TSTP Solution File: SET014+3 by E-SAT---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1
% Problem  : SET014+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n014.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 : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 19:21:34 EDT 2023

% Result   : Theorem 0.18s 0.47s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   45 (  12 unt;   0 def)
%            Number of atoms       :  112 (  15 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :   99 (  32   ~;  49   |;  11   &)
%                                         (   4 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   85 (   7 sgn;  33   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(prove_union_subset,conjecture,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & subset(X3,X2) )
     => subset(union(X1,X3),X2) ),
    file('/export/starexec/sandbox/tmp/tmp.wxj6Q27q17/E---3.1_14070.p',prove_union_subset) ).

fof(subset_defn,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/export/starexec/sandbox/tmp/tmp.wxj6Q27q17/E---3.1_14070.p',subset_defn) ).

fof(union_defn,axiom,
    ! [X1,X2,X3] :
      ( member(X3,union(X1,X2))
    <=> ( member(X3,X1)
        | member(X3,X2) ) ),
    file('/export/starexec/sandbox/tmp/tmp.wxj6Q27q17/E---3.1_14070.p',union_defn) ).

fof(equal_member_defn,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ! [X3] :
          ( member(X3,X1)
        <=> member(X3,X2) ) ),
    file('/export/starexec/sandbox/tmp/tmp.wxj6Q27q17/E---3.1_14070.p',equal_member_defn) ).

fof(commutativity_of_union,axiom,
    ! [X1,X2] : union(X1,X2) = union(X2,X1),
    file('/export/starexec/sandbox/tmp/tmp.wxj6Q27q17/E---3.1_14070.p',commutativity_of_union) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( subset(X1,X2)
          & subset(X3,X2) )
       => subset(union(X1,X3),X2) ),
    inference(assume_negation,[status(cth)],[prove_union_subset]) ).

fof(c_0_6,plain,
    ! [X7,X8,X9,X10,X11] :
      ( ( ~ subset(X7,X8)
        | ~ member(X9,X7)
        | member(X9,X8) )
      & ( member(esk1_2(X10,X11),X10)
        | subset(X10,X11) )
      & ( ~ member(esk1_2(X10,X11),X11)
        | subset(X10,X11) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[subset_defn])])])])])]) ).

fof(c_0_7,negated_conjecture,
    ( subset(esk3_0,esk4_0)
    & subset(esk5_0,esk4_0)
    & ~ subset(union(esk3_0,esk5_0),esk4_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

fof(c_0_8,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,union(X4,X5))
        | member(X6,X4)
        | member(X6,X5) )
      & ( ~ member(X6,X4)
        | member(X6,union(X4,X5)) )
      & ( ~ member(X6,X5)
        | member(X6,union(X4,X5)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).

cnf(c_0_9,plain,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    subset(esk5_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_11,plain,
    ! [X16,X17,X18,X19,X20,X21] :
      ( ( ~ member(X18,X16)
        | member(X18,X17)
        | X16 != X17 )
      & ( ~ member(X19,X17)
        | member(X19,X16)
        | X16 != X17 )
      & ( ~ member(esk2_2(X20,X21),X20)
        | ~ member(esk2_2(X20,X21),X21)
        | X20 = X21 )
      & ( member(esk2_2(X20,X21),X20)
        | member(esk2_2(X20,X21),X21)
        | X20 = X21 ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_member_defn])])])])])]) ).

cnf(c_0_12,negated_conjecture,
    subset(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_13,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_14,plain,
    ( member(X1,union(X3,X2))
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_15,negated_conjecture,
    ( member(X1,esk4_0)
    | ~ member(X1,esk5_0) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_16,plain,
    ( member(esk1_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_17,plain,
    ( member(X1,X2)
    | member(X1,X3)
    | ~ member(X1,union(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_18,plain,
    ( member(esk2_2(X1,X2),X1)
    | member(esk2_2(X1,X2),X2)
    | X1 = X2 ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_19,negated_conjecture,
    ( member(X1,esk4_0)
    | ~ member(X1,esk3_0) ),
    inference(spm,[status(thm)],[c_0_9,c_0_12]) ).

cnf(c_0_20,plain,
    ( subset(X1,union(X2,X3))
    | ~ member(esk1_2(X1,union(X2,X3)),X3) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_21,negated_conjecture,
    ( subset(esk5_0,X1)
    | member(esk1_2(esk5_0,X1),esk4_0) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

fof(c_0_22,plain,
    ! [X13,X14] : union(X13,X14) = union(X14,X13),
    inference(variable_rename,[status(thm)],[commutativity_of_union]) ).

cnf(c_0_23,plain,
    ( union(X1,X2) = X3
    | member(esk2_2(union(X1,X2),X3),X3)
    | member(esk2_2(union(X1,X2),X3),X1)
    | member(esk2_2(union(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_24,negated_conjecture,
    ( subset(esk3_0,X1)
    | member(esk1_2(esk3_0,X1),esk4_0) ),
    inference(spm,[status(thm)],[c_0_19,c_0_16]) ).

cnf(c_0_25,negated_conjecture,
    subset(esk5_0,union(X1,esk4_0)),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_26,plain,
    union(X1,X2) = union(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_27,plain,
    ( union(X1,X1) = X2
    | member(esk2_2(union(X1,X1),X2),X1)
    | member(esk2_2(union(X1,X1),X2),X2) ),
    inference(ef,[status(thm)],[c_0_23]) ).

cnf(c_0_28,negated_conjecture,
    subset(esk3_0,union(X1,esk4_0)),
    inference(spm,[status(thm)],[c_0_20,c_0_24]) ).

cnf(c_0_29,negated_conjecture,
    subset(esk5_0,union(esk4_0,X1)),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_30,plain,
    ( X1 = X2
    | ~ member(esk2_2(X1,X2),X1)
    | ~ member(esk2_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_31,plain,
    ( union(X1,X1) = X1
    | member(esk2_2(union(X1,X1),X1),X1) ),
    inference(ef,[status(thm)],[c_0_27]) ).

cnf(c_0_32,negated_conjecture,
    subset(esk3_0,union(esk4_0,X1)),
    inference(spm,[status(thm)],[c_0_28,c_0_26]) ).

cnf(c_0_33,negated_conjecture,
    ( member(X1,union(esk4_0,X2))
    | ~ member(X1,esk5_0) ),
    inference(spm,[status(thm)],[c_0_9,c_0_29]) ).

cnf(c_0_34,plain,
    ( union(X1,X1) = X1
    | ~ member(esk2_2(union(X1,X1),X1),union(X1,X1)) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_35,negated_conjecture,
    ( member(X1,union(esk4_0,X2))
    | ~ member(X1,esk3_0) ),
    inference(spm,[status(thm)],[c_0_9,c_0_32]) ).

cnf(c_0_36,negated_conjecture,
    ( subset(X1,union(esk4_0,X2))
    | ~ member(esk1_2(X1,union(esk4_0,X2)),esk5_0) ),
    inference(spm,[status(thm)],[c_0_13,c_0_33]) ).

cnf(c_0_37,plain,
    union(X1,X1) = X1,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_14]),c_0_31]) ).

cnf(c_0_38,negated_conjecture,
    ( subset(X1,union(esk4_0,X2))
    | ~ member(esk1_2(X1,union(esk4_0,X2)),esk3_0) ),
    inference(spm,[status(thm)],[c_0_13,c_0_35]) ).

cnf(c_0_39,negated_conjecture,
    ( subset(X1,esk4_0)
    | ~ member(esk1_2(X1,esk4_0),esk5_0) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_40,plain,
    ( subset(union(X1,X2),X3)
    | member(esk1_2(union(X1,X2),X3),X1)
    | member(esk1_2(union(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[c_0_17,c_0_16]) ).

cnf(c_0_41,negated_conjecture,
    ( subset(X1,esk4_0)
    | ~ member(esk1_2(X1,esk4_0),esk3_0) ),
    inference(spm,[status(thm)],[c_0_38,c_0_37]) ).

cnf(c_0_42,negated_conjecture,
    ( subset(union(esk5_0,X1),esk4_0)
    | member(esk1_2(union(esk5_0,X1),esk4_0),X1) ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_43,negated_conjecture,
    ~ subset(union(esk3_0,esk5_0),esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_44,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_26]),c_0_43]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET014+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.14  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n014.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   : 2400
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Oct  2 17:02:49 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.18/0.45  Running first-order model finding
% 0.18/0.45  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.wxj6Q27q17/E---3.1_14070.p
% 0.18/0.47  # Version: 3.1pre001
% 0.18/0.47  # Preprocessing class: FSSSSMSSSSSNFFN.
% 0.18/0.47  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.47  # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.18/0.47  # Starting new_bool_3 with 300s (1) cores
% 0.18/0.47  # Starting new_bool_1 with 300s (1) cores
% 0.18/0.47  # Starting sh5l with 300s (1) cores
% 0.18/0.47  # G-E--_302_C18_F1_URBAN_RG_S04BN with pid 14147 completed with status 0
% 0.18/0.47  # Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.18/0.47  # Preprocessing class: FSSSSMSSSSSNFFN.
% 0.18/0.47  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.47  # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.18/0.47  # No SInE strategy applied
% 0.18/0.47  # Search class: FGUSS-FFSF22-SFFFFFNN
% 0.18/0.47  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.47  # Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 0.18/0.47  # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.18/0.47  # Starting new_bool_3 with 136s (1) cores
% 0.18/0.47  # Starting new_bool_1 with 136s (1) cores
% 0.18/0.47  # Starting sh5l with 136s (1) cores
% 0.18/0.47  # U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 14151 completed with status 0
% 0.18/0.47  # Result found by U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 0.18/0.47  # Preprocessing class: FSSSSMSSSSSNFFN.
% 0.18/0.47  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.47  # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.18/0.47  # No SInE strategy applied
% 0.18/0.47  # Search class: FGUSS-FFSF22-SFFFFFNN
% 0.18/0.47  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.47  # Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 0.18/0.47  # Preprocessing time       : 0.001 s
% 0.18/0.47  # Presaturation interreduction done
% 0.18/0.47  
% 0.18/0.47  # Proof found!
% 0.18/0.47  # SZS status Theorem
% 0.18/0.47  # SZS output start CNFRefutation
% See solution above
% 0.18/0.47  # Parsed axioms                        : 6
% 0.18/0.47  # Removed by relevancy pruning/SinE    : 0
% 0.18/0.47  # Initial clauses                      : 15
% 0.18/0.47  # Removed in clause preprocessing      : 2
% 0.18/0.47  # Initial clauses in saturation        : 13
% 0.18/0.47  # Processed clauses                    : 327
% 0.18/0.47  # ...of these trivial                  : 94
% 0.18/0.47  # ...subsumed                          : 90
% 0.18/0.47  # ...remaining for further processing  : 142
% 0.18/0.47  # Other redundant clauses eliminated   : 0
% 0.18/0.47  # Clauses deleted for lack of memory   : 0
% 0.18/0.47  # Backward-subsumed                    : 0
% 0.18/0.47  # Backward-rewritten                   : 7
% 0.18/0.47  # Generated clauses                    : 944
% 0.18/0.47  # ...of the previous two non-redundant : 673
% 0.18/0.47  # ...aggressively subsumed             : 0
% 0.18/0.47  # Contextual simplify-reflections      : 1
% 0.18/0.47  # Paramodulations                      : 918
% 0.18/0.47  # Factorizations                       : 26
% 0.18/0.47  # NegExts                              : 0
% 0.18/0.47  # Equation resolutions                 : 0
% 0.18/0.47  # Total rewrite steps                  : 426
% 0.18/0.47  # Propositional unsat checks           : 0
% 0.18/0.47  #    Propositional check models        : 0
% 0.18/0.47  #    Propositional check unsatisfiable : 0
% 0.18/0.47  #    Propositional clauses             : 0
% 0.18/0.47  #    Propositional clauses after purity: 0
% 0.18/0.47  #    Propositional unsat core size     : 0
% 0.18/0.47  #    Propositional preprocessing time  : 0.000
% 0.18/0.47  #    Propositional encoding time       : 0.000
% 0.18/0.47  #    Propositional solver time         : 0.000
% 0.18/0.47  #    Success case prop preproc time    : 0.000
% 0.18/0.47  #    Success case prop encoding time   : 0.000
% 0.18/0.47  #    Success case prop solver time     : 0.000
% 0.18/0.47  # Current number of processed clauses  : 122
% 0.18/0.47  #    Positive orientable unit clauses  : 42
% 0.18/0.47  #    Positive unorientable unit clauses: 1
% 0.18/0.47  #    Negative unit clauses             : 1
% 0.18/0.47  #    Non-unit-clauses                  : 78
% 0.18/0.47  # Current number of unprocessed clauses: 360
% 0.18/0.47  # ...number of literals in the above   : 921
% 0.18/0.47  # Current number of archived formulas  : 0
% 0.18/0.47  # Current number of archived clauses   : 20
% 0.18/0.47  # Clause-clause subsumption calls (NU) : 879
% 0.18/0.47  # Rec. Clause-clause subsumption calls : 824
% 0.18/0.47  # Non-unit clause-clause subsumptions  : 91
% 0.18/0.47  # Unit Clause-clause subsumption calls : 29
% 0.18/0.47  # Rewrite failures with RHS unbound    : 0
% 0.18/0.47  # BW rewrite match attempts            : 47
% 0.18/0.47  # BW rewrite match successes           : 8
% 0.18/0.47  # Condensation attempts                : 0
% 0.18/0.47  # Condensation successes               : 0
% 0.18/0.47  # Termbank termtop insertions          : 11215
% 0.18/0.47  
% 0.18/0.47  # -------------------------------------------------
% 0.18/0.47  # User time                : 0.013 s
% 0.18/0.47  # System time              : 0.000 s
% 0.18/0.47  # Total time               : 0.013 s
% 0.18/0.47  # Maximum resident set size: 1716 pages
% 0.18/0.47  
% 0.18/0.47  # -------------------------------------------------
% 0.18/0.47  # User time                : 0.059 s
% 0.18/0.47  # System time              : 0.004 s
% 0.18/0.47  # Total time               : 0.063 s
% 0.18/0.47  # Maximum resident set size: 1672 pages
% 0.18/0.47  % E---3.1 exiting
%------------------------------------------------------------------------------