%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : KLE024+2 : 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 : n019.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 12:59:08 PM UTC 2026
% Result : Theorem 0.81s 0.67s
% Output : CNFRefutation 0.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 54 ( 27 unt; 0 def)
% Number of atoms : 109 ( 57 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 92 ( 37 ~; 33 |; 13 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 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 : 79 ( 4 sgn 42 !; 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(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(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(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(test_deMorgan2,axiom,
! [X4,X5] :
( ( test(X5)
& test(X4) )
=> c(multiplication(X4,X5)) = addition(c(X4),c(X5)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+2.ax',test_deMorgan2) ).
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_11,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])])])]) ).
fof(c_0_12,plain,
! [X29,X31,X32] :
( ( test(X31)
| ~ complement(X32,X31) )
& ( complement(esk1_1(X29),X29)
| ~ test(X29) ) ),
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_13,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_14,plain,
( ~ complement(X2,X1)
| multiplication(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( ~ test(X1)
| complement(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X12] : addition(X12,zero) = X12,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_17,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])])])]) ).
fof(c_0_18,plain,
! [X13] : addition(X13,X13) = X13,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_19,plain,
! [X40,X41] :
( c(multiplication(X40,X41)) = addition(c(X40),c(X41))
| ~ test(X41)
| ~ test(X40) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_deMorgan2])])]) ).
cnf(c_0_20,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( ~ test(X1)
| multiplication(X1,esk1_1(X1)) = zero ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( ~ complement(X2,X1)
| addition(X1,X2) = one ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_24,plain,
! [X17] : multiplication(X17,one) = X17,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_25,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_26,plain,
( ~ test(X1)
| c(X1) != X2
| complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,plain,
( ~ test(X2)
| ~ test(X1)
| c(multiplication(X1,X2)) = addition(c(X1),c(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,plain,
( ~ test(X1)
| multiplication(X1,addition(X2,esk1_1(X1))) = multiplication(X1,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_30,plain,
( ~ test(X1)
| addition(X1,esk1_1(X1)) = one ),
inference(spm,[status(thm)],[c_0_23,c_0_15]) ).
cnf(c_0_31,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_32,negated_conjecture,
( multiplication(multiplication(esk3_0,esk2_0),c(esk4_0)) != zero
& addition(multiplication(esk2_0,c(esk4_0)),multiplication(c(esk3_0),esk2_0)) = multiplication(c(esk3_0),esk2_0)
& test(esk4_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_25])])])]) ).
cnf(c_0_33,plain,
( ~ test(X1)
| complement(X1,c(X1)) ),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_34,plain,
( ~ test(X1)
| c(multiplication(X1,X1)) = c(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,plain,
( ~ test(X1)
| multiplication(X1,X1) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_36,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_37,plain,
! [X14,X15,X16] : multiplication(X14,multiplication(X15,X16)) = multiplication(multiplication(X14,X15),X16),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_38,plain,
( ~ complement(X1,X2)
| multiplication(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_39,plain,
! [X26] : multiplication(zero,X26) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_40,plain,
( ~ test(X1)
| ~ test(multiplication(X1,X1))
| complement(multiplication(X1,X1),c(X1)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_41,negated_conjecture,
multiplication(esk3_0,esk3_0) = esk3_0,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,plain,
( ~ test(X1)
| multiplication(X1,c(X1)) = zero ),
inference(spm,[status(thm)],[c_0_38,c_0_33]) ).
cnf(c_0_44,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,negated_conjecture,
complement(esk3_0,c(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_36])]) ).
cnf(c_0_46,plain,
( ~ test(X1)
| multiplication(X1,multiplication(c(X1),X2)) = zero ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_47,negated_conjecture,
multiplication(esk3_0,c(esk3_0)) = zero,
inference(spm,[status(thm)],[c_0_38,c_0_45]) ).
cnf(c_0_48,negated_conjecture,
multiplication(multiplication(esk3_0,esk2_0),c(esk4_0)) != zero,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_49,plain,
( ~ test(X1)
| multiplication(X1,addition(X2,multiplication(c(X1),X3))) = multiplication(X1,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_46]),c_0_22]) ).
cnf(c_0_50,negated_conjecture,
addition(multiplication(esk2_0,c(esk4_0)),multiplication(c(esk3_0),esk2_0)) = multiplication(c(esk3_0),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_51,negated_conjecture,
multiplication(esk3_0,multiplication(c(esk3_0),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_47]),c_0_44]) ).
cnf(c_0_52,negated_conjecture,
multiplication(esk3_0,multiplication(esk2_0,c(esk4_0))) != zero,
inference(rw,[status(thm)],[c_0_48,c_0_42]) ).
cnf(c_0_53,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_49,c_0_50]),c_0_51]),c_0_36])]),c_0_52]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE024+2 : 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 : n019.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 22:39:34 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
% 0.81/0.67 % Version: 3.5.1
% 0.81/0.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.81/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.81/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.81/0.67 % Starting new_bool_3 with 300s (1) cores
% 0.81/0.67 % Starting new_bool_1 with 300s (1) cores
% 0.81/0.67 % Starting sh5l with 300s (1) cores
% 0.81/0.67 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1068704 completed with status 0
% 0.81/0.67 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.81/0.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.81/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.81/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.81/0.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.81/0.67 % No SInE strategy applied
% 0.81/0.67 % Search class: FGUSM-FFMS21-MFFFFFNN
% 0.81/0.67 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.81/0.67 % Starting SubtermCWHack with 136s (1) cores
% 0.81/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.81/0.67 % Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 0.81/0.67 % Starting new_bool_3 with 136s (1) cores
% 0.81/0.67 % Starting new_bool_1 with 136s (1) cores
% 0.81/0.67 % SubtermCWHack with pid 1068708 completed with status 0
% 0.81/0.67 % Result found by SubtermCWHack
% 0.81/0.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.81/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.81/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.81/0.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.81/0.67 % No SInE strategy applied
% 0.81/0.67 % Search class: FGUSM-FFMS21-MFFFFFNN
% 0.81/0.67 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.81/0.67 % Starting SubtermCWHack with 136s (1) cores
% 0.81/0.67 % Preprocessing time : 0.002 s
% 0.81/0.67
% 0.81/0.67 % Proof found!
% 0.81/0.67 % SZS status Theorem
% 0.81/0.67 % SZS output start CNFRefutation
% See solution above
% 0.81/0.67 % Parsed axioms : 19
% 0.81/0.67 % Removed by relevancy pruning/SinE : 0
% 0.81/0.67 % Initial clauses : 28
% 0.81/0.67 % Removed in clause preprocessing : 0
% 0.81/0.67 % Initial clauses in saturation : 28
% 0.81/0.67 % Processed clauses : 1144
% 0.81/0.67 % ...of these trivial : 136
% 0.81/0.67 % ...subsumed : 662
% 0.81/0.67 % ...remaining for further processing : 346
% 0.81/0.67 % Other redundant clauses eliminated : 6
% 0.81/0.67 % Clauses deleted for lack of memory : 0
% 0.81/0.67 % Backward-subsumed : 37
% 0.81/0.67 % Backward-rewritten : 87
% 0.81/0.67 % Generated clauses : 12432
% 0.81/0.67 % ...of the previous two non-redundant : 7721
% 0.81/0.67 % ...aggressively subsumed : 0
% 0.81/0.67 % Contextual simplify-reflections : 13
% 0.81/0.67 % Paramodulations : 12422
% 0.81/0.67 % Factorizations : 3
% 0.81/0.67 % NegExts : 0
% 0.81/0.67 % Equation resolutions : 6
% 0.81/0.67 % Disequality decompositions : 0
% 0.81/0.67 % Total rewrite steps : 17019
% 0.81/0.67 % ...of those cached : 14831
% 0.81/0.67 % Propositional unsat checks : 0
% 0.81/0.67 % Propositional check models : 0
% 0.81/0.67 % Propositional check unsatisfiable : 0
% 0.81/0.67 % Propositional clauses : 0
% 0.81/0.67 % Propositional clauses after purity: 0
% 0.81/0.67 % Propositional unsat core size : 0
% 0.81/0.67 % Propositional preprocessing time : 0.000
% 0.81/0.67 % Propositional encoding time : 0.000
% 0.81/0.67 % Propositional solver time : 0.000
% 0.81/0.67 % Success case prop preproc time : 0.000
% 0.81/0.67 % Success case prop encoding time : 0.000
% 0.81/0.67 % Success case prop solver time : 0.000
% 0.81/0.67 % Current number of processed clauses : 220
% 0.81/0.67 % Positive orientable unit clauses : 107
% 0.81/0.67 % Positive unorientable unit clauses: 4
% 0.81/0.67 % Negative unit clauses : 4
% 0.81/0.67 % Non-unit-clauses : 105
% 0.81/0.67 % Current number of unprocessed clauses: 6407
% 0.81/0.67 % ...number of literals in the above : 18345
% 0.81/0.67 % Current number of archived formulas : 0
% 0.81/0.67 % Current number of archived clauses : 125
% 0.81/0.67 % Clause-clause subsumption calls (NU) : 4704
% 0.81/0.67 % Rec. Clause-clause subsumption calls : 3759
% 0.81/0.67 % Non-unit clause-clause subsumptions : 529
% 0.81/0.67 % Unit Clause-clause subsumption calls : 557
% 0.81/0.67 % Rewrite failures with RHS unbound : 0
% 0.81/0.67 % BW rewrite match attempts : 198
% 0.81/0.67 % BW rewrite match successes : 152
% 0.81/0.67 % Condensation attempts : 0
% 0.81/0.67 % Condensation successes : 0
% 0.81/0.67 % Termbank termtop insertions : 154523
% 0.81/0.67 % Search garbage collected termcells : 219
% 0.81/0.67
% 0.81/0.67 % -------------------------------------------------
% 0.81/0.67 % User time : 0.223 s
% 0.81/0.67 % System time : 0.006 s
% 0.81/0.67 % Total time : 0.229 s
% 0.81/0.67 % Maximum resident set size: 3600 pages
% 0.81/0.67
% 0.81/0.67 % -------------------------------------------------
% 0.81/0.67 % User time : 1.003 s
% 0.81/0.67 % System time : 0.051 s
% 0.81/0.67 % Total time : 1.054 s
% 0.81/0.67 % Maximum resident set size: 4864 pages
% 0.81/0.67 % E exiting
%------------------------------------------------------------------------------