TSTP Solution File: GRP682+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : GRP682+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n017.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 09:03:17 EDT 2022

% Result   : Theorem 0.24s 1.42s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   66 (  60 unt;   0 def)
%            Number of atoms       :   72 (  71 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   16 (  10   ~;   4   |;   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   :  138 (   0 sgn  38   !;   0   ?)

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

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

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

fof(c_0_8,plain,
    ! [X2] : rd(mult(X2,X2),X2) = X2,
    inference(variable_rename,[status(thm)],[f02]) ).

fof(c_0_9,plain,
    ! [X3,X4] : mult(rd(X4,X3),X3) = rd(mult(X4,X3),X3),
    inference(variable_rename,[status(thm)],[f04]) ).

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(X4,ld(X4,X3)) = ld(X4,mult(X4,X3)),
    inference(variable_rename,[status(thm)],[f03]) ).

fof(c_0_12,plain,
    ! [X2] : ld(X2,mult(X2,X2)) = X2,
    inference(variable_rename,[status(thm)],[f01]) ).

fof(c_0_13,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_14,plain,
    rd(mult(X1,X1),X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_15,plain,
    mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_16,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_17,plain,
    mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,plain,
    ld(X1,mult(X1,X1)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,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_13]) ).

cnf(c_0_20,plain,
    mult(rd(X1,X1),X1) = X1,
    inference(rw,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_21,plain,
    mult(rd(rd(X1,X1),X2),X2) = mult(X1,ld(X1,ld(X2,X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_15]),c_0_17]) ).

cnf(c_0_22,plain,
    mult(X1,ld(X1,X1)) = X1,
    inference(rw,[status(thm)],[c_0_18,c_0_17]) ).

cnf(c_0_23,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_19,c_0_17]),c_0_17]) ).

fof(c_0_24,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]) ).

cnf(c_0_25,plain,
    rd(X1,X1) = mult(X1,ld(X1,ld(X1,X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_20]),c_0_21]) ).

cnf(c_0_26,plain,
    mult(X1,ld(X1,ld(X1,X1))) = ld(X1,X1),
    inference(spm,[status(thm)],[c_0_17,c_0_22]) ).

cnf(c_0_27,plain,
    mult(mult(X1,ld(X1,X2)),ld(mult(X1,ld(X1,X2)),mult(X3,X4))) = mult(mult(X1,ld(X1,X3)),X4),
    inference(spm,[status(thm)],[c_0_23,c_0_17]) ).

cnf(c_0_28,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_24]) ).

cnf(c_0_29,plain,
    mult(ld(X1,X1),X1) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_25]),c_0_26]) ).

cnf(c_0_30,plain,
    mult(X1,ld(X1,mult(X2,X3))) = mult(mult(X1,ld(X1,X2)),X3),
    inference(spm,[status(thm)],[c_0_27,c_0_22]) ).

cnf(c_0_31,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_28,c_0_15]),c_0_15]) ).

cnf(c_0_32,plain,
    mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(mult(X1,ld(X1,ld(X3,X3))),X3),
    inference(spm,[status(thm)],[c_0_23,c_0_29]) ).

cnf(c_0_33,plain,
    mult(mult(X1,ld(X1,ld(X2,X2))),X2) = mult(X1,ld(X1,X2)),
    inference(spm,[status(thm)],[c_0_30,c_0_29]) ).

cnf(c_0_34,plain,
    mult(rd(X1,rd(X2,X3)),rd(X2,X3)) = mult(ld(X1,X1),mult(rd(X1,X3),X3)),
    inference(spm,[status(thm)],[c_0_31,c_0_29]) ).

cnf(c_0_35,plain,
    rd(X1,X1) = ld(X1,X1),
    inference(rw,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_36,plain,
    mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(X1,ld(X1,X3)),
    inference(rw,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_37,plain,
    mult(rd(X1,ld(X1,X1)),ld(X1,X1)) = rd(X1,ld(X1,X1)),
    inference(spm,[status(thm)],[c_0_15,c_0_22]) ).

cnf(c_0_38,plain,
    mult(rd(X1,ld(X2,X2)),ld(X2,X2)) = mult(ld(X1,X1),mult(rd(X1,X2),X2)),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_39,plain,
    mult(X1,ld(X1,ld(X1,X2))) = ld(X1,X2),
    inference(spm,[status(thm)],[c_0_22,c_0_36]) ).

cnf(c_0_40,plain,
    mult(X1,mult(X1,ld(X1,X2))) = mult(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_17]),c_0_22]) ).

cnf(c_0_41,plain,
    rd(X1,ld(X1,X1)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38]),c_0_25]),c_0_39]),c_0_29]),c_0_29]) ).

cnf(c_0_42,plain,
    mult(X1,mult(mult(X1,ld(X1,X2)),X3)) = mult(X1,mult(X2,X3)),
    inference(spm,[status(thm)],[c_0_40,c_0_30]) ).

cnf(c_0_43,plain,
    mult(ld(X1,X1),mult(ld(X1,X1),mult(rd(X1,X2),X2))) = mult(rd(X1,X2),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_41]),c_0_38]) ).

cnf(c_0_44,plain,
    mult(ld(X1,X2),mult(mult(X1,ld(X1,X3)),X4)) = mult(ld(X1,X2),mult(X3,X4)),
    inference(spm,[status(thm)],[c_0_42,c_0_36]) ).

cnf(c_0_45,plain,
    mult(rd(ld(X1,X1),X2),X2) = mult(X1,ld(X1,ld(X2,X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_25]),c_0_26]) ).

cnf(c_0_46,plain,
    mult(X1,ld(X1,ld(ld(X1,X2),X3))) = ld(ld(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_36,c_0_39]) ).

fof(c_0_47,negated_conjecture,
    ~ ! [X5,X6,X7] :
        ( ld(ld(X5,X6),mult(ld(X5,X6),X7)) = ld(X5,mult(X5,X7))
        & ld(rd(X5,X6),mult(rd(X5,X6),X7)) = ld(X5,mult(X5,X7)) ),
    inference(assume_negation,[status(cth)],[goals]) ).

cnf(c_0_48,plain,
    ld(ld(X1,X1),mult(rd(X1,X2),X2)) = mult(ld(X1,X1),mult(rd(X1,X2),X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_43]),c_0_17]),c_0_36]),c_0_30]),c_0_44]) ).

cnf(c_0_49,plain,
    ld(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_35]),c_0_29]),c_0_46]) ).

cnf(c_0_50,plain,
    ld(ld(X1,X2),mult(X1,ld(X1,X3))) = ld(ld(X1,X2),X3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_36]),c_0_36]),c_0_46]) ).

cnf(c_0_51,plain,
    mult(ld(X1,X2),mult(X1,ld(X1,X3))) = mult(ld(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_40,c_0_36]) ).

fof(c_0_52,negated_conjecture,
    ( ld(ld(esk1_0,esk2_0),mult(ld(esk1_0,esk2_0),esk3_0)) != ld(esk1_0,mult(esk1_0,esk3_0))
    | ld(rd(esk4_0,esk5_0),mult(rd(esk4_0,esk5_0),esk6_0)) != ld(esk4_0,mult(esk4_0,esk6_0)) ),
    inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])])]) ).

cnf(c_0_53,plain,
    ld(ld(X1,X1),ld(X2,X2)) = mult(ld(X1,X1),ld(X2,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_45]),c_0_49]),c_0_50]),c_0_49]),c_0_51]) ).

cnf(c_0_54,plain,
    mult(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
    inference(spm,[status(thm)],[c_0_22,c_0_49]) ).

cnf(c_0_55,negated_conjecture,
    ( ld(rd(esk4_0,esk5_0),mult(rd(esk4_0,esk5_0),esk6_0)) != ld(esk4_0,mult(esk4_0,esk6_0))
    | ld(ld(esk1_0,esk2_0),mult(ld(esk1_0,esk2_0),esk3_0)) != ld(esk1_0,mult(esk1_0,esk3_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_56,plain,
    mult(ld(X1,X1),mult(rd(X1,X2),X2)) = mult(rd(X1,X2),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_53]),c_0_54]),c_0_54]),c_0_38]),c_0_38]),c_0_43]) ).

cnf(c_0_57,negated_conjecture,
    ( mult(ld(esk1_0,esk2_0),ld(ld(esk1_0,esk2_0),esk3_0)) != mult(esk1_0,ld(esk1_0,esk3_0))
    | mult(rd(esk4_0,esk5_0),ld(rd(esk4_0,esk5_0),esk6_0)) != mult(esk4_0,ld(esk4_0,esk6_0)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_17]),c_0_17]),c_0_17]),c_0_17]) ).

cnf(c_0_58,plain,
    mult(mult(X1,ld(X1,X2)),ld(mult(X1,ld(X1,X2)),X3)) = mult(X1,ld(X1,X3)),
    inference(spm,[status(thm)],[c_0_36,c_0_17]) ).

cnf(c_0_59,plain,
    mult(rd(mult(X1,X2),X3),X3) = mult(X1,mult(rd(X2,X3),X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_34]),c_0_56]) ).

cnf(c_0_60,negated_conjecture,
    ( mult(mult(esk1_0,ld(esk1_0,ld(esk3_0,esk3_0))),esk3_0) != mult(esk1_0,ld(esk1_0,esk3_0))
    | mult(rd(esk4_0,esk5_0),ld(rd(esk4_0,esk5_0),esk6_0)) != mult(esk4_0,ld(esk4_0,esk6_0)) ),
    inference(rw,[status(thm)],[c_0_57,c_0_32]) ).

cnf(c_0_61,plain,
    mult(mult(X1,X2),ld(mult(X1,X2),X3)) = mult(X1,ld(X1,X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_17]),c_0_40]),c_0_40]) ).

cnf(c_0_62,plain,
    mult(rd(X1,X2),X2) = mult(X1,ld(X2,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_22]),c_0_45]),c_0_40]) ).

cnf(c_0_63,negated_conjecture,
    mult(rd(esk4_0,esk5_0),ld(rd(esk4_0,esk5_0),esk6_0)) != mult(esk4_0,ld(esk4_0,esk6_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_33])]) ).

cnf(c_0_64,plain,
    mult(rd(X1,X2),ld(rd(X1,X2),X3)) = mult(X1,ld(X1,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_61]) ).

cnf(c_0_65,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP682+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : run_ET %s %d
% 0.14/0.34  % Computer : n017.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Tue Jun 14 03:45:08 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.24/1.42  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.42  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.42  # Preprocessing time       : 0.014 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             : 66
% 0.24/1.42  # Proof object clause steps            : 49
% 0.24/1.42  # Proof object formula steps           : 17
% 0.24/1.42  # Proof object conjectures             : 8
% 0.24/1.42  # Proof object clause conjectures      : 5
% 0.24/1.42  # Proof object formula conjectures     : 3
% 0.24/1.42  # Proof object initial clauses used    : 8
% 0.24/1.42  # Proof object initial formulas used   : 8
% 0.24/1.42  # Proof object generating inferences   : 26
% 0.24/1.42  # Proof object simplifying inferences  : 55
% 0.24/1.42  # Training examples: 0 positive, 0 negative
% 0.24/1.42  # Parsed axioms                        : 8
% 0.24/1.42  # Removed by relevancy pruning/SinE    : 0
% 0.24/1.42  # Initial clauses                      : 8
% 0.24/1.42  # Removed in clause preprocessing      : 0
% 0.24/1.42  # Initial clauses in saturation        : 8
% 0.24/1.42  # Processed clauses                    : 319
% 0.24/1.42  # ...of these trivial                  : 88
% 0.24/1.42  # ...subsumed                          : 45
% 0.24/1.42  # ...remaining for further processing  : 186
% 0.24/1.42  # Other redundant clauses eliminated   : 0
% 0.24/1.42  # Clauses deleted for lack of memory   : 0
% 0.24/1.42  # Backward-subsumed                    : 1
% 0.24/1.42  # Backward-rewritten                   : 73
% 0.24/1.42  # Generated clauses                    : 12568
% 0.24/1.42  # ...of the previous two non-trivial   : 9059
% 0.24/1.42  # Contextual simplify-reflections      : 0
% 0.24/1.42  # Paramodulations                      : 12568
% 0.24/1.42  # Factorizations                       : 0
% 0.24/1.42  # Equation resolutions                 : 0
% 0.24/1.42  # Current number of processed clauses  : 112
% 0.24/1.42  #    Positive orientable unit clauses  : 104
% 0.24/1.42  #    Positive unorientable unit clauses: 8
% 0.24/1.42  #    Negative unit clauses             : 0
% 0.24/1.42  #    Non-unit-clauses                  : 0
% 0.24/1.42  # Current number of unprocessed clauses: 5709
% 0.24/1.42  # ...number of literals in the above   : 5709
% 0.24/1.42  # Current number of archived formulas  : 0
% 0.24/1.42  # Current number of archived clauses   : 74
% 0.24/1.42  # Clause-clause subsumption calls (NU) : 0
% 0.24/1.42  # Rec. Clause-clause subsumption calls : 0
% 0.24/1.42  # Non-unit clause-clause subsumptions  : 0
% 0.24/1.42  # Unit Clause-clause subsumption calls : 62
% 0.24/1.42  # Rewrite failures with RHS unbound    : 4
% 0.24/1.42  # BW rewrite match attempts            : 468
% 0.24/1.42  # BW rewrite match successes           : 105
% 0.24/1.42  # Condensation attempts                : 0
% 0.24/1.42  # Condensation successes               : 0
% 0.24/1.42  # Termbank termtop insertions          : 198655
% 0.24/1.42  
% 0.24/1.42  # -------------------------------------------------
% 0.24/1.42  # User time                : 0.226 s
% 0.24/1.42  # System time              : 0.007 s
% 0.24/1.42  # Total time               : 0.233 s
% 0.24/1.42  # Maximum resident set size: 10424 pages
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