%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE035+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 : n020.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 12:58:41 PM UTC 2026
% Result : Theorem 0.12s 0.48s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 33 unt; 0 def)
% Number of atoms : 58 ( 30 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 26 ( 8 ~; 4 |; 11 &)
% ( 1 <=>; 2 =>; 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5,X6,X7] :
( ( leq(multiplication(multiplication(X6,X5),c(X7)),zero)
& leq(multiplication(multiplication(X6,X4),c(X7)),zero)
& test(X6)
& test(X7) )
=> leq(multiplication(multiplication(X6,addition(X4,X5)),c(X7)),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(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
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_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(c_0_8,negated_conjecture,
~ ! [X4,X5,X6,X7] :
( ( leq(multiplication(multiplication(X6,X5),c(X7)),zero)
& leq(multiplication(multiplication(X6,X4),c(X7)),zero)
& test(X6)
& test(X7) )
=> leq(multiplication(multiplication(X6,addition(X4,X5)),c(X7)),zero) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_9,negated_conjecture,
( ~ leq(multiplication(multiplication(esk4_0,addition(esk2_0,esk3_0)),c(esk5_0)),zero)
& leq(multiplication(multiplication(esk4_0,esk3_0),c(esk5_0)),zero)
& leq(multiplication(multiplication(esk4_0,esk2_0),c(esk5_0)),zero)
& test(esk4_0)
& test(esk5_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_10,plain,
! [X15,X16,X17] : multiplication(X15,multiplication(X16,X17)) = multiplication(multiplication(X15,X16),X17),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_11,plain,
! [X28,X29] :
( ( leq(X28,X29)
| addition(X28,X29) != X29 )
& ( addition(X28,X29) = X29
| ~ leq(X28,X29) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])]) ).
cnf(c_0_12,negated_conjecture,
leq(multiplication(multiplication(esk4_0,esk3_0),c(esk5_0)),zero),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X13] : addition(X13,zero) = X13,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_15,plain,
! [X20,X21,X22] : multiplication(X20,addition(X21,X22)) = addition(multiplication(X20,X21),multiplication(X20,X22)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_16,plain,
( ~ leq(X1,X2)
| addition(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
leq(multiplication(esk4_0,multiplication(esk3_0,c(esk5_0))),zero),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
leq(multiplication(multiplication(esk4_0,esk2_0),c(esk5_0)),zero),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_20,plain,
! [X8,X9] : addition(X8,X9) = addition(X9,X8),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_21,plain,
! [X23,X24,X25] : multiplication(addition(X23,X24),X25) = addition(multiplication(X23,X25),multiplication(X24,X25)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_22,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,negated_conjecture,
multiplication(esk4_0,multiplication(esk3_0,c(esk5_0))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_24,negated_conjecture,
leq(multiplication(esk4_0,multiplication(esk2_0,c(esk5_0))),zero),
inference(rw,[status(thm)],[c_0_19,c_0_13]) ).
cnf(c_0_25,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,negated_conjecture,
multiplication(esk4_0,addition(X1,multiplication(esk3_0,c(esk5_0)))) = multiplication(esk4_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_18]) ).
cnf(c_0_28,negated_conjecture,
multiplication(esk4_0,multiplication(esk2_0,c(esk5_0))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_24]),c_0_18]) ).
cnf(c_0_29,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_25]) ).
fof(c_0_30,plain,
! [X14] : addition(X14,X14) = X14,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_31,negated_conjecture,
~ leq(multiplication(multiplication(esk4_0,addition(esk2_0,esk3_0)),c(esk5_0)),zero),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_32,negated_conjecture,
addition(multiplication(esk4_0,X1),multiplication(X2,addition(X1,multiplication(esk3_0,c(esk5_0))))) = multiplication(addition(esk4_0,X2),addition(X1,multiplication(esk3_0,c(esk5_0)))),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
multiplication(esk4_0,addition(multiplication(esk2_0,c(esk5_0)),X1)) = multiplication(esk4_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_28]),c_0_29]) ).
cnf(c_0_34,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_36,negated_conjecture,
~ leq(multiplication(esk4_0,multiplication(addition(esk2_0,esk3_0),c(esk5_0))),zero),
inference(rw,[status(thm)],[c_0_31,c_0_13]) ).
cnf(c_0_37,negated_conjecture,
multiplication(esk4_0,multiplication(addition(esk2_0,esk3_0),c(esk5_0))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_28]),c_0_23]),c_0_34]),c_0_34]),c_0_26]) ).
cnf(c_0_38,plain,
leq(X1,X1),
inference(spm,[status(thm)],[c_0_35,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE035+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n020.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 20 22:40:32 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.48 % Version: 3.5.1
% 0.12/0.48 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.48 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.48 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.48 % Starting sh5l with 300s (1) cores
% 0.12/0.48 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1382740 completed with status 0
% 0.12/0.48 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.12/0.48 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.48 % No SInE strategy applied
% 0.12/0.48 % Search class: FGUSM-FFMS21-MFFFFFNN
% 0.12/0.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.48 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.48 % Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 0.12/0.48 % Starting new_bool_3 with 136s (1) cores
% 0.12/0.48 % Starting new_bool_1 with 136s (1) cores
% 0.12/0.48 % new_bool_3 with pid 1382749 completed with status 0
% 0.12/0.48 % Result found by new_bool_3
% 0.12/0.48 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.48 % No SInE strategy applied
% 0.12/0.48 % Search class: FGUSM-FFMS21-MFFFFFNN
% 0.12/0.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.48 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.48 % Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 0.12/0.48 % Starting new_bool_3 with 136s (1) cores
% 0.12/0.48 % Preprocessing time : 0.001 s
% 0.12/0.48 % Presaturation interreduction done
% 0.12/0.48
% 0.12/0.48 % Proof found!
% 0.12/0.48 % SZS status Theorem
% 0.12/0.48 % SZS output start CNFRefutation
% See solution above
% 0.12/0.48 % Parsed axioms : 17
% 0.12/0.48 % Removed by relevancy pruning/SinE : 0
% 0.12/0.48 % Initial clauses : 27
% 0.12/0.48 % Removed in clause preprocessing : 0
% 0.12/0.48 % Initial clauses in saturation : 27
% 0.12/0.48 % Processed clauses : 662
% 0.12/0.48 % ...of these trivial : 36
% 0.12/0.48 % ...subsumed : 329
% 0.12/0.48 % ...remaining for further processing : 297
% 0.12/0.48 % Other redundant clauses eliminated : 51
% 0.12/0.48 % Clauses deleted for lack of memory : 0
% 0.12/0.48 % Backward-subsumed : 0
% 0.12/0.48 % Backward-rewritten : 16
% 0.12/0.48 % Generated clauses : 4244
% 0.12/0.48 % ...of the previous two non-redundant : 3124
% 0.12/0.48 % ...aggressively subsumed : 0
% 0.12/0.48 % Contextual simplify-reflections : 1
% 0.12/0.48 % Paramodulations : 4193
% 0.12/0.48 % Factorizations : 0
% 0.12/0.48 % NegExts : 0
% 0.12/0.48 % Equation resolutions : 51
% 0.12/0.48 % Disequality decompositions : 0
% 0.12/0.48 % Total rewrite steps : 4935
% 0.12/0.48 % ...of those cached : 3514
% 0.12/0.48 % Propositional unsat checks : 0
% 0.12/0.48 % Propositional check models : 0
% 0.12/0.48 % Propositional check unsatisfiable : 0
% 0.12/0.48 % Propositional clauses : 0
% 0.12/0.48 % Propositional clauses after purity: 0
% 0.12/0.48 % Propositional unsat core size : 0
% 0.12/0.48 % Propositional preprocessing time : 0.000
% 0.12/0.48 % Propositional encoding time : 0.000
% 0.12/0.48 % Propositional solver time : 0.000
% 0.12/0.48 % Success case prop preproc time : 0.000
% 0.12/0.48 % Success case prop encoding time : 0.000
% 0.12/0.48 % Success case prop solver time : 0.000
% 0.12/0.48 % Current number of processed clauses : 253
% 0.12/0.48 % Positive orientable unit clauses : 109
% 0.12/0.48 % Positive unorientable unit clauses: 3
% 0.12/0.48 % Negative unit clauses : 0
% 0.12/0.48 % Non-unit-clauses : 141
% 0.12/0.48 % Current number of unprocessed clauses: 2514
% 0.12/0.48 % ...number of literals in the above : 4099
% 0.12/0.48 % Current number of archived formulas : 0
% 0.12/0.48 % Current number of archived clauses : 43
% 0.12/0.48 % Clause-clause subsumption calls (NU) : 1960
% 0.12/0.48 % Rec. Clause-clause subsumption calls : 1906
% 0.12/0.48 % Non-unit clause-clause subsumptions : 318
% 0.12/0.48 % Unit Clause-clause subsumption calls : 77
% 0.12/0.48 % Rewrite failures with RHS unbound : 0
% 0.12/0.48 % BW rewrite match attempts : 115
% 0.12/0.48 % BW rewrite match successes : 38
% 0.12/0.48 % Condensation attempts : 0
% 0.12/0.48 % Condensation successes : 0
% 0.12/0.48 % Termbank termtop insertions : 58025
% 0.12/0.48 % Search garbage collected termcells : 211
% 0.12/0.48
% 0.12/0.48 % -------------------------------------------------
% 0.12/0.48 % User time : 0.041 s
% 0.12/0.48 % System time : 0.005 s
% 0.12/0.48 % Total time : 0.046 s
% 0.12/0.48 % Maximum resident set size: 3652 pages
% 0.12/0.48
% 0.12/0.48 % -------------------------------------------------
% 0.12/0.48 % User time : 0.190 s
% 0.12/0.48 % System time : 0.032 s
% 0.12/0.48 % Total time : 0.222 s
% 0.12/0.48 % Maximum resident set size: 4608 pages
% 0.12/0.48 % E exiting
%------------------------------------------------------------------------------