TSTP Solution File: GRP685+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : GRP685+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n023.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 : Sat Jul 16 09:03:18 EDT 2022

% Result   : Theorem 0.12s 1.30s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   57 (  52 unt;   0 def)
%            Number of atoms       :   62 (  61 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   13 (   8   ~;   3   |;   2   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :  115 (   0 sgn  38   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f01,axiom,
    ! [X1] : ld(X1,mult(X1,X1)) = X1,
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',f01) ).

fof(f03,axiom,
    ! [X2,X1] : mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',f03) ).

fof(f07,axiom,
    ! [X2,X1] : ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',f07) ).

fof(f04,axiom,
    ! [X2,X1] : mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',f04) ).

fof(f02,axiom,
    ! [X1] : rd(mult(X1,X1),X1) = X1,
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',f02) ).

fof(f06,axiom,
    ! [X3,X4,X2,X1] : rd(mult(mult(X1,X2),rd(X4,X3)),rd(X4,X3)) = mult(X1,rd(mult(X2,X3),X3)),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',f06) ).

fof(f05,axiom,
    ! [X3,X4,X2,X1] : ld(ld(X1,X2),mult(ld(X1,X2),mult(X4,X3))) = mult(ld(X1,mult(X1,X4)),X3),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',f05) ).

fof(goals,conjecture,
    ! [X5,X6,X7] :
      ( rd(mult(X5,ld(X6,X7)),ld(X6,X7)) = rd(mult(X5,X7),X7)
      & rd(mult(X5,rd(X6,X7)),rd(X6,X7)) = rd(mult(X5,X7),X7) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals) ).

fof(c_0_8,plain,
    ! [X2] : ld(X2,mult(X2,X2)) = X2,
    inference(variable_rename,[status(thm)],[f01]) ).

fof(c_0_9,plain,
    ! [X3,X4] : mult(X4,ld(X4,X3)) = ld(X4,mult(X4,X3)),
    inference(variable_rename,[status(thm)],[f03]) ).

fof(c_0_10,plain,
    ! [X3,X4] : ld(X4,mult(X4,ld(X3,X3))) = rd(mult(rd(X4,X4),X3),X3),
    inference(variable_rename,[status(thm)],[f07]) ).

fof(c_0_11,plain,
    ! [X3,X4] : mult(rd(X4,X3),X3) = rd(mult(X4,X3),X3),
    inference(variable_rename,[status(thm)],[f04]) ).

fof(c_0_12,plain,
    ! [X2] : rd(mult(X2,X2),X2) = X2,
    inference(variable_rename,[status(thm)],[f02]) ).

fof(c_0_13,plain,
    ! [X5,X6,X7,X8] : rd(mult(mult(X8,X7),rd(X6,X5)),rd(X6,X5)) = mult(X8,rd(mult(X7,X5),X5)),
    inference(variable_rename,[status(thm)],[f06]) ).

fof(c_0_14,plain,
    ! [X5,X6,X7,X8] : ld(ld(X8,X7),mult(ld(X8,X7),mult(X6,X5))) = mult(ld(X8,mult(X8,X6)),X5),
    inference(variable_rename,[status(thm)],[f05]) ).

cnf(c_0_15,plain,
    ld(X1,mult(X1,X1)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_16,plain,
    mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_17,plain,
    ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_18,plain,
    mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_19,plain,
    rd(mult(X1,X1),X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_20,plain,
    rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_21,plain,
    ld(ld(X1,X2),mult(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_22,plain,
    mult(X1,ld(X1,X1)) = X1,
    inference(rw,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_23,plain,
    mult(X1,ld(X1,ld(X2,X2))) = mult(rd(rd(X1,X1),X2),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_16]),c_0_18]) ).

cnf(c_0_24,plain,
    mult(rd(X1,X1),X1) = X1,
    inference(rw,[status(thm)],[c_0_19,c_0_18]) ).

cnf(c_0_25,plain,
    mult(rd(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,mult(rd(X2,X4),X4)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_18]),c_0_18]) ).

cnf(c_0_26,plain,
    mult(ld(X1,X2),ld(ld(X1,X2),mult(X3,X4))) = mult(mult(X1,ld(X1,X3)),X4),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_16]),c_0_16]) ).

cnf(c_0_27,plain,
    ld(X1,X1) = mult(rd(rd(X1,X1),X1),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_22]),c_0_23]) ).

cnf(c_0_28,plain,
    mult(rd(rd(X1,X1),X1),X1) = rd(X1,X1),
    inference(spm,[status(thm)],[c_0_18,c_0_24]) ).

cnf(c_0_29,plain,
    mult(rd(mult(X1,X2),mult(rd(X3,X4),X4)),mult(rd(X3,X4),X4)) = mult(X1,mult(rd(X2,X4),X4)),
    inference(spm,[status(thm)],[c_0_25,c_0_18]) ).

cnf(c_0_30,plain,
    mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(mult(X1,ld(X1,rd(X3,X3))),X3),
    inference(spm,[status(thm)],[c_0_26,c_0_24]) ).

cnf(c_0_31,plain,
    ld(X1,X1) = rd(X1,X1),
    inference(rw,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_32,plain,
    mult(rd(mult(X1,X2),X3),X3) = mult(X1,mult(rd(X2,X3),X3)),
    inference(spm,[status(thm)],[c_0_29,c_0_24]) ).

cnf(c_0_33,plain,
    mult(X1,rd(X1,X1)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_27]),c_0_28]) ).

cnf(c_0_34,plain,
    mult(rd(X1,X1),ld(rd(X1,X1),X2)) = mult(mult(X1,ld(X1,rd(X2,X2))),X2),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_35,plain,
    mult(X1,ld(X1,rd(X2,X2))) = mult(rd(rd(X1,X1),X2),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_27]),c_0_28]) ).

cnf(c_0_36,plain,
    mult(mult(rd(X1,X2),X2),X2) = mult(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_18]),c_0_24]) ).

fof(c_0_37,negated_conjecture,
    ~ ! [X5,X6,X7] :
        ( rd(mult(X5,ld(X6,X7)),ld(X6,X7)) = rd(mult(X5,X7),X7)
        & rd(mult(X5,rd(X6,X7)),rd(X6,X7)) = rd(mult(X5,X7),X7) ),
    inference(assume_negation,[status(cth)],[goals]) ).

cnf(c_0_38,plain,
    mult(rd(X1,rd(X2,X3)),rd(X2,X3)) = mult(X1,mult(rd(rd(X1,X1),X3),X3)),
    inference(spm,[status(thm)],[c_0_25,c_0_33]) ).

cnf(c_0_39,plain,
    mult(X1,mult(rd(rd(X1,X1),X2),X2)) = mult(rd(X1,X2),X2),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_40,plain,
    mult(rd(X1,X1),ld(rd(X1,X1),X2)) = mult(rd(X1,X1),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).

fof(c_0_41,negated_conjecture,
    ( rd(mult(esk1_0,ld(esk2_0,esk3_0)),ld(esk2_0,esk3_0)) != rd(mult(esk1_0,esk3_0),esk3_0)
    | rd(mult(esk4_0,rd(esk5_0,esk6_0)),rd(esk5_0,esk6_0)) != rd(mult(esk4_0,esk6_0),esk6_0) ),
    inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])]) ).

cnf(c_0_42,plain,
    mult(rd(X1,rd(X2,X3)),rd(X2,X3)) = mult(rd(X1,X3),X3),
    inference(rw,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_43,plain,
    mult(rd(X1,X1),ld(rd(X1,X1),X1)) = ld(rd(X1,X1),X1),
    inference(spm,[status(thm)],[c_0_16,c_0_24]) ).

cnf(c_0_44,plain,
    mult(X1,ld(X1,rd(X1,X1))) = rd(X1,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_33]),c_0_27]),c_0_28]) ).

cnf(c_0_45,plain,
    mult(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_31]),c_0_33]) ).

cnf(c_0_46,negated_conjecture,
    ( rd(mult(esk4_0,rd(esk5_0,esk6_0)),rd(esk5_0,esk6_0)) != rd(mult(esk4_0,esk6_0),esk6_0)
    | rd(mult(esk1_0,ld(esk2_0,esk3_0)),ld(esk2_0,esk3_0)) != rd(mult(esk1_0,esk3_0),esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_47,plain,
    mult(rd(X1,mult(rd(X2,X3),X3)),mult(rd(X2,X3),X3)) = mult(rd(X1,X3),X3),
    inference(spm,[status(thm)],[c_0_42,c_0_18]) ).

cnf(c_0_48,plain,
    mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(rd(X1,X1),X3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_35]),c_0_36]) ).

cnf(c_0_49,plain,
    ld(rd(X1,X1),X1) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_34]),c_0_44]),c_0_24]) ).

cnf(c_0_50,plain,
    rd(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_45]),c_0_31]),c_0_31]),c_0_33]) ).

cnf(c_0_51,negated_conjecture,
    ( mult(rd(esk1_0,ld(esk2_0,esk3_0)),ld(esk2_0,esk3_0)) != mult(rd(esk1_0,esk3_0),esk3_0)
    | mult(rd(esk4_0,rd(esk5_0,esk6_0)),rd(esk5_0,esk6_0)) != mult(rd(esk4_0,esk6_0),esk6_0) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_18]),c_0_18]),c_0_18]),c_0_18]) ).

cnf(c_0_52,plain,
    mult(rd(X1,mult(X2,X3)),mult(X2,X3)) = mult(rd(X1,X3),X3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_18]),c_0_36]),c_0_36]) ).

cnf(c_0_53,plain,
    mult(X1,ld(X1,X2)) = mult(rd(X1,X1),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).

cnf(c_0_54,negated_conjecture,
    mult(rd(esk1_0,ld(esk2_0,esk3_0)),ld(esk2_0,esk3_0)) != mult(rd(esk1_0,esk3_0),esk3_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_42])]) ).

cnf(c_0_55,plain,
    mult(rd(X1,ld(X2,X3)),ld(X2,X3)) = mult(rd(X1,X3),X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_52]) ).

cnf(c_0_56,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : GRP685+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.07  % Command  : run_ET %s %d
% 0.06/0.26  % Computer : n023.cluster.edu
% 0.06/0.26  % Model    : x86_64 x86_64
% 0.06/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26  % Memory   : 8042.1875MB
% 0.06/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26  % CPULimit : 300
% 0.06/0.26  % WCLimit  : 600
% 0.06/0.26  % DateTime : Tue Jun 14 06:35:05 EDT 2022
% 0.06/0.26  % CPUTime  : 
% 0.12/1.30  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.12/1.30  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.12/1.30  # Preprocessing time       : 0.008 s
% 0.12/1.30  
% 0.12/1.30  # Proof found!
% 0.12/1.30  # SZS status Theorem
% 0.12/1.30  # SZS output start CNFRefutation
% See solution above
% 0.12/1.30  # Proof object total steps             : 57
% 0.12/1.30  # Proof object clause steps            : 40
% 0.12/1.30  # Proof object formula steps           : 17
% 0.12/1.30  # Proof object conjectures             : 7
% 0.12/1.30  # Proof object clause conjectures      : 4
% 0.12/1.30  # Proof object formula conjectures     : 3
% 0.12/1.30  # Proof object initial clauses used    : 8
% 0.12/1.30  # Proof object initial formulas used   : 8
% 0.12/1.30  # Proof object generating inferences   : 17
% 0.12/1.30  # Proof object simplifying inferences  : 41
% 0.12/1.30  # Training examples: 0 positive, 0 negative
% 0.12/1.30  # Parsed axioms                        : 8
% 0.12/1.30  # Removed by relevancy pruning/SinE    : 0
% 0.12/1.30  # Initial clauses                      : 8
% 0.12/1.30  # Removed in clause preprocessing      : 0
% 0.12/1.30  # Initial clauses in saturation        : 8
% 0.12/1.30  # Processed clauses                    : 198
% 0.12/1.30  # ...of these trivial                  : 42
% 0.12/1.30  # ...subsumed                          : 30
% 0.12/1.30  # ...remaining for further processing  : 126
% 0.12/1.30  # Other redundant clauses eliminated   : 0
% 0.12/1.30  # Clauses deleted for lack of memory   : 0
% 0.12/1.30  # Backward-subsumed                    : 1
% 0.12/1.30  # Backward-rewritten                   : 62
% 0.12/1.30  # Generated clauses                    : 4747
% 0.12/1.30  # ...of the previous two non-trivial   : 3196
% 0.12/1.30  # Contextual simplify-reflections      : 0
% 0.12/1.30  # Paramodulations                      : 4747
% 0.12/1.30  # Factorizations                       : 0
% 0.12/1.30  # Equation resolutions                 : 0
% 0.12/1.30  # Current number of processed clauses  : 63
% 0.12/1.30  #    Positive orientable unit clauses  : 62
% 0.12/1.30  #    Positive unorientable unit clauses: 1
% 0.12/1.30  #    Negative unit clauses             : 0
% 0.12/1.30  #    Non-unit-clauses                  : 0
% 0.12/1.30  # Current number of unprocessed clauses: 1246
% 0.12/1.30  # ...number of literals in the above   : 1246
% 0.12/1.30  # Current number of archived formulas  : 0
% 0.12/1.30  # Current number of archived clauses   : 63
% 0.12/1.30  # Clause-clause subsumption calls (NU) : 0
% 0.12/1.30  # Rec. Clause-clause subsumption calls : 0
% 0.12/1.30  # Non-unit clause-clause subsumptions  : 0
% 0.12/1.30  # Unit Clause-clause subsumption calls : 29
% 0.12/1.30  # Rewrite failures with RHS unbound    : 25
% 0.12/1.30  # BW rewrite match attempts            : 294
% 0.12/1.30  # BW rewrite match successes           : 122
% 0.12/1.30  # Condensation attempts                : 0
% 0.12/1.30  # Condensation successes               : 0
% 0.12/1.30  # Termbank termtop insertions          : 72631
% 0.12/1.30  
% 0.12/1.30  # -------------------------------------------------
% 0.12/1.30  # User time                : 0.055 s
% 0.12/1.30  # System time              : 0.005 s
% 0.12/1.30  # Total time               : 0.060 s
% 0.12/1.30  # Maximum resident set size: 5404 pages
%------------------------------------------------------------------------------