TSTP Solution File: CAT003-1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : CAT003-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n027.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 : Mon May 20 18:59:07 EDT 2024

% Result   : Unsatisfiable 9.08s 1.62s
% Output   : CNFRefutation 9.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   17
% Syntax   : Number of clauses     :   72 (  31 unt;   0 nHn;  66 RR)
%            Number of literals    :  149 (  12 equ;  80 neg)
%            Maximal clause size   :    4 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :  133 (  13 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(associative_property1,axiom,
    ( defined(X1,X2)
    | ~ product(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',associative_property1) ).

cnf(associative_property2,axiom,
    ( defined(X2,X4)
    | ~ product(X1,X2,X3)
    | ~ defined(X3,X4) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',associative_property2) ).

cnf(ga_equals_d,hypothesis,
    product(g,a,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ga_equals_d) ).

cnf(category_theory_axiom1,axiom,
    ( defined(X1,X5)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ defined(X3,X4) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom1) ).

cnf(ab_equals_c,hypothesis,
    product(a,b,c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_equals_c) ).

cnf(identity1,axiom,
    ( product(X1,X2,X2)
    | ~ defined(X1,X2)
    | ~ identity_map(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',identity1) ).

cnf(product_on_domain,axiom,
    product(X1,domain(X1),X1),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',product_on_domain) ).

cnf(domain_is_an_identity_map,axiom,
    identity_map(domain(X1)),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',domain_is_an_identity_map) ).

cnf(category_theory_axiom3,axiom,
    ( defined(X4,X1)
    | ~ product(X1,X2,X3)
    | ~ defined(X4,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom3) ).

cnf(ha_equals_d,hypothesis,
    product(h,a,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ha_equals_d) ).

cnf(category_theory_axiom6,axiom,
    ( defined(X1,X3)
    | ~ defined(X1,X2)
    | ~ defined(X2,X3)
    | ~ identity_map(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom6) ).

cnf(closure_of_composition,axiom,
    ( product(X1,X2,compose(X1,X2))
    | ~ defined(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',closure_of_composition) ).

cnf(category_theory_axiom5,axiom,
    ( product(X6,X2,X5)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X3,X5)
    | ~ product(X4,X1,X6) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom5) ).

cnf(mapping_from_x_to_its_domain,axiom,
    defined(X1,domain(X1)),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',mapping_from_x_to_its_domain) ).

cnf(composition_is_well_defined,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',composition_is_well_defined) ).

cnf(cancellation_for_product,hypothesis,
    ( X1 = X3
    | ~ product(X1,c,X2)
    | ~ product(X3,c,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation_for_product) ).

cnf(prove_h_equals_g,negated_conjecture,
    h != g,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_h_equals_g) ).

cnf(c_0_17,plain,
    ( defined(X1,X2)
    | ~ product(X1,X2,X3) ),
    inference(fof_simplification,[status(thm)],[associative_property1]) ).

cnf(c_0_18,plain,
    ( defined(X2,X4)
    | ~ product(X1,X2,X3)
    | ~ defined(X3,X4) ),
    inference(fof_simplification,[status(thm)],[associative_property2]) ).

cnf(c_0_19,plain,
    ( defined(X1,X2)
    | ~ product(X1,X2,X3) ),
    c_0_17 ).

cnf(c_0_20,hypothesis,
    product(g,a,d),
    ga_equals_d ).

cnf(c_0_21,plain,
    ( defined(X1,X5)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ defined(X3,X4) ),
    inference(fof_simplification,[status(thm)],[category_theory_axiom1]) ).

cnf(c_0_22,hypothesis,
    product(a,b,c),
    ab_equals_c ).

cnf(c_0_23,plain,
    ( defined(X2,X4)
    | ~ product(X1,X2,X3)
    | ~ defined(X3,X4) ),
    c_0_18 ).

cnf(c_0_24,hypothesis,
    defined(g,a),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_25,plain,
    ( defined(X1,X5)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ defined(X3,X4) ),
    c_0_21 ).

cnf(c_0_26,hypothesis,
    defined(a,b),
    inference(spm,[status(thm)],[c_0_19,c_0_22]) ).

cnf(c_0_27,plain,
    ( product(X1,X2,X2)
    | ~ defined(X1,X2)
    | ~ identity_map(X1) ),
    inference(fof_simplification,[status(thm)],[identity1]) ).

cnf(c_0_28,hypothesis,
    ( defined(X1,a)
    | ~ product(X2,X1,g) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_29,axiom,
    product(X1,domain(X1),X1),
    product_on_domain ).

cnf(c_0_30,hypothesis,
    ( defined(X1,X2)
    | ~ product(X3,b,X2)
    | ~ product(X1,X3,a) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_31,plain,
    ( product(X1,X2,X2)
    | ~ defined(X1,X2)
    | ~ identity_map(X1) ),
    c_0_27 ).

cnf(c_0_32,hypothesis,
    defined(domain(g),a),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_33,axiom,
    identity_map(domain(X1)),
    domain_is_an_identity_map ).

cnf(c_0_34,plain,
    ( defined(X4,X1)
    | ~ product(X1,X2,X3)
    | ~ defined(X4,X3) ),
    inference(fof_simplification,[status(thm)],[category_theory_axiom3]) ).

cnf(c_0_35,hypothesis,
    product(h,a,d),
    ha_equals_d ).

cnf(c_0_36,plain,
    ( defined(X1,X3)
    | ~ defined(X1,X2)
    | ~ defined(X2,X3)
    | ~ identity_map(X2) ),
    inference(fof_simplification,[status(thm)],[category_theory_axiom6]) ).

cnf(c_0_37,hypothesis,
    ( defined(X1,c)
    | ~ product(X1,a,a) ),
    inference(spm,[status(thm)],[c_0_30,c_0_22]) ).

cnf(c_0_38,hypothesis,
    product(domain(g),a,a),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).

cnf(c_0_39,plain,
    ( defined(X4,X1)
    | ~ product(X1,X2,X3)
    | ~ defined(X4,X3) ),
    c_0_34 ).

cnf(c_0_40,hypothesis,
    defined(h,a),
    inference(spm,[status(thm)],[c_0_19,c_0_35]) ).

cnf(c_0_41,plain,
    ( defined(X1,X3)
    | ~ defined(X1,X2)
    | ~ defined(X2,X3)
    | ~ identity_map(X2) ),
    c_0_36 ).

cnf(c_0_42,hypothesis,
    defined(domain(g),c),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_43,hypothesis,
    ( defined(h,X1)
    | ~ product(X1,X2,a) ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_44,plain,
    ( product(X1,X2,compose(X1,X2))
    | ~ defined(X1,X2) ),
    inference(fof_simplification,[status(thm)],[closure_of_composition]) ).

cnf(c_0_45,hypothesis,
    ( defined(X1,c)
    | ~ defined(X1,domain(g)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_33])]) ).

cnf(c_0_46,hypothesis,
    defined(h,domain(g)),
    inference(spm,[status(thm)],[c_0_43,c_0_38]) ).

cnf(c_0_47,plain,
    ( product(X6,X2,X5)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X3,X5)
    | ~ product(X4,X1,X6) ),
    inference(fof_simplification,[status(thm)],[category_theory_axiom5]) ).

cnf(c_0_48,plain,
    ( product(X1,X2,compose(X1,X2))
    | ~ defined(X1,X2) ),
    c_0_44 ).

cnf(c_0_49,hypothesis,
    defined(h,c),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

cnf(c_0_50,axiom,
    defined(X1,domain(X1)),
    mapping_from_x_to_its_domain ).

cnf(c_0_51,plain,
    ( product(X6,X2,X5)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X3,X5)
    | ~ product(X4,X1,X6) ),
    c_0_47 ).

cnf(c_0_52,hypothesis,
    product(h,c,compose(h,c)),
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_53,hypothesis,
    defined(g,c),
    inference(spm,[status(thm)],[c_0_45,c_0_50]) ).

cnf(c_0_54,hypothesis,
    ( product(X1,X2,compose(h,c))
    | ~ product(h,X3,X1)
    | ~ product(X3,X2,c) ),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_55,hypothesis,
    product(g,c,compose(g,c)),
    inference(spm,[status(thm)],[c_0_48,c_0_53]) ).

cnf(c_0_56,plain,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    inference(fof_simplification,[status(thm)],[composition_is_well_defined]) ).

cnf(c_0_57,hypothesis,
    ( product(d,X1,compose(h,c))
    | ~ product(a,X1,c) ),
    inference(spm,[status(thm)],[c_0_54,c_0_35]) ).

cnf(c_0_58,hypothesis,
    ( product(X1,X2,compose(g,c))
    | ~ product(g,X3,X1)
    | ~ product(X3,X2,c) ),
    inference(spm,[status(thm)],[c_0_51,c_0_55]) ).

cnf(c_0_59,plain,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    c_0_56 ).

cnf(c_0_60,hypothesis,
    product(d,b,compose(h,c)),
    inference(spm,[status(thm)],[c_0_57,c_0_22]) ).

cnf(c_0_61,hypothesis,
    ( product(d,X1,compose(g,c))
    | ~ product(a,X1,c) ),
    inference(spm,[status(thm)],[c_0_58,c_0_20]) ).

cnf(c_0_62,hypothesis,
    ( X1 = X3
    | ~ product(X1,c,X2)
    | ~ product(X3,c,X2) ),
    inference(fof_simplification,[status(thm)],[cancellation_for_product]) ).

cnf(c_0_63,hypothesis,
    ( X1 = compose(h,c)
    | ~ product(d,b,X1) ),
    inference(spm,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_64,hypothesis,
    product(d,b,compose(g,c)),
    inference(spm,[status(thm)],[c_0_61,c_0_22]) ).

cnf(c_0_65,hypothesis,
    ( X1 = X3
    | ~ product(X1,c,X2)
    | ~ product(X3,c,X2) ),
    c_0_62 ).

cnf(c_0_66,hypothesis,
    compose(g,c) = compose(h,c),
    inference(spm,[status(thm)],[c_0_63,c_0_64]) ).

cnf(c_0_67,negated_conjecture,
    h != g,
    inference(fof_simplification,[status(thm)],[prove_h_equals_g]) ).

cnf(c_0_68,hypothesis,
    ( X1 = h
    | ~ product(X1,c,compose(h,c)) ),
    inference(spm,[status(thm)],[c_0_65,c_0_52]) ).

cnf(c_0_69,hypothesis,
    product(g,c,compose(h,c)),
    inference(rw,[status(thm)],[c_0_55,c_0_66]) ).

cnf(c_0_70,negated_conjecture,
    h != g,
    c_0_67 ).

cnf(c_0_71,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem    : CAT003-1 : TPTP v8.2.0. Released v1.0.0.
% 0.10/0.12  % Command    : run_E %s %d THM
% 0.11/0.32  % Computer : n027.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Sat May 18 11:38:23 EDT 2024
% 0.11/0.33  % CPUTime    : 
% 0.17/0.45  Running first-order theorem proving
% 0.17/0.45  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.08/1.62  # Version: 3.1.0
% 9.08/1.62  # Preprocessing class: FSMSSMSSSSSNFFN.
% 9.08/1.62  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.08/1.62  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 9.08/1.62  # Starting new_bool_3 with 300s (1) cores
% 9.08/1.62  # Starting new_bool_1 with 300s (1) cores
% 9.08/1.62  # Starting sh5l with 300s (1) cores
% 9.08/1.62  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 16680 completed with status 0
% 9.08/1.62  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 9.08/1.62  # Preprocessing class: FSMSSMSSSSSNFFN.
% 9.08/1.62  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.08/1.62  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 9.08/1.62  # No SInE strategy applied
% 9.08/1.62  # Search class: FHUSM-FFSS21-SFFFFFNN
% 9.08/1.62  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 9.08/1.62  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 811s (1) cores
% 9.08/1.62  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 9.08/1.62  # Starting new_bool_3 with 136s (1) cores
% 9.08/1.62  # Starting new_bool_1 with 136s (1) cores
% 9.08/1.62  # Starting sh5l with 136s (1) cores
% 9.08/1.62  # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 16684 completed with status 0
% 9.08/1.62  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 9.08/1.62  # Preprocessing class: FSMSSMSSSSSNFFN.
% 9.08/1.62  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.08/1.62  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 9.08/1.62  # No SInE strategy applied
% 9.08/1.62  # Search class: FHUSM-FFSS21-SFFFFFNN
% 9.08/1.62  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 9.08/1.62  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 811s (1) cores
% 9.08/1.62  # Preprocessing time       : 0.001 s
% 9.08/1.62  # Presaturation interreduction done
% 9.08/1.62  
% 9.08/1.62  # Proof found!
% 9.08/1.62  # SZS status Unsatisfiable
% 9.08/1.62  # SZS output start CNFRefutation
% See solution above
% 9.08/1.62  # Parsed axioms                        : 23
% 9.08/1.62  # Removed by relevancy pruning/SinE    : 0
% 9.08/1.62  # Initial clauses                      : 23
% 9.08/1.62  # Removed in clause preprocessing      : 0
% 9.08/1.62  # Initial clauses in saturation        : 23
% 9.08/1.62  # Processed clauses                    : 11480
% 9.08/1.62  # ...of these trivial                  : 639
% 9.08/1.62  # ...subsumed                          : 6895
% 9.08/1.62  # ...remaining for further processing  : 3946
% 9.08/1.62  # Other redundant clauses eliminated   : 0
% 9.08/1.62  # Clauses deleted for lack of memory   : 0
% 9.08/1.62  # Backward-subsumed                    : 47
% 9.08/1.62  # Backward-rewritten                   : 1965
% 9.08/1.62  # Generated clauses                    : 31604
% 9.08/1.62  # ...of the previous two non-redundant : 24779
% 9.08/1.62  # ...aggressively subsumed             : 0
% 9.08/1.62  # Contextual simplify-reflections      : 0
% 9.08/1.62  # Paramodulations                      : 31604
% 9.08/1.62  # Factorizations                       : 0
% 9.08/1.62  # NegExts                              : 0
% 9.08/1.62  # Equation resolutions                 : 0
% 9.08/1.62  # Disequality decompositions           : 0
% 9.08/1.62  # Total rewrite steps                  : 30799
% 9.08/1.62  # ...of those cached                   : 29824
% 9.08/1.62  # Propositional unsat checks           : 0
% 9.08/1.62  #    Propositional check models        : 0
% 9.08/1.62  #    Propositional check unsatisfiable : 0
% 9.08/1.62  #    Propositional clauses             : 0
% 9.08/1.62  #    Propositional clauses after purity: 0
% 9.08/1.62  #    Propositional unsat core size     : 0
% 9.08/1.62  #    Propositional preprocessing time  : 0.000
% 9.08/1.62  #    Propositional encoding time       : 0.000
% 9.08/1.62  #    Propositional solver time         : 0.000
% 9.08/1.62  #    Success case prop preproc time    : 0.000
% 9.08/1.62  #    Success case prop encoding time   : 0.000
% 9.08/1.62  #    Success case prop solver time     : 0.000
% 9.08/1.62  # Current number of processed clauses  : 1911
% 9.08/1.62  #    Positive orientable unit clauses  : 116
% 9.08/1.62  #    Positive unorientable unit clauses: 0
% 9.08/1.62  #    Negative unit clauses             : 1
% 9.08/1.62  #    Non-unit-clauses                  : 1794
% 9.08/1.62  # Current number of unprocessed clauses: 9916
% 9.08/1.62  # ...number of literals in the above   : 21390
% 9.08/1.62  # Current number of archived formulas  : 0
% 9.08/1.62  # Current number of archived clauses   : 2035
% 9.08/1.62  # Clause-clause subsumption calls (NU) : 1223040
% 9.08/1.62  # Rec. Clause-clause subsumption calls : 1057639
% 9.08/1.62  # Non-unit clause-clause subsumptions  : 6942
% 9.08/1.62  # Unit Clause-clause subsumption calls : 2279
% 9.08/1.62  # Rewrite failures with RHS unbound    : 0
% 9.08/1.62  # BW rewrite match attempts            : 1451
% 9.08/1.62  # BW rewrite match successes           : 191
% 9.08/1.62  # Condensation attempts                : 0
% 9.08/1.62  # Condensation successes               : 0
% 9.08/1.62  # Termbank termtop insertions          : 394253
% 9.08/1.62  # Search garbage collected termcells   : 62
% 9.08/1.62  
% 9.08/1.62  # -------------------------------------------------
% 9.08/1.62  # User time                : 1.141 s
% 9.08/1.62  # System time              : 0.019 s
% 9.08/1.62  # Total time               : 1.159 s
% 9.08/1.62  # Maximum resident set size: 1644 pages
% 9.08/1.62  
% 9.08/1.62  # -------------------------------------------------
% 9.08/1.62  # User time                : 5.702 s
% 9.08/1.62  # System time              : 0.050 s
% 9.08/1.62  # Total time               : 5.752 s
% 9.08/1.62  # Maximum resident set size: 1716 pages
% 9.08/1.62  % E---3.1 exiting
% 9.08/1.62  % E exiting
%------------------------------------------------------------------------------