%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE024+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 : n026.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 12:58:38 PM UTC 2026
% Result : Theorem 0.11s 0.46s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 25 unt; 0 def)
% Number of atoms : 95 ( 53 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 78 ( 31 ~; 27 |; 12 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 71 ( 4 sgn 36 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
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(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(goals,conjecture,
! [X4,X5,X6] :
( ( test(X6)
& test(X5) )
=> ( addition(multiplication(X4,c(X6)),multiplication(c(X5),X4)) = multiplication(c(X5),X4)
=> multiplication(multiplication(X5,X4),c(X6)) = zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(c_0_9,plain,
! [X35,X36] :
( ( complement(X36,X35)
| addition(X35,X36) != one
| multiplication(X36,X35) != zero
| multiplication(X35,X36) != zero )
& ( ~ complement(X36,X35)
| addition(X35,X36) = one )
& ( ~ complement(X36,X35)
| multiplication(X36,X35) = zero )
& ( ~ complement(X36,X35)
| multiplication(X35,X36) = 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_10,plain,
! [X31,X33,X34] :
( ( test(X33)
| ~ complement(X34,X33) )
& ( complement(esk4_1(X31),X31)
| ~ test(X31) ) ),
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])])])])])]) ).
fof(c_0_11,plain,
! [X22,X23] :
( ( ~ test(X22)
| c(X22) = X23
| ~ complement(X22,X23) )
& ( ~ test(X22)
| complement(X22,X23)
| c(X22) != X23 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])])]) ).
fof(c_0_12,plain,
! [X16,X17,X18] : multiplication(X16,addition(X17,X18)) = addition(multiplication(X16,X17),multiplication(X16,X18)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_13,plain,
( ~ complement(X2,X1)
| multiplication(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( ~ test(X1)
| complement(esk4_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X10] : addition(X10,zero) = X10,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_16,plain,
( ~ test(X1)
| c(X1) != X2
| complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( ~ test(X1)
| multiplication(X1,esk4_1(X1)) = zero ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( ~ complement(X2,X1)
| addition(X1,X2) = one ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_21,plain,
! [X37] : multiplication(X37,one) = X37,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_22,negated_conjecture,
~ ! [X4,X5,X6] :
( ( test(X6)
& test(X5) )
=> ( addition(multiplication(X4,c(X6)),multiplication(c(X5),X4)) = multiplication(c(X5),X4)
=> multiplication(multiplication(X5,X4),c(X6)) = zero ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_23,plain,
( ~ complement(X1,X2)
| multiplication(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_24,plain,
( ~ test(X1)
| complement(X1,c(X1)) ),
inference(er,[status(thm)],[c_0_16]) ).
fof(c_0_25,plain,
! [X13,X14,X15] : multiplication(X13,multiplication(X14,X15)) = multiplication(multiplication(X13,X14),X15),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_26,plain,
( ~ test(X1)
| multiplication(X1,addition(X2,esk4_1(X1))) = multiplication(X1,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_27,plain,
( ~ test(X1)
| addition(X1,esk4_1(X1)) = one ),
inference(spm,[status(thm)],[c_0_20,c_0_14]) ).
cnf(c_0_28,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_29,negated_conjecture,
( multiplication(multiplication(esk2_0,esk1_0),c(esk3_0)) != zero
& addition(multiplication(esk1_0,c(esk3_0)),multiplication(c(esk2_0),esk1_0)) = multiplication(c(esk2_0),esk1_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_22])])])]) ).
cnf(c_0_30,plain,
( ~ test(X1)
| multiplication(X1,c(X1)) = zero ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
( ~ test(X1)
| multiplication(X1,X1) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_33,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_34,plain,
! [X12] : multiplication(zero,X12) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_35,plain,
( ~ test(multiplication(X1,X2))
| multiplication(X1,multiplication(X2,c(multiplication(X1,X2)))) = zero ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
multiplication(esk2_0,esk2_0) = esk2_0,
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,negated_conjecture,
multiplication(esk2_0,multiplication(esk2_0,c(esk2_0))) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_33])]) ).
cnf(c_0_39,negated_conjecture,
multiplication(esk2_0,multiplication(esk2_0,X1)) = multiplication(esk2_0,X1),
inference(spm,[status(thm)],[c_0_31,c_0_36]) ).
cnf(c_0_40,plain,
( ~ test(X1)
| multiplication(X1,multiplication(c(X1),X2)) = zero ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_30]),c_0_37]) ).
cnf(c_0_41,negated_conjecture,
multiplication(esk2_0,c(esk2_0)) = zero,
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
multiplication(multiplication(esk2_0,esk1_0),c(esk3_0)) != zero,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_43,plain,
( ~ test(X1)
| multiplication(X1,addition(X2,multiplication(c(X1),X3))) = multiplication(X1,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_40]),c_0_19]) ).
cnf(c_0_44,negated_conjecture,
addition(multiplication(esk1_0,c(esk3_0)),multiplication(c(esk2_0),esk1_0)) = multiplication(c(esk2_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_45,negated_conjecture,
multiplication(esk2_0,multiplication(c(esk2_0),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_41]),c_0_37]) ).
cnf(c_0_46,negated_conjecture,
multiplication(esk2_0,multiplication(esk1_0,c(esk3_0))) != zero,
inference(rw,[status(thm)],[c_0_42,c_0_31]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_33])]),c_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE024+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n026.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 22:41:21 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.46 % Version: 3.5.1
% 0.11/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.46 % Starting sh5l with 300s (1) cores
% 0.11/0.46 % new_bool_1 with pid 748409 completed with status 0
% 0.11/0.46 % Result found by new_bool_1
% 0.11/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.46 % Search class: FGUSM-FFSS21-MFFFFFNN
% 0.11/0.46 % partial match(1): FGUSM-FFSS21-SFFFFFNN
% 0.11/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.46 % SubtermCWHack with pid 748415 completed with status 0
% 0.11/0.46 % Result found by SubtermCWHack
% 0.11/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.46 % Search class: FGUSM-FFSS21-MFFFFFNN
% 0.11/0.46 % partial match(1): FGUSM-FFSS21-SFFFFFNN
% 0.11/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.46 % Preprocessing time : 0.001 s
% 0.11/0.46
% 0.11/0.46 % Proof found!
% 0.11/0.46 % SZS status Theorem
% 0.11/0.46 % SZS output start CNFRefutation
% See solution above
% 0.11/0.46 % Parsed axioms : 17
% 0.11/0.46 % Removed by relevancy pruning/SinE : 1
% 0.11/0.46 % Initial clauses : 24
% 0.11/0.46 % Removed in clause preprocessing : 0
% 0.11/0.46 % Initial clauses in saturation : 24
% 0.11/0.46 % Processed clauses : 737
% 0.11/0.46 % ...of these trivial : 65
% 0.11/0.46 % ...subsumed : 456
% 0.11/0.46 % ...remaining for further processing : 216
% 0.11/0.46 % Other redundant clauses eliminated : 14
% 0.11/0.46 % Clauses deleted for lack of memory : 0
% 0.11/0.46 % Backward-subsumed : 8
% 0.11/0.46 % Backward-rewritten : 28
% 0.11/0.46 % Generated clauses : 6531
% 0.11/0.46 % ...of the previous two non-redundant : 3891
% 0.11/0.46 % ...aggressively subsumed : 0
% 0.11/0.46 % Contextual simplify-reflections : 1
% 0.11/0.46 % Paramodulations : 6517
% 0.11/0.46 % Factorizations : 0
% 0.11/0.46 % NegExts : 0
% 0.11/0.46 % Equation resolutions : 14
% 0.11/0.46 % Disequality decompositions : 0
% 0.11/0.46 % Total rewrite steps : 8418
% 0.11/0.46 % ...of those cached : 7136
% 0.11/0.46 % Propositional unsat checks : 0
% 0.11/0.46 % Propositional check models : 0
% 0.11/0.46 % Propositional check unsatisfiable : 0
% 0.11/0.46 % Propositional clauses : 0
% 0.11/0.46 % Propositional clauses after purity: 0
% 0.11/0.46 % Propositional unsat core size : 0
% 0.11/0.46 % Propositional preprocessing time : 0.000
% 0.11/0.46 % Propositional encoding time : 0.000
% 0.11/0.46 % Propositional solver time : 0.000
% 0.11/0.46 % Success case prop preproc time : 0.000
% 0.11/0.46 % Success case prop encoding time : 0.000
% 0.11/0.46 % Success case prop solver time : 0.000
% 0.11/0.46 % Current number of processed clauses : 179
% 0.11/0.46 % Positive orientable unit clauses : 91
% 0.11/0.46 % Positive unorientable unit clauses: 3
% 0.11/0.46 % Negative unit clauses : 2
% 0.11/0.46 % Non-unit-clauses : 83
% 0.11/0.46 % Current number of unprocessed clauses: 3084
% 0.11/0.46 % ...number of literals in the above : 6119
% 0.11/0.46 % Current number of archived formulas : 0
% 0.11/0.46 % Current number of archived clauses : 36
% 0.11/0.46 % Clause-clause subsumption calls (NU) : 1998
% 0.11/0.46 % Rec. Clause-clause subsumption calls : 1822
% 0.11/0.46 % Non-unit clause-clause subsumptions : 359
% 0.11/0.46 % Unit Clause-clause subsumption calls : 189
% 0.11/0.46 % Rewrite failures with RHS unbound : 0
% 0.11/0.46 % BW rewrite match attempts : 142
% 0.11/0.46 % BW rewrite match successes : 112
% 0.11/0.46 % Condensation attempts : 0
% 0.11/0.46 % Condensation successes : 0
% 0.11/0.46 % Termbank termtop insertions : 69326
% 0.11/0.46 % Search garbage collected termcells : 177
% 0.11/0.46
% 0.11/0.46 % -------------------------------------------------
% 0.11/0.46 % User time : 0.035 s
% 0.11/0.46 % System time : 0.003 s
% 0.11/0.46 % Total time : 0.038 s
% 0.11/0.46 % Maximum resident set size: 3648 pages
% 0.11/0.46
% 0.11/0.46 % -------------------------------------------------
% 0.11/0.46 % User time : 0.036 s
% 0.11/0.46 % System time : 0.008 s
% 0.11/0.46 % Total time : 0.044 s
% 0.11/0.46 % Maximum resident set size: 4608 pages
% 0.11/0.46 % E exiting
%------------------------------------------------------------------------------