46 % BW rewrite match attempts : 164
% 0.10/0.46 % BW rewrite match successes : 107
% 0.10/0.46 % Condensation attempts : 0
% 0.10/0.46 % Condensation successes : 0
% 0.10/0.46 % Termbank termtop insertions : 14252
% 0.10/0.46 % Search garbage collected termcells : 200
% 0.10/0.46
% 0.10/0.46 % -------------------------------------------------
% 0.10/0.46 % User time : 0.023 s
% 0.10/0.46 % System time : 0.006 s
% 0.10/0.46 % Total time : 0.029 s
% 0.10/0.46 % Maximum resident set size: 3648 pages
% 0.10/0.46
% 0.10/0.46 % -------------------------------------------------
% 0.10/0.46 % User time : 0.101 s
% 0.10/0.46 % System time : 0.017 s
% 0.10/0.46 % Total time : 0.118 s
% 0.10/0.46 % Maximum resident set size: 4608 pages
% 0.10/0.46 % E exiting
%------------------------------------------------------------------------------