%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE026+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 : n013.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 0.03s 0.43s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 28 unt; 0 def)
% Number of atoms : 76 ( 44 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 53 ( 19 ~; 15 |; 12 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 44 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5,X6] :
( ( test(X6)
& test(X5) )
=> ( multiplication(X5,X4) = multiplication(multiplication(X5,X4),X6)
=> leq(multiplication(X5,X4),multiplication(X4,X6)) ) ),
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_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_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
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(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(c_0_10,negated_conjecture,
~ ! [X4,X5,X6] :
( ( test(X6)
& test(X5) )
=> ( multiplication(X5,X4) = multiplication(multiplication(X5,X4),X6)
=> leq(multiplication(X5,X4),multiplication(X4,X6)) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_11,negated_conjecture,
( ~ leq(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0))
& multiplication(esk3_0,esk2_0) = multiplication(multiplication(esk3_0,esk2_0),esk4_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_10])])])]) ).
fof(c_0_12,plain,
! [X14,X15,X16] : multiplication(X14,multiplication(X15,X16)) = multiplication(multiplication(X14,X15),X16),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_13,plain,
! [X22,X23,X24] : multiplication(addition(X22,X23),X24) = addition(multiplication(X22,X24),multiplication(X23,X24)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_14,negated_conjecture,
multiplication(esk3_0,esk2_0) = multiplication(multiplication(esk3_0,esk2_0),esk4_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X7,X8] : addition(X7,X8) = addition(X8,X7),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_17,plain,
! [X9,X10,X11] : addition(X11,addition(X10,X9)) = addition(addition(X11,X10),X9),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_18,plain,
! [X13] : addition(X13,X13) = X13,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_19,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_20,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])])])])])]) ).
cnf(c_0_21,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,negated_conjecture,
multiplication(esk3_0,multiplication(esk2_0,esk4_0)) = multiplication(esk3_0,esk2_0),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_23,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_24,plain,
! [X18] : multiplication(one,X18) = X18,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_25,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,plain,
( ~ complement(X2,X1)
| addition(X1,X2) = one ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
( ~ test(X1)
| complement(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_29,plain,
! [X27,X28] :
( ( leq(X27,X28)
| addition(X27,X28) != X28 )
& ( addition(X27,X28) = X28
| ~ leq(X27,X28) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])]) ).
cnf(c_0_30,negated_conjecture,
addition(multiplication(esk3_0,esk2_0),multiplication(X1,multiplication(esk2_0,esk4_0))) = multiplication(addition(X1,esk3_0),multiplication(esk2_0,esk4_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_31,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,plain,
( ~ test(X1)
| addition(X1,esk1_1(X1)) = one ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,negated_conjecture,
addition(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)) = multiplication(addition(one,esk3_0),multiplication(esk2_0,esk4_0)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
~ leq(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_37,plain,
( ~ test(X1)
| addition(X1,one) = one ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_39,negated_conjecture,
multiplication(addition(one,esk3_0),multiplication(esk2_0,esk4_0)) != multiplication(esk2_0,esk4_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_40,negated_conjecture,
addition(one,esk3_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_23]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40]),c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE026+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.03/0.36 % CPULimit : 300
% 0.03/0.36 % WCLimit : 300
% 0.03/0.36 % DateTime : Sun Sep 20 22:38:50 UTC 2026
% 0.03/0.37 % CPUTime :
% 0.03/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/0.40 Running first-order theorem proving
% 0.03/0.40 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
% 0.03/0.43 % Version: 3.5.1
% 0.03/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.03/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.03/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.03/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.03/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.03/0.43 % Starting sh5l with 300s (1) cores
% 0.03/0.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3562637 completed with status 0
% 0.03/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.03/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.03/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.03/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.03/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.03/0.43 % No SInE strategy applied
% 0.03/0.43 % Search class: FGUSM-FFMS21-SFFFFFNN
% 0.03/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.03/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.03/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.03/0.43 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.03/0.43 % Starting new_bool_3 with 136s (1) cores
% 0.03/0.43 % Starting new_bool_1 with 136s (1) cores
% 0.03/0.43 % new_bool_3 with pid 3562644 completed with status 0
% 0.03/0.43 % Result found by new_bool_3
% 0.03/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.03/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.03/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.03/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.03/0.43 % No SInE strategy applied
% 0.03/0.43 % Search class: FGUSM-FFMS21-SFFFFFNN
% 0.03/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.03/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.03/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.03/0.43 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.03/0.43 % Starting new_bool_3 with 136s (1) cores
% 0.03/0.43 % Preprocessing time : 0.001 s
% 0.03/0.43 % Presaturation interreduction done
% 0.03/0.43
% 0.03/0.43 % Proof found!
% 0.03/0.43 % SZS status Theorem
% 0.03/0.43 % SZS output start CNFRefutation
% See solution above
% 0.03/0.44 % Parsed axioms : 19
% 0.03/0.44 % Removed by relevancy pruning/SinE : 0
% 0.03/0.44 % Initial clauses : 28
% 0.03/0.44 % Removed in clause preprocessing : 0
% 0.03/0.44 % Initial clauses in saturation : 28
% 0.03/0.44 % Processed clauses : 221
% 0.03/0.44 % ...of these trivial : 12
% 0.03/0.44 % ...subsumed : 55
% 0.03/0.44 % ...remaining for further processing : 154
% 0.03/0.44 % Other redundant clauses eliminated : 21
% 0.03/0.44 % Clauses deleted for lack of memory : 0
% 0.03/0.44 % Backward-subsumed : 1
% 0.03/0.44 % Backward-rewritten : 5
% 0.03/0.44 % Generated clauses : 1075
% 0.03/0.44 % ...of the previous two non-redundant : 760
% 0.03/0.44 % ...aggressively subsumed : 0
% 0.03/0.44 % Contextual simplify-reflections : 0
% 0.03/0.44 % Paramodulations : 1054
% 0.03/0.44 % Factorizations : 0
% 0.03/0.44 % NegExts : 0
% 0.03/0.44 % Equation resolutions : 21
% 0.03/0.44 % Disequality decompositions : 0
% 0.03/0.44 % Total rewrite steps : 973
% 0.03/0.44 % ...of those cached : 654
% 0.03/0.44 % Propositional unsat checks : 0
% 0.03/0.44 % Propositional check models : 0
% 0.03/0.44 % Propositional check unsatisfiable : 0
% 0.03/0.44 % Propositional clauses : 0
% 0.03/0.44 % Propositional clauses after purity: 0
% 0.03/0.44 % Propositional unsat core size : 0
% 0.03/0.44 % Propositional preprocessing time : 0.000
% 0.03/0.44 % Propositional encoding time : 0.000
% 0.03/0.44 % Propositional solver time : 0.000
% 0.03/0.44 % Success case prop preproc time : 0.000
% 0.03/0.44 % Success case prop encoding time : 0.000
% 0.03/0.44 % Success case prop solver time : 0.000
% 0.03/0.44 % Current number of processed clauses : 119
% 0.03/0.44 % Positive orientable unit clauses : 51
% 0.03/0.44 % Positive unorientable unit clauses: 3
% 0.03/0.44 % Negative unit clauses : 1
% 0.03/0.44 % Non-unit-clauses : 64
% 0.03/0.44 % Current number of unprocessed clauses: 593
% 0.03/0.44 % ...number of literals in the above : 1075
% 0.03/0.44 % Current number of archived formulas : 0
% 0.03/0.44 % Current number of archived clauses : 34
% 0.03/0.44 % Clause-clause subsumption calls (NU) : 607
% 0.03/0.44 % Rec. Clause-clause subsumption calls : 561
% 0.03/0.44 % Non-unit clause-clause subsumptions : 49
% 0.03/0.44 % Unit Clause-clause subsumption calls : 39
% 0.03/0.44 % Rewrite failures with RHS unbound : 0
% 0.03/0.44 % BW rewrite match attempts : 69
% 0.03/0.44 % BW rewrite match successes : 27
% 0.03/0.44 % Condensation attempts : 0
% 0.03/0.44 % Condensation successes : 0
% 0.03/0.44 % Termbank termtop insertions : 13374
% 0.03/0.44 % Search garbage collected termcells : 216
% 0.03/0.44
% 0.03/0.44 % -------------------------------------------------
% 0.03/0.44 % User time : 0.012 s
% 0.03/0.44 % System time : 0.005 s
% 0.03/0.44 % Total time : 0.017 s
% 0.03/0.44 % Maximum resident set size: 3396 pages
% 0.03/0.44
% 0.03/0.44 % -------------------------------------------------
% 0.03/0.44 % User time : 0.059 s
% 0.03/0.44 % System time : 0.015 s
% 0.03/0.44 % Total time : 0.074 s
% 0.03/0.44 % Maximum resident set size: 4608 pages
% 0.03/0.44 % E exiting
%------------------------------------------------------------------------------