TSTP Solution File: KLE026+2 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : KLE026+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 01:55:26 EDT 2022
% Result : Theorem 0.24s 1.42s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 23 unt; 0 def)
% Number of atoms : 71 ( 39 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 53 ( 19 ~; 15 |; 12 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 66 ( 5 sgn 44 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(test_2,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( multiplication(X4,X5) = zero
& multiplication(X5,X4) = zero
& addition(X4,X5) = one ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(goals,conjecture,
! [X4,X5,X6] :
( ( test(X5)
& test(X6) )
=> ( multiplication(X5,X4) = multiplication(multiplication(X5,X4),X6)
=> leq(multiplication(X5,X4),multiplication(X4,X6)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals) ).
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(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
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(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).
fof(c_0_9,plain,
! [X6,X7,X6,X7] :
( ( multiplication(X6,X7) = zero
| ~ complement(X7,X6) )
& ( multiplication(X7,X6) = zero
| ~ complement(X7,X6) )
& ( addition(X6,X7) = one
| ~ complement(X7,X6) )
& ( multiplication(X6,X7) != zero
| multiplication(X7,X6) != zero
| addition(X6,X7) != one
| complement(X7,X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])])])]) ).
fof(c_0_10,plain,
! [X6,X6,X8] :
( ( ~ test(X6)
| complement(esk1_1(X6),X6) )
& ( ~ complement(X8,X6)
| test(X6) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_1])])])])])]) ).
fof(c_0_11,negated_conjecture,
~ ! [X4,X5,X6] :
( ( test(X5)
& test(X6) )
=> ( multiplication(X5,X4) = multiplication(multiplication(X5,X4),X6)
=> leq(multiplication(X5,X4),multiplication(X4,X6)) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_12,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_13,plain,
( addition(X2,X1) = one
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_16,negated_conjecture,
( test(esk3_0)
& test(esk4_0)
& multiplication(esk3_0,esk2_0) = multiplication(multiplication(esk3_0,esk2_0),esk4_0)
& ~ leq(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_17,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_18,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_19,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_20,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,plain,
( addition(X1,esk1_1(X1)) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_22,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,negated_conjecture,
multiplication(esk3_0,esk2_0) = multiplication(multiplication(esk3_0,esk2_0),esk4_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_25,plain,
! [X3,X4,X3,X4] :
( ( ~ leq(X3,X4)
| addition(X3,X4) = X4 )
& ( addition(X3,X4) != X4
| leq(X3,X4) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])])]) ).
cnf(c_0_26,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
( addition(multiplication(X1,X2),multiplication(esk1_1(X1),X2)) = X2
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_29,negated_conjecture,
multiplication(esk3_0,multiplication(esk2_0,esk4_0)) = multiplication(esk3_0,esk2_0),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_31,negated_conjecture,
~ leq(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_32,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,negated_conjecture,
addition(multiplication(esk3_0,esk2_0),multiplication(esk1_1(esk3_0),multiplication(esk2_0,esk4_0))) = multiplication(esk2_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_35,negated_conjecture,
addition(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)) != multiplication(esk2_0,esk4_0),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : KLE026+2 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 14:37:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.24/1.42 # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.24/1.42 # Preprocessing time : 0.015 s
% 0.24/1.42
% 0.24/1.42 # Proof found!
% 0.24/1.42 # SZS status Theorem
% 0.24/1.42 # SZS output start CNFRefutation
% See solution above
% 0.24/1.42 # Proof object total steps : 37
% 0.24/1.42 # Proof object clause steps : 18
% 0.24/1.42 # Proof object formula steps : 19
% 0.24/1.42 # Proof object conjectures : 10
% 0.24/1.42 # Proof object clause conjectures : 7
% 0.24/1.42 # Proof object formula conjectures : 3
% 0.24/1.42 # Proof object initial clauses used : 11
% 0.24/1.42 # Proof object initial formulas used : 9
% 0.24/1.42 # Proof object generating inferences : 6
% 0.24/1.42 # Proof object simplifying inferences : 5
% 0.24/1.42 # Training examples: 0 positive, 0 negative
% 0.24/1.42 # Parsed axioms : 19
% 0.24/1.42 # Removed by relevancy pruning/SinE : 0
% 0.24/1.42 # Initial clauses : 28
% 0.24/1.42 # Removed in clause preprocessing : 0
% 0.24/1.42 # Initial clauses in saturation : 28
% 0.24/1.42 # Processed clauses : 224
% 0.24/1.42 # ...of these trivial : 9
% 0.24/1.42 # ...subsumed : 78
% 0.24/1.42 # ...remaining for further processing : 137
% 0.24/1.42 # Other redundant clauses eliminated : 1
% 0.24/1.42 # Clauses deleted for lack of memory : 0
% 0.24/1.42 # Backward-subsumed : 2
% 0.24/1.42 # Backward-rewritten : 8
% 0.24/1.42 # Generated clauses : 1744
% 0.24/1.42 # ...of the previous two non-trivial : 1417
% 0.24/1.42 # Contextual simplify-reflections : 35
% 0.24/1.42 # Paramodulations : 1736
% 0.24/1.42 # Factorizations : 0
% 0.24/1.42 # Equation resolutions : 8
% 0.24/1.42 # Current number of processed clauses : 127
% 0.24/1.42 # Positive orientable unit clauses : 29
% 0.24/1.42 # Positive unorientable unit clauses: 3
% 0.24/1.42 # Negative unit clauses : 6
% 0.24/1.42 # Non-unit-clauses : 89
% 0.24/1.42 # Current number of unprocessed clauses: 1186
% 0.24/1.42 # ...number of literals in the above : 4434
% 0.24/1.42 # Current number of archived formulas : 0
% 0.24/1.42 # Current number of archived clauses : 10
% 0.24/1.42 # Clause-clause subsumption calls (NU) : 2269
% 0.24/1.42 # Rec. Clause-clause subsumption calls : 1776
% 0.24/1.42 # Non-unit clause-clause subsumptions : 84
% 0.24/1.42 # Unit Clause-clause subsumption calls : 145
% 0.24/1.42 # Rewrite failures with RHS unbound : 0
% 0.24/1.42 # BW rewrite match attempts : 38
% 0.24/1.42 # BW rewrite match successes : 27
% 0.24/1.42 # Condensation attempts : 0
% 0.24/1.42 # Condensation successes : 0
% 0.24/1.42 # Termbank termtop insertions : 30791
% 0.24/1.42
% 0.24/1.42 # -------------------------------------------------
% 0.24/1.42 # User time : 0.046 s
% 0.24/1.42 # System time : 0.002 s
% 0.24/1.42 # Total time : 0.048 s
% 0.24/1.42 # Maximum resident set size: 4404 pages
% 0.24/23.41 eprover: CPU time limit exceeded, terminating
% 0.24/23.42 eprover: CPU time limit exceeded, terminating
% 0.24/23.42 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.42 eprover: No such file or directory
% 0.24/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.43 eprover: No such file or directory
% 0.24/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.44 eprover: No such file or directory
% 0.24/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.44 eprover: No such file or directory
% 0.24/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.44 eprover: No such file or directory
% 0.24/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.44 eprover: No such file or directory
% 0.24/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.44 eprover: No such file or directory
% 0.24/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.45 eprover: No such file or directory
% 0.24/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.45 eprover: No such file or directory
% 0.24/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.45 eprover: No such file or directory
% 0.24/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.45 eprover: No such file or directory
% 0.24/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.45 eprover: No such file or directory
% 0.24/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.46 eprover: No such file or directory
% 0.24/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.46 eprover: No such file or directory
% 0.24/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.46 eprover: No such file or directory
% 0.24/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.46 eprover: No such file or directory
% 0.24/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.47 eprover: No such file or directory
% 0.24/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.47 eprover: No such file or directory
% 0.24/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.47 eprover: No such file or directory
% 0.24/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.48 eprover: No such file or directory
% 0.24/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.48 eprover: No such file or directory
% 0.24/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.48 eprover: No such file or directory
%------------------------------------------------------------------------------