## TSTP Solution File: KLE089+1 by ET---2.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : KLE089+1 : TPTP v7.3.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n126.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32218.5MB
% OS       : Linux 3.10.0-862.11.6.el7.x86_64
% CPULimit : 300s
% DateTime : Thu Mar  7 09:54:22 EST 2019

% Result   : Theorem 0.09s
% Output   : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   51 (  48 unt;   0 def)
%            Number of atoms       :   54 (  53 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    7 (   4   ~;   0   |;   1   &)
%                                         (   0 <=>;   0  =>;   2  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   68 (   3 sgn  40   !;   0   ?)

%------------------------------------------------------------------------------
%----WARNING: ET---2.0 format not known, defaulting to TPTP
fof(goals,conjecture,
! [X4,X5] :
( multiplication(domain(X4),X5) = zero
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals) ).

fof(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain4) ).

! [X1] : addition(X1,X1) = X1,

fof(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain3) ).

fof(left_distributivity,axiom,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).

fof(domain1,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain1) ).

! [X1] : addition(X1,zero) = X1,

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(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).

fof(c_0_12,negated_conjecture,
~ ! [X4,X5] :
( multiplication(domain(X4),X5) = zero
inference(assume_negation,[status(cth)],[goals]) ).

fof(c_0_13,negated_conjecture,
& multiplication(domain(esk1_0),esk2_0) != zero ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_12])])])]) ).

fof(c_0_14,plain,
! [X5] : domain(X5) = antidomain(antidomain(X5)),
inference(variable_rename,[status(thm)],[domain4]) ).

cnf(c_0_15,negated_conjecture,
inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_16,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_17,plain,

fof(c_0_18,plain,

cnf(c_0_19,negated_conjecture,
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_20,plain,
inference(split_conjunct,[status(thm)],[c_0_17]) ).

fof(c_0_21,plain,
! [X2] : addition(X2,X2) = X2,

fof(c_0_22,plain,
! [X5] : addition(antidomain(antidomain(X5)),antidomain(X5)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).

cnf(c_0_23,plain,
inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_24,negated_conjecture,
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_25,plain,
inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_26,plain,
inference(split_conjunct,[status(thm)],[c_0_22]) ).

fof(c_0_27,plain,
inference(variable_rename,[status(thm)],[left_distributivity]) ).

fof(c_0_28,plain,
! [X5] : multiplication(antidomain(X5),X5) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).

fof(c_0_29,plain,
! [X2] : addition(X2,zero) = X2,

cnf(c_0_30,negated_conjecture,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_31,plain,
inference(spm,[status(thm)],[c_0_23,c_0_25]) ).

cnf(c_0_32,plain,
inference(rw,[status(thm)],[c_0_26,c_0_20]) ).

fof(c_0_33,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).

fof(c_0_34,plain,
! [X2] : multiplication(zero,X2) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).

cnf(c_0_35,plain,
inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_36,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_37,plain,
inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_38,negated_conjecture,
inference(spm,[status(thm)],[c_0_30,c_0_20]) ).

cnf(c_0_39,plain,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_20]) ).

fof(c_0_40,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).

cnf(c_0_41,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_42,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_43,plain,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).

cnf(c_0_44,negated_conjecture,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_32]),c_0_20]),c_0_39]),c_0_20]) ).

cnf(c_0_45,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_46,negated_conjecture,
multiplication(domain(esk1_0),esk2_0) != zero,
inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_47,plain,
multiplication(antidomain(X1),multiplication(X1,X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_36]),c_0_42]) ).

cnf(c_0_48,negated_conjecture,
multiplication(antidomain(esk1_0),esk2_0) = esk2_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).

cnf(c_0_49,negated_conjecture,
multiplication(antidomain(antidomain(esk1_0)),esk2_0) != zero,
inference(rw,[status(thm)],[c_0_46,c_0_16]) ).

cnf(c_0_50,negated_conjecture,
\$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),
[proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04  % Problem  : KLE089+1 : TPTP v7.3.0. Released v4.0.0.
% 0.00/0.05  % Command  : run_ET %s %d
% 0.03/0.25  % Computer : n126.star.cs.uiowa.edu
% 0.03/0.25  % Model    : x86_64 x86_64
% 0.03/0.25  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.25  % Memory   : 32218.5MB
% 0.03/0.25  % OS       : Linux 3.10.0-862.11.6.el7.x86_64
% 0.03/0.25  % CPULimit : 300
% 0.03/0.25  % DateTime : Thu Mar  7 02:20:47 CST 2019
% 0.03/0.25  % CPUTime  :
% 0.09/1.34  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 46 seconds:
% 0.09/1.34  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.09/1.34  # Preprocessing time     : 0.010 s
% 0.09/1.34
% 0.09/1.34  # Proof found!
% 0.09/1.34  # SZS status Theorem
% 0.09/1.34  # SZS output start CNFRefutation
% See solution above
% 0.09/1.34  # SZS output end CNFRefutation
% 0.09/1.34  # Proof object total steps           : 51
% 0.09/1.34  # Proof object clause steps          : 26
% 0.09/1.34  # Proof object formula steps         : 25
% 0.09/1.34  # Proof object conjectures           : 13
% 0.09/1.34  # Proof object clause conjectures    : 10
% 0.09/1.34  # Proof object formula conjectures   : 3
% 0.09/1.34  # Proof object initial clauses used  : 13
% 0.09/1.34  # Proof object initial formulas used : 12
% 0.09/1.34  # Proof object generating inferences : 9
% 0.09/1.34  # Proof object simplifying inferences: 12
% 0.09/1.34  # Training examples: 0 positive, 0 negative
% 0.09/1.34  # Parsed axioms                      : 21
% 0.09/1.34  # Removed by relevancy pruning/SinE  : 2
% 0.09/1.34  # Initial clauses                    : 20
% 0.09/1.34  # Removed in clause preprocessing    : 1
% 0.09/1.34  # Initial clauses in saturation      : 19
% 0.09/1.34  # Processed clauses                  : 117
% 0.09/1.34  # ...of these trivial                : 19
% 0.09/1.34  # ...subsumed                        : 17
% 0.09/1.34  # ...remaining for further processing: 81
% 0.09/1.34  # Other redundant clauses eliminated : 0
% 0.09/1.34  # Clauses deleted for lack of memory : 0
% 0.09/1.34  # Backward-subsumed                  : 0
% 0.09/1.34  # Backward-rewritten                 : 10
% 0.09/1.34  # Generated clauses                  : 1486
% 0.09/1.34  # ...of the previous two non-trivial : 999
% 0.09/1.34  # Contextual simplify-reflections    : 0
% 0.09/1.34  # Paramodulations                    : 1486
% 0.09/1.34  # Factorizations                     : 0
% 0.09/1.34  # Equation resolutions               : 0
% 0.09/1.34  # Current number of processed clauses: 71
% 0.09/1.34  #    Positive orientable unit clauses: 64
% 0.09/1.34  #    Positive unorientable unit clauses: 6
% 0.09/1.34  #    Negative unit clauses           : 1
% 0.09/1.34  #    Non-unit-clauses                : 0
% 0.09/1.34  # Current number of unprocessed clauses: 853
% 0.09/1.34  # ...number of literals in the above : 853
% 0.09/1.34  # Current number of archived formulas: 0
% 0.09/1.34  # Current number of archived clauses : 11
% 0.09/1.34  # Clause-clause subsumption calls (NU) : 0
% 0.09/1.34  # Rec. Clause-clause subsumption calls : 0
% 0.09/1.34  # Non-unit clause-clause subsumptions: 0
% 0.09/1.34  # Unit Clause-clause subsumption calls : 7
% 0.09/1.34  # Rewrite failures with RHS unbound  : 0
% 0.09/1.34  # BW rewrite match attempts          : 78
% 0.09/1.34  # BW rewrite match successes         : 43
% 0.09/1.34  # Condensation attempts              : 0
% 0.09/1.34  # Condensation successes             : 0
% 0.09/1.34  # Termbank termtop insertions        : 16615
% 0.09/1.34
% 0.09/1.34  # -------------------------------------------------
% 0.09/1.34  # User time              : 0.020 s
% 0.09/1.34  # System time            : 0.003 s
% 0.09/1.34  # Total time             : 0.023 s
% 0.09/1.34  # Maximum resident set size: 3872 pages
%------------------------------------------------------------------------------
```