%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : KLE009+4 : 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 : n002.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 12:59:04 PM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 20 unt; 0 def)
% Number of atoms : 82 ( 35 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 75 ( 32 ~; 24 |; 13 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5] :
( ( test(X4)
& test(X5) )
=> ( leq(addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))),one)
& leq(one,addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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(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(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(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(c_0_9,negated_conjecture,
~ ! [X4,X5] :
( ( test(X4)
& test(X5) )
=> ( leq(addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))),one)
& leq(one,addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5)))) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_10,negated_conjecture,
( ( ~ leq(addition(addition(addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))),one)
| ~ leq(one,addition(addition(addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0)))) )
& test(esk2_0)
& test(esk3_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_11,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
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,
! [X34,X35] :
( ( ~ test(X34)
| c(X34) = X35
| ~ complement(X34,X35) )
& ( ~ test(X34)
| complement(X34,X35)
| c(X34) != X35 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])])]) ).
cnf(c_0_14,negated_conjecture,
( ~ leq(addition(addition(addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))),one)
| ~ leq(one,addition(addition(addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X18,X19,X20] : multiplication(X18,addition(X19,X20)) = addition(multiplication(X18,X19),multiplication(X18,X20)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_18,plain,
! [X32,X33] :
( ( complement(X33,X32)
| addition(X32,X33) != one
| multiplication(X33,X32) != zero
| multiplication(X32,X33) != zero )
& ( ~ complement(X33,X32)
| addition(X32,X33) = one )
& ( ~ complement(X33,X32)
| multiplication(X33,X32) = zero )
& ( ~ complement(X33,X32)
| multiplication(X32,X33) = 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_19,plain,
( ~ test(X1)
| c(X1) != X2
| complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
( ~ leq(addition(multiplication(c(esk2_0),c(esk3_0)),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))))),one)
| ~ leq(one,addition(multiplication(c(esk2_0),c(esk3_0)),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0)))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_15]),c_0_15]),c_0_15]) ).
cnf(c_0_21,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( ~ complement(X2,X1)
| addition(X1,X2) = one ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( ~ test(X1)
| complement(X1,c(X1)) ),
inference(er,[status(thm)],[c_0_19]) ).
fof(c_0_25,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_26,negated_conjecture,
( ~ leq(addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,addition(esk3_0,c(esk3_0))),multiplication(c(esk2_0),c(esk3_0)))),one)
| ~ leq(one,addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,addition(esk3_0,c(esk3_0))),multiplication(c(esk2_0),c(esk3_0))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_21]),c_0_22]) ).
cnf(c_0_27,plain,
( ~ test(X1)
| addition(X1,c(X1)) = one ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_15]) ).
cnf(c_0_28,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_30,negated_conjecture,
( ~ leq(addition(esk2_0,multiplication(c(esk2_0),addition(esk3_0,c(esk3_0)))),one)
| ~ leq(one,addition(esk2_0,multiplication(c(esk2_0),addition(esk3_0,c(esk3_0))))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_26,c_0_27]),c_0_28]),c_0_21]),c_0_22]),c_0_15]),c_0_28]),c_0_21]),c_0_22]),c_0_15]),c_0_29])]) ).
cnf(c_0_31,negated_conjecture,
( ~ leq(addition(esk2_0,c(esk2_0)),one)
| ~ leq(one,addition(esk2_0,c(esk2_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_27]),c_0_28]),c_0_28]),c_0_29])]) ).
cnf(c_0_32,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_33,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])])]) ).
fof(c_0_34,plain,
! [X12] : addition(X12,X12) = X12,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_35,negated_conjecture,
~ leq(one,one),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_27]),c_0_32])]) ).
cnf(c_0_36,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE009+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 22:40:32 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.45 % Version: 3.5.1
% 0.11/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.45 % Starting sh5l with 300s (1) cores
% 0.11/0.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1856821 completed with status 0
% 0.11/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.11/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.45 % No SInE strategy applied
% 0.11/0.45 % Search class: FGHSM-FFMF21-MFFFFFNN
% 0.11/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.11/0.45 % Starting U----_210g_02_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.11/0.45 % Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S00EN with 136s (1) cores
% 0.11/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.11/0.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1856829 completed with status 0
% 0.11/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.11/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.45 % No SInE strategy applied
% 0.11/0.45 % Search class: FGHSM-FFMF21-MFFFFFNN
% 0.11/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.11/0.45 % Preprocessing time : 0.001 s
% 0.11/0.45 % Presaturation interreduction done
% 0.11/0.45
% 0.11/0.45 % Proof found!
% 0.11/0.45 % SZS status Theorem
% 0.11/0.45 % SZS output start CNFRefutation
% See solution above
% 0.11/0.45 % Parsed axioms : 19
% 0.11/0.45 % Removed by relevancy pruning/SinE : 0
% 0.11/0.45 % Initial clauses : 27
% 0.11/0.45 % Removed in clause preprocessing : 0
% 0.11/0.45 % Initial clauses in saturation : 27
% 0.11/0.45 % Processed clauses : 103
% 0.11/0.45 % ...of these trivial : 1
% 0.11/0.45 % ...subsumed : 9
% 0.11/0.45 % ...remaining for further processing : 93
% 0.11/0.45 % Other redundant clauses eliminated : 1
% 0.11/0.45 % Clauses deleted for lack of memory : 0
% 0.11/0.45 % Backward-subsumed : 2
% 0.11/0.45 % Backward-rewritten : 8
% 0.11/0.45 % Generated clauses : 220
% 0.11/0.45 % ...of the previous two non-redundant : 157
% 0.11/0.45 % ...aggressively subsumed : 0
% 0.11/0.45 % Contextual simplify-reflections : 3
% 0.11/0.45 % Paramodulations : 218
% 0.11/0.45 % Factorizations : 1
% 0.11/0.45 % NegExts : 0
% 0.11/0.45 % Equation resolutions : 1
% 0.11/0.45 % Disequality decompositions : 0
% 0.11/0.45 % Total rewrite steps : 267
% 0.11/0.45 % ...of those cached : 159
% 0.11/0.45 % Propositional unsat checks : 0
% 0.11/0.45 % Propositional check models : 0
% 0.11/0.45 % Propositional check unsatisfiable : 0
% 0.11/0.45 % Propositional clauses : 0
% 0.11/0.45 % Propositional clauses after purity: 0
% 0.11/0.45 % Propositional unsat core size : 0
% 0.11/0.45 % Propositional preprocessing time : 0.000
% 0.11/0.45 % Propositional encoding time : 0.000
% 0.11/0.45 % Propositional solver time : 0.000
% 0.11/0.45 % Success case prop preproc time : 0.000
% 0.11/0.45 % Success case prop encoding time : 0.000
% 0.11/0.45 % Success case prop solver time : 0.000
% 0.11/0.45 % Current number of processed clauses : 55
% 0.11/0.45 % Positive orientable unit clauses : 14
% 0.11/0.45 % Positive unorientable unit clauses: 2
% 0.11/0.45 % Negative unit clauses : 2
% 0.11/0.45 % Non-unit-clauses : 37
% 0.11/0.45 % Current number of unprocessed clauses: 107
% 0.11/0.45 % ...number of literals in the above : 199
% 0.11/0.45 % Current number of archived formulas : 0
% 0.11/0.45 % Current number of archived clauses : 37
% 0.11/0.45 % Clause-clause subsumption calls (NU) : 271
% 0.11/0.45 % Rec. Clause-clause subsumption calls : 256
% 0.11/0.45 % Non-unit clause-clause subsumptions : 10
% 0.11/0.45 % Unit Clause-clause subsumption calls : 22
% 0.11/0.45 % Rewrite failures with RHS unbound : 0
% 0.11/0.45 % BW rewrite match attempts : 36
% 0.11/0.45 % BW rewrite match successes : 34
% 0.11/0.45 % Condensation attempts : 0
% 0.11/0.45 % Condensation successes : 0
% 0.11/0.45 % Termbank termtop insertions : 4081
% 0.11/0.45 % Search garbage collected termcells : 215
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.008 s
% 0.11/0.45 % System time : 0.003 s
% 0.11/0.45 % Total time : 0.011 s
% 0.11/0.45 % Maximum resident set size: 3652 pages
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.030 s
% 0.11/0.45 % System time : 0.016 s
% 0.11/0.45 % Total time : 0.046 s
% 0.11/0.45 % Maximum resident set size: 4608 pages
% 0.11/0.45 % E exiting
%------------------------------------------------------------------------------