## TSTP Solution File: KLE011+1 by ET---2.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : KLE011+1 : TPTP v7.3.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n046.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 09:54:09 EST 2019

% Result   : Theorem 0.12s
% Output   : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   53 (  37 unt;   0 def)
%            Number of atoms       :   90 (  54 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :   66 (  29   ~;  20   |;  11   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   86 (   4 sgn  47   !;   1   ?)

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

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

fof(test_3,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).

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

fof(test_2,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( multiplication(X4,X5) = zero
& multiplication(X5,X4) = zero
& addition(X4,X5) = one ) ),
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(right_distributivity,axiom,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).

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

fof(c_0_11,negated_conjecture,
~ ! [X4,X5] :
( ( test(X5)
& test(X4) )
inference(assume_negation,[status(cth)],[goals]) ).

fof(c_0_12,negated_conjecture,
( test(esk2_0)
& test(esk1_0)
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).

fof(c_0_13,plain,

fof(c_0_14,plain,

cnf(c_0_15,negated_conjecture,
inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_16,plain,
inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_17,plain,
inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_18,plain,
inference(variable_rename,[status(thm)],[left_distributivity]) ).

fof(c_0_19,plain,
! [X6,X7,X7] :
( ( c(X6) != X7
| complement(X6,X7)
| ~ test(X6) )
& ( ~ complement(X6,X7)
| c(X6) = X7
| ~ test(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_3])])])])]) ).

fof(c_0_20,plain,
! [X2] : addition(X2,X2) = X2,

fof(c_0_21,plain,
! [X6,X7,X6,X7] :
( ( multiplication(X6,X7) = zero
| ~ complement(X7,X6) )
& ( multiplication(X7,X6) = zero
| ~ complement(X7,X6) )
| ~ complement(X7,X6) )
& ( multiplication(X6,X7) != zero
| multiplication(X7,X6) != zero
| 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_22,plain,
! [X6,X6,X8] :
( ( ~ test(X6)
| complement(esk3_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])])])])])]) ).

cnf(c_0_23,negated_conjecture,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]) ).

cnf(c_0_24,plain,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_16]),c_0_17]) ).

cnf(c_0_25,plain,
inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_26,plain,
( complement(X1,X2)
| ~ test(X1)
| c(X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_27,plain,
inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_28,plain,
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_29,plain,
( complement(esk3_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).

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

cnf(c_0_31,plain,
inference(spm,[status(thm)],[c_0_17,c_0_25]) ).

cnf(c_0_32,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_26]) ).

fof(c_0_33,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).

fof(c_0_34,plain,
inference(variable_rename,[status(thm)],[right_distributivity]) ).

cnf(c_0_35,plain,
inference(spm,[status(thm)],[c_0_17,c_0_27]) ).

cnf(c_0_36,plain,
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_37,negated_conjecture,
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_38,plain,
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_32]),c_0_16]) ).

cnf(c_0_39,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_40,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_41,plain,
inference(split_conjunct,[status(thm)],[c_0_34]) ).

fof(c_0_42,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).

cnf(c_0_43,plain,
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_44,negated_conjecture,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40])]),c_0_16]),c_0_24]),c_0_41]),c_0_24]) ).

cnf(c_0_45,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_42]) ).

cnf(c_0_46,plain,
inference(spm,[status(thm)],[c_0_17,c_0_41]) ).

cnf(c_0_47,negated_conjecture,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_40]),c_0_16]) ).

cnf(c_0_48,negated_conjecture,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_38]),c_0_45]),c_0_40])]) ).

cnf(c_0_49,negated_conjecture,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_45]),c_0_45]) ).

cnf(c_0_50,negated_conjecture,
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_51,negated_conjecture,
test(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_52,negated_conjecture,
\$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_38]),c_0_51])]),
[proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05  % Problem  : KLE011+1 : TPTP v7.3.0. Released v4.0.0.
% 0.00/0.05  % Command  : run_ET %s %d
% 0.03/0.26  % Computer : n046.star.cs.uiowa.edu
% 0.03/0.26  % Model    : x86_64 x86_64
% 0.03/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.26  % Memory   : 32218.5MB
% 0.03/0.26  % OS       : Linux 3.10.0-862.11.6.el7.x86_64
% 0.03/0.26  % CPULimit : 300
% 0.03/0.26  % DateTime : Thu Mar  7 02:20:57 CST 2019
% 0.09/0.26  % CPUTime  :
% 0.12/1.32  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 46 seconds:
% 0.12/1.32  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.12/1.32  # Preprocessing time     : 0.010 s
% 0.12/1.32
% 0.12/1.32  # Proof found!
% 0.12/1.32  # SZS status Theorem
% 0.12/1.32  # SZS output start CNFRefutation
% See solution above
% 0.12/1.32  # SZS output end CNFRefutation
% 0.12/1.32  # Proof object total steps           : 53
% 0.12/1.32  # Proof object clause steps          : 30
% 0.12/1.32  # Proof object formula steps         : 23
% 0.12/1.32  # Proof object conjectures           : 15
% 0.12/1.32  # Proof object clause conjectures    : 12
% 0.12/1.32  # Proof object formula conjectures   : 3
% 0.12/1.32  # Proof object initial clauses used  : 13
% 0.12/1.32  # Proof object initial formulas used : 11
% 0.12/1.32  # Proof object generating inferences : 13
% 0.12/1.32  # Proof object simplifying inferences: 22
% 0.12/1.32  # Training examples: 0 positive, 0 negative
% 0.12/1.32  # Parsed axioms                      : 17
% 0.12/1.32  # Removed by relevancy pruning/SinE  : 1
% 0.12/1.32  # Initial clauses                    : 23
% 0.12/1.32  # Removed in clause preprocessing    : 0
% 0.12/1.32  # Initial clauses in saturation      : 23
% 0.12/1.32  # Processed clauses                  : 2301
% 0.12/1.32  # ...of these trivial                : 479
% 0.12/1.32  # ...subsumed                        : 1292
% 0.12/1.32  # ...remaining for further processing: 530
% 0.12/1.32  # Other redundant clauses eliminated : 4
% 0.12/1.32  # Clauses deleted for lack of memory : 0
% 0.12/1.32  # Backward-subsumed                  : 50
% 0.12/1.32  # Backward-rewritten                 : 139
% 0.12/1.32  # Generated clauses                  : 28940
% 0.12/1.32  # ...of the previous two non-trivial : 21789
% 0.12/1.32  # Contextual simplify-reflections    : 613
% 0.12/1.32  # Paramodulations                    : 28930
% 0.12/1.32  # Factorizations                     : 0
% 0.12/1.32  # Equation resolutions               : 10
% 0.12/1.32  # Current number of processed clauses: 341
% 0.12/1.32  #    Positive orientable unit clauses: 178
% 0.12/1.32  #    Positive unorientable unit clauses: 18
% 0.12/1.32  #    Negative unit clauses           : 5
% 0.12/1.32  #    Non-unit-clauses                : 140
% 0.12/1.32  # Current number of unprocessed clauses: 15383
% 0.12/1.32  # ...number of literals in the above : 31237
% 0.12/1.32  # Current number of archived formulas: 0
% 0.12/1.32  # Current number of archived clauses : 189
% 0.12/1.32  # Clause-clause subsumption calls (NU) : 17166
% 0.12/1.32  # Rec. Clause-clause subsumption calls : 9746
% 0.12/1.32  # Non-unit clause-clause subsumptions: 1427
% 0.12/1.32  # Unit Clause-clause subsumption calls : 333
% 0.12/1.32  # Rewrite failures with RHS unbound  : 0
% 0.12/1.32  # BW rewrite match attempts          : 6827
% 0.12/1.32  # BW rewrite match successes         : 242
% 0.12/1.32  # Condensation attempts              : 0
% 0.12/1.32  # Condensation successes             : 0
% 0.12/1.32  # Termbank termtop insertions        : 567196
% 0.12/1.32
% 0.12/1.32  # -------------------------------------------------
% 0.12/1.32  # User time              : 0.407 s
% 0.12/1.32  # System time            : 0.014 s
% 0.12/1.32  # Total time             : 0.421 s
% 0.12/1.32  # Maximum resident set size: 21028 pages
%------------------------------------------------------------------------------
```