%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE024+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 : n008.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 12:58:39 PM UTC 2026
% Result : Theorem 0.18s 0.68s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 21 unt; 0 def)
% Number of atoms : 63 ( 38 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 50 ( 18 ~; 14 |; 11 &)
% ( 2 <=>; 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 46 ( 3 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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/sandbox2/benchmark/theBenchmark.p',goals) ).
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_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
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(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(c_0_7,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_8,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_9,plain,
( ~ test(X1)
| c(X1) != X2
| complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,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_8])])])]) ).
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])])])]) ).
cnf(c_0_12,plain,
( ~ test(X1)
| complement(X1,c(X1)) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X14,X15,X16] : multiplication(X14,multiplication(X15,X16)) = multiplication(multiplication(X14,X15),X16),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_15,plain,
( ~ complement(X1,X2)
| multiplication(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
complement(esk3_0,c(esk3_0)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_17,plain,
! [X26] : multiplication(zero,X26) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_18,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_19,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
multiplication(esk3_0,c(esk3_0)) = zero,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,plain,
! [X12] : addition(X12,zero) = X12,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_23,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
multiplication(esk3_0,multiplication(c(esk3_0),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_25,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
multiplication(multiplication(esk3_0,esk2_0),c(esk4_0)) != zero,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_27,negated_conjecture,
multiplication(esk3_0,addition(X1,multiplication(c(esk3_0),X2))) = multiplication(esk3_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_28,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_10]) ).
cnf(c_0_29,negated_conjecture,
multiplication(esk3_0,multiplication(esk2_0,c(esk4_0))) != zero,
inference(rw,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_24]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE024+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 22:40:09 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 0.18/0.68 % Version: 3.5.1
% 0.18/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.18/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.18/0.68 % Starting new_bool_3 with 300s (1) cores
% 0.18/0.68 % Starting new_bool_1 with 300s (1) cores
% 0.18/0.68 % Starting sh5l with 300s (1) cores
% 0.18/0.68 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3751435 completed with status 0
% 0.18/0.68 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.18/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.18/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.18/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/0.68 % No SInE strategy applied
% 0.18/0.68 % Search class: FGUSM-FFMS21-MFFFFFNN
% 0.18/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.68 % Starting SubtermCWHack with 136s (1) cores
% 0.18/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.18/0.68 % Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 0.18/0.68 % Starting new_bool_3 with 136s (1) cores
% 0.18/0.68 % Starting new_bool_1 with 136s (1) cores
% 0.18/0.68 % G-E--_208_C18_F1_AE_CS_SP_PI_S0a with pid 3751441 completed with status 0
% 0.18/0.68 % Result found by G-E--_208_C18_F1_AE_CS_SP_PI_S0a
% 0.18/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.18/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.18/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/0.68 % No SInE strategy applied
% 0.18/0.68 % Search class: FGUSM-FFMS21-MFFFFFNN
% 0.18/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.68 % Starting SubtermCWHack with 136s (1) cores
% 0.18/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.18/0.68 % Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 0.18/0.68 % Preprocessing time : 0.001 s
% 0.18/0.68
% 0.18/0.68 % Proof found!
% 0.18/0.68 % SZS status Theorem
% 0.18/0.68 % SZS output start CNFRefutation
% See solution above
% 0.18/0.68 % Parsed axioms : 19
% 0.18/0.68 % Removed by relevancy pruning/SinE : 0
% 0.18/0.68 % Initial clauses : 28
% 0.18/0.68 % Removed in clause preprocessing : 0
% 0.18/0.68 % Initial clauses in saturation : 28
% 0.18/0.68 % Processed clauses : 996
% 0.18/0.68 % ...of these trivial : 87
% 0.18/0.68 % ...subsumed : 438
% 0.18/0.68 % ...remaining for further processing : 471
% 0.18/0.68 % Other redundant clauses eliminated : 0
% 0.18/0.68 % Clauses deleted for lack of memory : 0
% 0.18/0.68 % Backward-subsumed : 6
% 0.18/0.68 % Backward-rewritten : 74
% 0.18/0.68 % Generated clauses : 7705
% 0.18/0.68 % ...of the previous two non-redundant : 5570
% 0.18/0.68 % ...aggressively subsumed : 0
% 0.18/0.68 % Contextual simplify-reflections : 0
% 0.18/0.68 % Paramodulations : 7692
% 0.18/0.68 % Factorizations : 1
% 0.18/0.68 % NegExts : 0
% 0.18/0.68 % Equation resolutions : 12
% 0.18/0.68 % Disequality decompositions : 0
% 0.18/0.68 % Total rewrite steps : 10217
% 0.18/0.68 % ...of those cached : 8352
% 0.18/0.68 % Propositional unsat checks : 0
% 0.18/0.68 % Propositional check models : 0
% 0.18/0.68 % Propositional check unsatisfiable : 0
% 0.18/0.68 % Propositional clauses : 0
% 0.18/0.68 % Propositional clauses after purity: 0
% 0.18/0.68 % Propositional unsat core size : 0
% 0.18/0.68 % Propositional preprocessing time : 0.000
% 0.18/0.68 % Propositional encoding time : 0.000
% 0.18/0.68 % Propositional solver time : 0.000
% 0.18/0.68 % Success case prop preproc time : 0.000
% 0.18/0.68 % Success case prop encoding time : 0.000
% 0.18/0.68 % Success case prop solver time : 0.000
% 0.18/0.68 % Current number of processed clauses : 391
% 0.18/0.68 % Positive orientable unit clauses : 178
% 0.18/0.68 % Positive unorientable unit clauses: 5
% 0.18/0.68 % Negative unit clauses : 1
% 0.18/0.68 % Non-unit-clauses : 207
% 0.18/0.68 % Current number of unprocessed clauses: 4499
% 0.18/0.68 % ...number of literals in the above : 9135
% 0.18/0.68 % Current number of archived formulas : 0
% 0.18/0.68 % Current number of archived clauses : 80
% 0.18/0.68 % Clause-clause subsumption calls (NU) : 5388
% 0.18/0.68 % Rec. Clause-clause subsumption calls : 4943
% 0.18/0.68 % Non-unit clause-clause subsumptions : 434
% 0.18/0.68 % Unit Clause-clause subsumption calls : 495
% 0.18/0.68 % Rewrite failures with RHS unbound : 0
% 0.18/0.68 % BW rewrite match attempts : 143
% 0.18/0.68 % BW rewrite match successes : 64
% 0.18/0.68 % Condensation attempts : 0
% 0.18/0.68 % Condensation successes : 0
% 0.18/0.68 % Termbank termtop insertions : 112301
% 0.18/0.68 % Search garbage collected termcells : 219
% 0.18/0.68
% 0.18/0.68 % -------------------------------------------------
% 0.18/0.68 % User time : 0.107 s
% 0.18/0.68 % System time : 0.014 s
% 0.18/0.68 % Total time : 0.121 s
% 0.18/0.68 % Maximum resident set size: 3652 pages
% 0.18/0.68
% 0.18/0.68 % -------------------------------------------------
% 0.18/0.68 % User time : 0.661 s
% 0.18/0.68 % System time : 0.053 s
% 0.18/0.68 % Total time : 0.714 s
% 0.18/0.68 % Maximum resident set size: 4864 pages
% 0.18/0.68 % E exiting
%------------------------------------------------------------------------------