%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE021+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 : n011.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 0.23s 0.59s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 15 unt; 0 def)
% Number of atoms : 68 ( 31 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 63 ( 26 ~; 21 |; 10 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 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 : 45 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5] :
( test(X5)
=> ( leq(addition(multiplication(X5,X4),multiplication(c(X5),X4)),X4)
& leq(X4,addition(multiplication(X5,X4),multiplication(c(X5),X4))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
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(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_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(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(c_0_8,negated_conjecture,
~ ! [X4,X5] :
( test(X5)
=> ( leq(addition(multiplication(X5,X4),multiplication(c(X5),X4)),X4)
& leq(X4,addition(multiplication(X5,X4),multiplication(c(X5),X4))) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_9,plain,
! [X25,X26] :
( ( ~ test(X25)
| c(X25) = X26
| ~ complement(X25,X26) )
& ( ~ test(X25)
| complement(X25,X26)
| c(X25) != X26 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])])]) ).
fof(c_0_10,negated_conjecture,
( ( ~ leq(addition(multiplication(esk2_0,esk1_0),multiplication(c(esk2_0),esk1_0)),esk1_0)
| ~ leq(esk1_0,addition(multiplication(esk2_0,esk1_0),multiplication(c(esk2_0),esk1_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_8])])])]) ).
fof(c_0_11,plain,
! [X19,X20,X21] : multiplication(addition(X19,X20),X21) = addition(multiplication(X19,X21),multiplication(X20,X21)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_12,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_13,plain,
( ~ test(X1)
| c(X1) != X2
| complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X10,X11] : addition(X10,X11) = addition(X11,X10),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_15,negated_conjecture,
( ~ leq(addition(multiplication(esk2_0,esk1_0),multiplication(c(esk2_0),esk1_0)),esk1_0)
| ~ leq(esk1_0,addition(multiplication(esk2_0,esk1_0),multiplication(c(esk2_0),esk1_0))) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( ~ complement(X2,X1)
| addition(X1,X2) = one ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( ~ test(X1)
| complement(X1,c(X1)) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_20,plain,
! [X38] : multiplication(one,X38) = X38,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_21,negated_conjecture,
( ~ leq(multiplication(addition(esk2_0,c(esk2_0)),esk1_0),esk1_0)
| ~ leq(esk1_0,multiplication(addition(esk2_0,c(esk2_0)),esk1_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]) ).
cnf(c_0_22,plain,
( ~ test(X1)
| addition(X1,c(X1)) = one ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_23,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_25,plain,
! [X8,X9] :
( ( leq(X8,X9)
| addition(X8,X9) != X9 )
& ( addition(X8,X9) = X9
| ~ leq(X8,X9) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])]) ).
fof(c_0_26,plain,
! [X15] : addition(X15,X15) = X15,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_27,negated_conjecture,
~ leq(esk1_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_23]),c_0_24])]) ).
cnf(c_0_28,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE021+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.46 % Computer : n011.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Sun Sep 20 22:39:10 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.54 Running first-order theorem proving
% 0.23/0.54 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
% 0.23/0.59 % Version: 3.5.1
% 0.23/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.59 % Starting sh5l with 300s (1) cores
% 0.23/0.59 % new_bool_1 with pid 341470 completed with status 0
% 0.23/0.59 % Result found by new_bool_1
% 0.23/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.59 % Search class: FGHSM-FFMF21-MFFFFFNN
% 0.23/0.59 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.59 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.59 % SubtermCWHack with pid 341478 completed with status 0
% 0.23/0.59 % Result found by SubtermCWHack
% 0.23/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.59 % Search class: FGHSM-FFMF21-MFFFFFNN
% 0.23/0.59 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.59 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.59 % Preprocessing time : 0.001 s
% 0.23/0.59
% 0.23/0.59 % Proof found!
% 0.23/0.59 % SZS status Theorem
% 0.23/0.59 % SZS output start CNFRefutation
% See solution above
% 0.23/0.60 % Parsed axioms : 17
% 0.23/0.60 % Removed by relevancy pruning/SinE : 0
% 0.23/0.60 % Initial clauses : 24
% 0.23/0.60 % Removed in clause preprocessing : 0
% 0.23/0.60 % Initial clauses in saturation : 24
% 0.23/0.60 % Processed clauses : 100
% 0.23/0.60 % ...of these trivial : 6
% 0.23/0.60 % ...subsumed : 33
% 0.23/0.60 % ...remaining for further processing : 61
% 0.23/0.60 % Other redundant clauses eliminated : 1
% 0.23/0.60 % Clauses deleted for lack of memory : 0
% 0.23/0.60 % Backward-subsumed : 0
% 0.23/0.60 % Backward-rewritten : 0
% 0.23/0.60 % Generated clauses : 435
% 0.23/0.60 % ...of the previous two non-redundant : 254
% 0.23/0.60 % ...aggressively subsumed : 0
% 0.23/0.60 % Contextual simplify-reflections : 1
% 0.23/0.60 % Paramodulations : 434
% 0.23/0.60 % Factorizations : 0
% 0.23/0.60 % NegExts : 0
% 0.23/0.60 % Equation resolutions : 1
% 0.23/0.60 % Disequality decompositions : 0
% 0.23/0.60 % Total rewrite steps : 374
% 0.23/0.60 % ...of those cached : 242
% 0.23/0.60 % Propositional unsat checks : 0
% 0.23/0.60 % Propositional check models : 0
% 0.23/0.60 % Propositional check unsatisfiable : 0
% 0.23/0.60 % Propositional clauses : 0
% 0.23/0.60 % Propositional clauses after purity: 0
% 0.23/0.60 % Propositional unsat core size : 0
% 0.23/0.60 % Propositional preprocessing time : 0.000
% 0.23/0.60 % Propositional encoding time : 0.000
% 0.23/0.60 % Propositional solver time : 0.000
% 0.23/0.60 % Success case prop preproc time : 0.000
% 0.23/0.60 % Success case prop encoding time : 0.000
% 0.23/0.60 % Success case prop solver time : 0.000
% 0.23/0.60 % Current number of processed clauses : 60
% 0.23/0.60 % Positive orientable unit clauses : 18
% 0.23/0.60 % Positive unorientable unit clauses: 3
% 0.23/0.60 % Negative unit clauses : 1
% 0.23/0.60 % Non-unit-clauses : 38
% 0.23/0.60 % Current number of unprocessed clauses: 178
% 0.23/0.60 % ...number of literals in the above : 258
% 0.23/0.60 % Current number of archived formulas : 0
% 0.23/0.60 % Current number of archived clauses : 0
% 0.23/0.60 % Clause-clause subsumption calls (NU) : 257
% 0.23/0.60 % Rec. Clause-clause subsumption calls : 230
% 0.23/0.60 % Non-unit clause-clause subsumptions : 20
% 0.23/0.60 % Unit Clause-clause subsumption calls : 9
% 0.23/0.60 % Rewrite failures with RHS unbound : 0
% 0.23/0.60 % BW rewrite match attempts : 31
% 0.23/0.60 % BW rewrite match successes : 26
% 0.23/0.60 % Condensation attempts : 0
% 0.23/0.60 % Condensation successes : 0
% 0.23/0.60 % Termbank termtop insertions : 4397
% 0.23/0.60 % Search garbage collected termcells : 177
% 0.23/0.60
% 0.23/0.60 % -------------------------------------------------
% 0.23/0.60 % User time : 0.008 s
% 0.23/0.60 % System time : 0.006 s
% 0.23/0.60 % Total time : 0.014 s
% 0.23/0.60 % Maximum resident set size: 3648 pages
% 0.23/0.60
% 0.23/0.60 % -------------------------------------------------
% 0.23/0.60 % User time : 0.009 s
% 0.23/0.60 % System time : 0.014 s
% 0.23/0.60 % Total time : 0.023 s
% 0.23/0.60 % Maximum resident set size: 4864 pages
% 0.23/0.60 % E exiting
%------------------------------------------------------------------------------