%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE034+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 : n003.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 0.25s 0.61s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 54 ( 39 unt; 0 def)
% Number of atoms : 99 ( 50 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 68 ( 23 ~; 19 |; 20 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 72 ( 2 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5,X6,X7,X8] :
( ( leq(multiplication(multiplication(X7,X5),c(X8)),zero)
& leq(multiplication(multiplication(X6,X4),c(X7)),zero)
& test(X8)
& test(X6)
& test(X7) )
=> leq(multiplication(multiplication(multiplication(X6,X4),X5),c(X8)),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
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(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
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(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(c_0_11,negated_conjecture,
~ ! [X4,X5,X6,X7,X8] :
( ( leq(multiplication(multiplication(X7,X5),c(X8)),zero)
& leq(multiplication(multiplication(X6,X4),c(X7)),zero)
& test(X8)
& test(X6)
& test(X7) )
=> leq(multiplication(multiplication(multiplication(X6,X4),X5),c(X8)),zero) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_12,negated_conjecture,
( ~ leq(multiplication(multiplication(multiplication(esk4_0,esk2_0),esk3_0),c(esk6_0)),zero)
& leq(multiplication(multiplication(esk5_0,esk3_0),c(esk6_0)),zero)
& leq(multiplication(multiplication(esk4_0,esk2_0),c(esk5_0)),zero)
& test(esk6_0)
& 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_11])])])]) ).
fof(c_0_13,plain,
! [X16,X17,X18] : multiplication(X16,multiplication(X17,X18)) = multiplication(multiplication(X16,X17),X18),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_14,plain,
! [X29,X30] :
( ( leq(X29,X30)
| addition(X29,X30) != X30 )
& ( addition(X29,X30) = X30
| ~ leq(X29,X30) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])]) ).
cnf(c_0_15,negated_conjecture,
leq(multiplication(multiplication(esk5_0,esk3_0),c(esk6_0)),zero),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
leq(multiplication(multiplication(esk4_0,esk2_0),c(esk5_0)),zero),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( ~ leq(X1,X2)
| addition(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
leq(multiplication(esk5_0,multiplication(esk3_0,c(esk6_0))),zero),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_20,plain,
! [X14] : addition(X14,zero) = X14,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_21,plain,
! [X9,X10] : addition(X9,X10) = addition(X10,X9),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_22,plain,
! [X37,X38] :
( ( ~ test(X37)
| c(X37) = X38
| ~ complement(X37,X38) )
& ( ~ test(X37)
| complement(X37,X38)
| c(X37) != X38 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])])]) ).
cnf(c_0_23,negated_conjecture,
leq(multiplication(esk4_0,multiplication(esk2_0,c(esk5_0))),zero),
inference(rw,[status(thm)],[c_0_17,c_0_16]) ).
fof(c_0_24,plain,
! [X24,X25,X26] : multiplication(addition(X24,X25),X26) = addition(multiplication(X24,X26),multiplication(X25,X26)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_25,negated_conjecture,
addition(multiplication(esk5_0,multiplication(esk3_0,c(esk6_0))),zero) = zero,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_28,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])])])]) ).
cnf(c_0_29,plain,
( ~ test(X1)
| c(X1) != X2
| complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,negated_conjecture,
addition(multiplication(esk4_0,multiplication(esk2_0,c(esk5_0))),zero) = zero,
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
fof(c_0_31,plain,
! [X28] : multiplication(zero,X28) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_32,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,negated_conjecture,
multiplication(esk5_0,multiplication(esk3_0,c(esk6_0))) = zero,
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_34,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,plain,
( ~ complement(X2,X1)
| addition(X1,X2) = one ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
( ~ test(X1)
| complement(X1,c(X1)) ),
inference(er,[status(thm)],[c_0_29]) ).
fof(c_0_37,plain,
! [X20] : multiplication(one,X20) = X20,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_38,negated_conjecture,
multiplication(esk4_0,multiplication(esk2_0,c(esk5_0))) = zero,
inference(rw,[status(thm)],[c_0_30,c_0_26]) ).
cnf(c_0_39,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,negated_conjecture,
multiplication(addition(esk5_0,X1),multiplication(esk3_0,c(esk6_0))) = multiplication(X1,multiplication(esk3_0,c(esk6_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_41,plain,
( ~ test(X1)
| addition(X1,c(X1)) = one ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_27]) ).
cnf(c_0_42,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,negated_conjecture,
test(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_44,plain,
! [X15] : addition(X15,X15) = X15,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_45,negated_conjecture,
~ leq(multiplication(multiplication(multiplication(esk4_0,esk2_0),esk3_0),c(esk6_0)),zero),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_46,negated_conjecture,
multiplication(esk4_0,multiplication(esk2_0,multiplication(c(esk5_0),X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_38]),c_0_39]),c_0_16]) ).
cnf(c_0_47,negated_conjecture,
multiplication(c(esk5_0),multiplication(esk3_0,c(esk6_0))) = multiplication(esk3_0,c(esk6_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_43])]) ).
cnf(c_0_48,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_49,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_50,negated_conjecture,
~ leq(multiplication(esk4_0,multiplication(esk2_0,multiplication(esk3_0,c(esk6_0)))),zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_16]),c_0_16]) ).
cnf(c_0_51,negated_conjecture,
multiplication(esk4_0,multiplication(esk2_0,multiplication(esk3_0,c(esk6_0)))) = zero,
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,plain,
leq(X1,X1),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_52])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE034+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 % Computer : n003.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sun Sep 20 22:41:15 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.48 Running first-order theorem proving
% 0.19/0.49 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
% 0.25/0.61 % Version: 3.5.1
% 0.25/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.61 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.61 % Starting sh5l with 300s (1) cores
% 0.25/0.61 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2771820 completed with status 0
% 0.25/0.61 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.25/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.61 % No SInE strategy applied
% 0.25/0.61 % Search class: FGUSM-FFMS21-MFFFFFNN
% 0.25/0.61 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.61 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.25/0.61 % Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 0.25/0.61 % Starting new_bool_3 with 136s (1) cores
% 0.25/0.61 % Starting new_bool_1 with 136s (1) cores
% 0.25/0.61 % new_bool_1 with pid 2771831 completed with status 0
% 0.25/0.61 % Result found by new_bool_1
% 0.25/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.61 % No SInE strategy applied
% 0.25/0.61 % Search class: FGUSM-FFMS21-MFFFFFNN
% 0.25/0.61 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.61 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.25/0.61 % Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 0.25/0.61 % Starting new_bool_3 with 136s (1) cores
% 0.25/0.61 % Starting new_bool_1 with 136s (1) cores
% 0.25/0.61 % Preprocessing time : 0.001 s
% 0.25/0.61 % Presaturation interreduction done
% 0.25/0.61
% 0.25/0.61 % Proof found!
% 0.25/0.61 % SZS status Theorem
% 0.25/0.61 % SZS output start CNFRefutation
% See solution above
% 0.25/0.61 % Parsed axioms : 19
% 0.25/0.61 % Removed by relevancy pruning/SinE : 0
% 0.25/0.61 % Initial clauses : 30
% 0.25/0.61 % Removed in clause preprocessing : 0
% 0.25/0.61 % Initial clauses in saturation : 30
% 0.25/0.61 % Processed clauses : 631
% 0.25/0.61 % ...of these trivial : 13
% 0.25/0.61 % ...subsumed : 329
% 0.25/0.61 % ...remaining for further processing : 289
% 0.25/0.61 % Other redundant clauses eliminated : 52
% 0.25/0.61 % Clauses deleted for lack of memory : 0
% 0.25/0.61 % Backward-subsumed : 7
% 0.25/0.61 % Backward-rewritten : 15
% 0.25/0.61 % Generated clauses : 3536
% 0.25/0.61 % ...of the previous two non-redundant : 2630
% 0.25/0.61 % ...aggressively subsumed : 0
% 0.25/0.61 % Contextual simplify-reflections : 8
% 0.25/0.61 % Paramodulations : 3484
% 0.25/0.61 % Factorizations : 0
% 0.25/0.61 % NegExts : 0
% 0.25/0.61 % Equation resolutions : 52
% 0.25/0.61 % Disequality decompositions : 0
% 0.25/0.61 % Total rewrite steps : 3979
% 0.25/0.61 % ...of those cached : 3041
% 0.25/0.61 % Propositional unsat checks : 0
% 0.25/0.61 % Propositional check models : 0
% 0.25/0.61 % Propositional check unsatisfiable : 0
% 0.25/0.61 % Propositional clauses : 0
% 0.25/0.61 % Propositional clauses after purity: 0
% 0.25/0.61 % Propositional unsat core size : 0
% 0.25/0.61 % Propositional preprocessing time : 0.000
% 0.25/0.61 % Propositional encoding time : 0.000
% 0.25/0.61 % Propositional solver time : 0.000
% 0.25/0.61 % Success case prop preproc time : 0.000
% 0.25/0.61 % Success case prop encoding time : 0.000
% 0.25/0.61 % Success case prop solver time : 0.000
% 0.25/0.61 % Current number of processed clauses : 236
% 0.25/0.61 % Positive orientable unit clauses : 77
% 0.25/0.61 % Positive unorientable unit clauses: 3
% 0.25/0.61 % Negative unit clauses : 0
% 0.25/0.61 % Non-unit-clauses : 156
% 0.25/0.61 % Current number of unprocessed clauses: 2056
% 0.25/0.61 % ...number of literals in the above : 4697
% 0.25/0.61 % Current number of archived formulas : 0
% 0.25/0.61 % Current number of archived clauses : 52
% 0.25/0.61 % Clause-clause subsumption calls (NU) : 2877
% 0.25/0.61 % Rec. Clause-clause subsumption calls : 2520
% 0.25/0.61 % Non-unit clause-clause subsumptions : 336
% 0.25/0.61 % Unit Clause-clause subsumption calls : 64
% 0.25/0.61 % Rewrite failures with RHS unbound : 0
% 0.25/0.61 % BW rewrite match attempts : 107
% 0.25/0.61 % BW rewrite match successes : 41
% 0.25/0.61 % Condensation attempts : 0
% 0.25/0.61 % Condensation successes : 0
% 0.25/0.61 % Termbank termtop insertions : 49124
% 0.25/0.61 % Search garbage collected termcells : 253
% 0.25/0.61
% 0.25/0.61 % -------------------------------------------------
% 0.25/0.61 % User time : 0.060 s
% 0.25/0.61 % System time : 0.007 s
% 0.25/0.61 % Total time : 0.067 s
% 0.25/0.61 % Maximum resident set size: 3600 pages
% 0.25/0.61
% 0.25/0.61 % -------------------------------------------------
% 0.25/0.61 % User time : 0.218 s
% 0.25/0.61 % System time : 0.033 s
% 0.25/0.61 % Total time : 0.251 s
% 0.25/0.61 % Maximum resident set size: 4864 pages
% 0.25/0.61 % E exiting
%------------------------------------------------------------------------------