TSTP Solution File: NUM030-1 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : NUM030-1 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n010.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  : 300s
% DateTime : Tue May 21 01:18:10 EDT 2024

% Result   : Unsatisfiable 16.95s 2.59s
% Output   : CNFRefutation 16.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   13
% Syntax   : Number of clauses     :   50 (  21 unt;   9 nHn;  29 RR)
%            Number of literals    :   88 (  15 equ;  36 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   2 con; 0-2 aty)
%            Number of variables   :   79 (   7 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(subclass_members,axiom,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).

cnf(class_elements_are_sets,axiom,
    subclass(X1,universal_class),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).

cnf(not_subclass_members2,axiom,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).

cnf(complement2,axiom,
    ( member(X1,complement(X2))
    | member(X1,X2)
    | ~ member(X1,universal_class) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).

cnf(not_subclass_members1,axiom,
    ( member(not_subclass_element(X1,X2),X1)
    | subclass(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).

cnf(complement1,axiom,
    ( ~ member(X1,complement(X2))
    | ~ member(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).

cnf(subclass_implies_equal,axiom,
    ( X1 = X2
    | ~ subclass(X1,X2)
    | ~ subclass(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).

cnf(intersection2,axiom,
    ( member(X1,X3)
    | ~ member(X1,intersection(X2,X3)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).

cnf(prove_symmetrization_property3_1,negated_conjecture,
    symmetrization_of(x) = x,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_symmetrization_property3_1) ).

cnf(symmetrization,axiom,
    union(X1,inverse(X1)) = symmetrization_of(X1),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',symmetrization) ).

cnf(inverse,axiom,
    domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inverse) ).

cnf(union,axiom,
    complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).

cnf(prove_symmetrization_property3_2,negated_conjecture,
    ~ subclass(inverse(x),x),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_symmetrization_property3_2) ).

cnf(c_0_13,plain,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    inference(fof_simplification,[status(thm)],[subclass_members]) ).

cnf(c_0_14,plain,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    c_0_13 ).

cnf(c_0_15,axiom,
    subclass(X1,universal_class),
    class_elements_are_sets ).

cnf(c_0_16,plain,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    inference(fof_simplification,[status(thm)],[not_subclass_members2]) ).

cnf(c_0_17,plain,
    ( member(X1,complement(X2))
    | member(X1,X2)
    | ~ member(X1,universal_class) ),
    inference(fof_simplification,[status(thm)],[complement2]) ).

cnf(c_0_18,plain,
    ( member(X1,universal_class)
    | ~ member(X1,X2) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_19,axiom,
    ( member(not_subclass_element(X1,X2),X1)
    | subclass(X1,X2) ),
    not_subclass_members1 ).

cnf(c_0_20,plain,
    ( ~ member(X1,complement(X2))
    | ~ member(X1,X2) ),
    inference(fof_simplification,[status(thm)],[complement1]) ).

cnf(c_0_21,plain,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    c_0_16 ).

cnf(c_0_22,plain,
    ( member(X1,complement(X2))
    | member(X1,X2)
    | ~ member(X1,universal_class) ),
    c_0_17 ).

cnf(c_0_23,plain,
    ( member(not_subclass_element(X1,X2),universal_class)
    | subclass(X1,X2) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_24,plain,
    ( ~ member(X1,complement(X2))
    | ~ member(X1,X2) ),
    c_0_20 ).

cnf(c_0_25,plain,
    ( member(not_subclass_element(X1,complement(X2)),X2)
    | subclass(X1,complement(X2)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).

cnf(c_0_26,plain,
    ( X1 = X2
    | ~ subclass(X1,X2)
    | ~ subclass(X2,X1) ),
    inference(fof_simplification,[status(thm)],[subclass_implies_equal]) ).

cnf(c_0_27,plain,
    ( subclass(X1,complement(complement(X2)))
    | ~ member(not_subclass_element(X1,complement(complement(X2))),X2) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_28,plain,
    ( subclass(complement(X1),X2)
    | ~ member(not_subclass_element(complement(X1),X2),X1) ),
    inference(spm,[status(thm)],[c_0_24,c_0_19]) ).

cnf(c_0_29,plain,
    ( X1 = X2
    | ~ subclass(X1,X2)
    | ~ subclass(X2,X1) ),
    c_0_26 ).

cnf(c_0_30,plain,
    subclass(X1,complement(complement(X1))),
    inference(spm,[status(thm)],[c_0_27,c_0_19]) ).

cnf(c_0_31,plain,
    ( member(not_subclass_element(complement(complement(X1)),X2),X1)
    | subclass(complement(complement(X1)),X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_22]),c_0_23]) ).

cnf(c_0_32,plain,
    ( complement(complement(X1)) = X1
    | ~ subclass(complement(complement(X1)),X1) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_33,plain,
    subclass(complement(complement(X1)),X1),
    inference(spm,[status(thm)],[c_0_21,c_0_31]) ).

cnf(c_0_34,plain,
    ( member(X1,X3)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(fof_simplification,[status(thm)],[intersection2]) ).

cnf(c_0_35,plain,
    complement(complement(X1)) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]) ).

cnf(c_0_36,plain,
    ( member(X1,X3)
    | ~ member(X1,intersection(X2,X3)) ),
    c_0_34 ).

cnf(c_0_37,negated_conjecture,
    symmetrization_of(x) = x,
    prove_symmetrization_property3_1 ).

cnf(c_0_38,axiom,
    union(X1,inverse(X1)) = symmetrization_of(X1),
    symmetrization ).

cnf(c_0_39,axiom,
    domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
    inverse ).

cnf(c_0_40,axiom,
    complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
    union ).

cnf(c_0_41,negated_conjecture,
    ~ subclass(inverse(x),x),
    inference(fof_simplification,[status(thm)],[prove_symmetrization_property3_2]) ).

cnf(c_0_42,plain,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),complement(X1)) ),
    inference(spm,[status(thm)],[c_0_28,c_0_35]) ).

cnf(c_0_43,plain,
    ( member(not_subclass_element(X1,complement(intersection(X2,X3))),X3)
    | subclass(X1,complement(intersection(X2,X3))) ),
    inference(spm,[status(thm)],[c_0_36,c_0_25]) ).

cnf(c_0_44,negated_conjecture,
    complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))) = x,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40]) ).

cnf(c_0_45,negated_conjecture,
    ~ subclass(inverse(x),x),
    c_0_41 ).

cnf(c_0_46,plain,
    subclass(X1,complement(intersection(X2,complement(X1)))),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_47,negated_conjecture,
    intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))) = complement(x),
    inference(spm,[status(thm)],[c_0_35,c_0_44]) ).

cnf(c_0_48,negated_conjecture,
    ~ subclass(domain_of(flip(cross_product(x,universal_class))),x),
    inference(rw,[status(thm)],[c_0_45,c_0_39]) ).

cnf(c_0_49,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_35]),c_0_48]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem    : NUM030-1 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.11/0.13  % Command    : run_E %s %d THM
% 0.13/0.33  % Computer : n010.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Mon May 20 06:37:08 EDT 2024
% 0.13/0.33  % CPUTime    : 
% 0.18/0.46  Running first-order model finding
% 0.18/0.46  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/benchmark/theBenchmark.p
% 16.95/2.59  # Version: 3.1.0
% 16.95/2.59  # Preprocessing class: FSLSSMSMSSSNFFN.
% 16.95/2.59  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 16.95/2.59  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 16.95/2.59  # Starting new_bool_3 with 300s (1) cores
% 16.95/2.59  # Starting new_bool_1 with 300s (1) cores
% 16.95/2.59  # Starting sh5l with 300s (1) cores
% 16.95/2.59  # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 18070 completed with status 0
% 16.95/2.59  # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 16.95/2.59  # Preprocessing class: FSLSSMSMSSSNFFN.
% 16.95/2.59  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 16.95/2.59  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 16.95/2.59  # No SInE strategy applied
% 16.95/2.59  # Search class: FGHSM-FFLM31-DFFFFFNN
% 16.95/2.59  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 16.95/2.59  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 313s (1) cores
% 16.95/2.59  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 16.95/2.59  # Starting new_bool_1 with 308s (1) cores
% 16.95/2.59  # Starting sh5l with 304s (1) cores
% 16.95/2.59  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 16.95/2.59  # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 18079 completed with status 0
% 16.95/2.59  # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 16.95/2.59  # Preprocessing class: FSLSSMSMSSSNFFN.
% 16.95/2.59  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 16.95/2.59  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 16.95/2.59  # No SInE strategy applied
% 16.95/2.59  # Search class: FGHSM-FFLM31-DFFFFFNN
% 16.95/2.59  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 16.95/2.59  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 313s (1) cores
% 16.95/2.59  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 16.95/2.59  # Preprocessing time       : 0.005 s
% 16.95/2.59  # Presaturation interreduction done
% 16.95/2.59  
% 16.95/2.59  # Proof found!
% 16.95/2.59  # SZS status Unsatisfiable
% 16.95/2.59  # SZS output start CNFRefutation
% See solution above
% 16.95/2.59  # Parsed axioms                        : 160
% 16.95/2.59  # Removed by relevancy pruning/SinE    : 0
% 16.95/2.59  # Initial clauses                      : 160
% 16.95/2.59  # Removed in clause preprocessing      : 19
% 16.95/2.59  # Initial clauses in saturation        : 141
% 16.95/2.59  # Processed clauses                    : 13311
% 16.95/2.59  # ...of these trivial                  : 89
% 16.95/2.59  # ...subsumed                          : 10350
% 16.95/2.59  # ...remaining for further processing  : 2872
% 16.95/2.59  # Other redundant clauses eliminated   : 22
% 16.95/2.59  # Clauses deleted for lack of memory   : 0
% 16.95/2.59  # Backward-subsumed                    : 201
% 16.95/2.59  # Backward-rewritten                   : 356
% 16.95/2.59  # Generated clauses                    : 84126
% 16.95/2.59  # ...of the previous two non-redundant : 68918
% 16.95/2.59  # ...aggressively subsumed             : 0
% 16.95/2.59  # Contextual simplify-reflections      : 59
% 16.95/2.59  # Paramodulations                      : 84088
% 16.95/2.59  # Factorizations                       : 16
% 16.95/2.59  # NegExts                              : 0
% 16.95/2.59  # Equation resolutions                 : 22
% 16.95/2.59  # Disequality decompositions           : 0
% 16.95/2.59  # Total rewrite steps                  : 38240
% 16.95/2.59  # ...of those cached                   : 35584
% 16.95/2.59  # Propositional unsat checks           : 0
% 16.95/2.59  #    Propositional check models        : 0
% 16.95/2.59  #    Propositional check unsatisfiable : 0
% 16.95/2.59  #    Propositional clauses             : 0
% 16.95/2.59  #    Propositional clauses after purity: 0
% 16.95/2.59  #    Propositional unsat core size     : 0
% 16.95/2.59  #    Propositional preprocessing time  : 0.000
% 16.95/2.59  #    Propositional encoding time       : 0.000
% 16.95/2.59  #    Propositional solver time         : 0.000
% 16.95/2.59  #    Success case prop preproc time    : 0.000
% 16.95/2.59  #    Success case prop encoding time   : 0.000
% 16.95/2.59  #    Success case prop solver time     : 0.000
% 16.95/2.59  # Current number of processed clauses  : 2169
% 16.95/2.59  #    Positive orientable unit clauses  : 249
% 16.95/2.59  #    Positive unorientable unit clauses: 4
% 16.95/2.59  #    Negative unit clauses             : 5
% 16.95/2.59  #    Non-unit-clauses                  : 1911
% 16.95/2.59  # Current number of unprocessed clauses: 54962
% 16.95/2.59  # ...number of literals in the above   : 199106
% 16.95/2.59  # Current number of archived formulas  : 0
% 16.95/2.59  # Current number of archived clauses   : 716
% 16.95/2.59  # Clause-clause subsumption calls (NU) : 1154380
% 16.95/2.59  # Rec. Clause-clause subsumption calls : 590141
% 16.95/2.59  # Non-unit clause-clause subsumptions  : 7480
% 16.95/2.59  # Unit Clause-clause subsumption calls : 27498
% 16.95/2.59  # Rewrite failures with RHS unbound    : 16
% 16.95/2.59  # BW rewrite match attempts            : 1220
% 16.95/2.59  # BW rewrite match successes           : 920
% 16.95/2.59  # Condensation attempts                : 0
% 16.95/2.59  # Condensation successes               : 0
% 16.95/2.59  # Termbank termtop insertions          : 3173278
% 16.95/2.59  # Search garbage collected termcells   : 287
% 16.95/2.59  
% 16.95/2.59  # -------------------------------------------------
% 16.95/2.59  # User time                : 1.964 s
% 16.95/2.59  # System time              : 0.047 s
% 16.95/2.59  # Total time               : 2.011 s
% 16.95/2.59  # Maximum resident set size: 2192 pages
% 16.95/2.59  
% 16.95/2.59  # -------------------------------------------------
% 16.95/2.59  # User time                : 10.215 s
% 16.95/2.59  # System time              : 0.145 s
% 16.95/2.59  # Total time               : 10.360 s
% 16.95/2.59  # Maximum resident set size: 1844 pages
% 16.95/2.59  % E---3.1 exiting
%------------------------------------------------------------------------------