%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE009+2 : 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 : n001.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 12:58:34 PM UTC 2026
% Result : Theorem 0.18s 0.65s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 22 unt; 0 def)
% Number of atoms : 63 ( 37 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 53 ( 23 ~; 15 |; 10 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5] :
( ( test(X4)
& test(X5) )
=> one = addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(test_3,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(c_0_7,negated_conjecture,
~ ! [X4,X5] :
( ( test(X4)
& test(X5) )
=> 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_8,negated_conjecture,
( 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_7])])])]) ).
fof(c_0_9,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_10,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_11,negated_conjecture,
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_8]) ).
cnf(c_0_12,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,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_14,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_15,plain,
( ~ test(X1)
| c(X1) != X2
| complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
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,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_12]) ).
cnf(c_0_17,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
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(X1,c(X1)) ),
inference(er,[status(thm)],[c_0_15]) ).
fof(c_0_20,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_21,plain,
! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_22,negated_conjecture,
addition(multiplication(c(esk2_0),c(esk3_0)),addition(multiplication(c(esk2_0),esk3_0),multiplication(esk2_0,addition(esk3_0,c(esk3_0))))) != one,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
( ~ test(X1)
| addition(X1,c(X1)) = one ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_12]) ).
cnf(c_0_24,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_26,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,negated_conjecture,
addition(multiplication(c(esk2_0),c(esk3_0)),addition(esk2_0,multiplication(c(esk2_0),esk3_0))) != one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_12]),c_0_25])]) ).
cnf(c_0_28,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_12,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
addition(esk2_0,multiplication(c(esk2_0),addition(esk3_0,c(esk3_0)))) != one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_17]) ).
cnf(c_0_30,negated_conjecture,
addition(esk2_0,c(esk2_0)) != one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_31,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_23]),c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE009+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.56 % Computer : n001.cluster.edu
% 0.15/0.56 % Model : x86_64 x86_64
% 0.15/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.56 % Memory : 8046.5625MB
% 0.15/0.56 % OS : Linux 6.8.0-71-generic
% 0.15/0.56 % CPULimit : 300
% 0.15/0.56 % WCLimit : 300
% 0.15/0.56 % DateTime : Sun Sep 20 22:43:28 UTC 2026
% 0.15/0.57 % CPUTime :
% 0.15/0.57 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.61 Running first-order theorem proving
% 0.18/0.61 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
% 0.18/0.65 % Version: 3.5.1
% 0.18/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.18/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.18/0.65 % Starting new_bool_3 with 300s (1) cores
% 0.18/0.65 % Starting new_bool_1 with 300s (1) cores
% 0.18/0.65 % Starting sh5l with 300s (1) cores
% 0.18/0.65 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1565157 completed with status 0
% 0.18/0.65 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.18/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.18/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.18/0.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/0.65 % No SInE strategy applied
% 0.18/0.65 % Search class: FGUSM-FFMF21-MFFFFFNN
% 0.18/0.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.65 % Starting SubtermCWHack with 136s (1) cores
% 0.18/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.18/0.65 % Starting G-E--_200_B02_F1_AE_CS_SP_PI_S0S with 136s (1) cores
% 0.18/0.65 % Starting new_bool_3 with 136s (1) cores
% 0.18/0.65 % Starting new_bool_1 with 136s (1) cores
% 0.18/0.65 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1565166 completed with status 0
% 0.18/0.65 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.18/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.18/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.18/0.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/0.65 % No SInE strategy applied
% 0.18/0.65 % Search class: FGUSM-FFMF21-MFFFFFNN
% 0.18/0.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.65 % Starting SubtermCWHack with 136s (1) cores
% 0.18/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.18/0.65 % Preprocessing time : 0.002 s
% 0.18/0.65 % Presaturation interreduction done
% 0.18/0.65
% 0.18/0.65 % Proof found!
% 0.18/0.65 % SZS status Theorem
% 0.18/0.65 % SZS output start CNFRefutation
% See solution above
% 0.18/0.65 % Parsed axioms : 19
% 0.18/0.65 % Removed by relevancy pruning/SinE : 0
% 0.18/0.65 % Initial clauses : 27
% 0.18/0.65 % Removed in clause preprocessing : 0
% 0.18/0.65 % Initial clauses in saturation : 27
% 0.18/0.65 % Processed clauses : 90
% 0.18/0.65 % ...of these trivial : 1
% 0.18/0.65 % ...subsumed : 7
% 0.18/0.65 % ...remaining for further processing : 82
% 0.18/0.65 % Other redundant clauses eliminated : 1
% 0.18/0.65 % Clauses deleted for lack of memory : 0
% 0.18/0.65 % Backward-subsumed : 0
% 0.18/0.65 % Backward-rewritten : 6
% 0.18/0.65 % Generated clauses : 211
% 0.18/0.65 % ...of the previous two non-redundant : 140
% 0.18/0.65 % ...aggressively subsumed : 0
% 0.18/0.65 % Contextual simplify-reflections : 3
% 0.18/0.65 % Paramodulations : 209
% 0.18/0.65 % Factorizations : 1
% 0.18/0.65 % NegExts : 0
% 0.18/0.65 % Equation resolutions : 1
% 0.18/0.65 % Disequality decompositions : 0
% 0.18/0.65 % Total rewrite steps : 185
% 0.18/0.65 % ...of those cached : 91
% 0.18/0.65 % Propositional unsat checks : 0
% 0.18/0.65 % Propositional check models : 0
% 0.18/0.65 % Propositional check unsatisfiable : 0
% 0.18/0.65 % Propositional clauses : 0
% 0.18/0.65 % Propositional clauses after purity: 0
% 0.18/0.65 % Propositional unsat core size : 0
% 0.18/0.65 % Propositional preprocessing time : 0.000
% 0.18/0.65 % Propositional encoding time : 0.000
% 0.18/0.65 % Propositional solver time : 0.000
% 0.18/0.65 % Success case prop preproc time : 0.000
% 0.18/0.65 % Success case prop encoding time : 0.000
% 0.18/0.65 % Success case prop solver time : 0.000
% 0.18/0.65 % Current number of processed clauses : 48
% 0.18/0.65 % Positive orientable unit clauses : 14
% 0.18/0.65 % Positive unorientable unit clauses: 2
% 0.18/0.65 % Negative unit clauses : 2
% 0.18/0.65 % Non-unit-clauses : 30
% 0.18/0.65 % Current number of unprocessed clauses: 104
% 0.18/0.65 % ...number of literals in the above : 205
% 0.18/0.65 % Current number of archived formulas : 0
% 0.18/0.65 % Current number of archived clauses : 33
% 0.18/0.65 % Clause-clause subsumption calls (NU) : 149
% 0.18/0.65 % Rec. Clause-clause subsumption calls : 136
% 0.18/0.65 % Non-unit clause-clause subsumptions : 8
% 0.18/0.65 % Unit Clause-clause subsumption calls : 14
% 0.18/0.65 % Rewrite failures with RHS unbound : 0
% 0.18/0.65 % BW rewrite match attempts : 38
% 0.18/0.65 % BW rewrite match successes : 34
% 0.18/0.65 % Condensation attempts : 0
% 0.18/0.65 % Condensation successes : 0
% 0.18/0.65 % Termbank termtop insertions : 3376
% 0.18/0.65 % Search garbage collected termcells : 205
% 0.18/0.65
% 0.18/0.65 % -------------------------------------------------
% 0.18/0.65 % User time : 0.013 s
% 0.18/0.65 % System time : 0.001 s
% 0.18/0.65 % Total time : 0.015 s
% 0.18/0.65 % Maximum resident set size: 3652 pages
% 0.18/0.65
% 0.18/0.65 % -------------------------------------------------
% 0.18/0.65 % User time : 0.045 s
% 0.18/0.65 % System time : 0.015 s
% 0.18/0.65 % Total time : 0.060 s
% 0.18/0.65 % Maximum resident set size: 4864 pages
% 0.18/0.65 % E exiting
%------------------------------------------------------------------------------