TSTP Solution File: REL012+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : REL012+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n005.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 : Mon Jul 18 19:19:10 EDT 2022

% Result   : Theorem 0.23s 1.41s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   77 (  77 unt;   0 def)
%            Number of atoms       :   77 (  76 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    4 (   4   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-2 aty)
%            Number of variables   :  109 (   2 sgn  42   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(converse_multiplicativity,axiom,
    ! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).

fof(converse_idempotence,axiom,
    ! [X1] : converse(converse(X1)) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).

fof(composition_identity,axiom,
    ! [X1] : composition(X1,one) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_identity) ).

fof(def_zero,axiom,
    ! [X1] : zero = meet(X1,complement(X1)),
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',def_zero) ).

fof(maddux4_definiton_of_meet,axiom,
    ! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux4_definiton_of_meet) ).

fof(converse_cancellativity,axiom,
    ! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).

fof(maddux1_join_commutativity,axiom,
    ! [X1,X2] : join(X1,X2) = join(X2,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).

fof(maddux3_a_kind_of_de_Morgan,axiom,
    ! [X1,X2] : X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux3_a_kind_of_de_Morgan) ).

fof(def_top,axiom,
    ! [X1] : top = join(X1,complement(X1)),
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',def_top) ).

fof(maddux2_join_associativity,axiom,
    ! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux2_join_associativity) ).

fof(converse_additivity,axiom,
    ! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_additivity) ).

fof(goals,conjecture,
    ! [X1,X2] : join(composition(complement(composition(X1,X2)),converse(X2)),complement(X1)) = complement(X1),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',goals) ).

fof(c_0_12,plain,
    ! [X3,X4] : converse(composition(X3,X4)) = composition(converse(X4),converse(X3)),
    inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).

fof(c_0_13,plain,
    ! [X2] : converse(converse(X2)) = X2,
    inference(variable_rename,[status(thm)],[converse_idempotence]) ).

cnf(c_0_14,plain,
    converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_15,plain,
    converse(converse(X1)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_16,plain,
    ! [X2] : composition(X2,one) = X2,
    inference(variable_rename,[status(thm)],[composition_identity]) ).

cnf(c_0_17,plain,
    converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_18,plain,
    composition(X1,one) = X1,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_19,plain,
    ! [X2] : zero = meet(X2,complement(X2)),
    inference(variable_rename,[status(thm)],[def_zero]) ).

fof(c_0_20,plain,
    ! [X3,X4] : meet(X3,X4) = complement(join(complement(X3),complement(X4))),
    inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).

fof(c_0_21,plain,
    ! [X3,X4] : join(composition(converse(X3),complement(composition(X3,X4))),complement(X4)) = complement(X4),
    inference(variable_rename,[status(thm)],[converse_cancellativity]) ).

fof(c_0_22,plain,
    ! [X3,X4] : join(X3,X4) = join(X4,X3),
    inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).

cnf(c_0_23,plain,
    composition(converse(one),X1) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_15]) ).

fof(c_0_24,plain,
    ! [X3,X4] : X3 = join(complement(join(complement(X3),complement(X4))),complement(join(complement(X3),X4))),
    inference(variable_rename,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).

cnf(c_0_25,plain,
    zero = meet(X1,complement(X1)),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_26,plain,
    meet(X1,X2) = complement(join(complement(X1),complement(X2))),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

fof(c_0_27,plain,
    ! [X2] : top = join(X2,complement(X2)),
    inference(variable_rename,[status(thm)],[def_top]) ).

cnf(c_0_28,plain,
    join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_29,plain,
    join(X1,X2) = join(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_30,plain,
    converse(one) = one,
    inference(spm,[status(thm)],[c_0_18,c_0_23]) ).

cnf(c_0_31,plain,
    X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

fof(c_0_32,plain,
    ! [X4,X5,X6] : join(X4,join(X5,X6)) = join(join(X4,X5),X6),
    inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).

cnf(c_0_33,plain,
    zero = complement(join(complement(X1),complement(complement(X1)))),
    inference(rw,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_34,plain,
    top = join(X1,complement(X1)),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_35,plain,
    join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
    inference(rw,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_36,plain,
    composition(one,X1) = X1,
    inference(rw,[status(thm)],[c_0_23,c_0_30]) ).

cnf(c_0_37,plain,
    join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
    inference(rw,[status(thm)],[c_0_31,c_0_29]) ).

cnf(c_0_38,plain,
    join(X1,join(X2,X3)) = join(join(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_39,plain,
    complement(top) = zero,
    inference(rw,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_40,plain,
    join(complement(X1),complement(X1)) = complement(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_30]),c_0_36]) ).

cnf(c_0_41,plain,
    join(complement(X1),complement(join(complement(X1),join(complement(X2),complement(join(complement(X1),X2)))))) = join(complement(X1),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_37]),c_0_29]),c_0_38]),c_0_29]) ).

cnf(c_0_42,plain,
    join(zero,complement(complement(X1))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_34]),c_0_39]),c_0_40]),c_0_29]) ).

cnf(c_0_43,plain,
    join(zero,complement(X1)) = complement(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_40]),c_0_40]),c_0_34]),c_0_39]),c_0_29]) ).

fof(c_0_44,plain,
    ! [X3,X4] : converse(join(X3,X4)) = join(converse(X3),converse(X4)),
    inference(variable_rename,[status(thm)],[converse_additivity]) ).

cnf(c_0_45,plain,
    complement(complement(X1)) = X1,
    inference(rw,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_46,plain,
    converse(join(X1,X2)) = join(converse(X1),converse(X2)),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_47,plain,
    join(X1,join(X2,complement(join(X1,X2)))) = top,
    inference(spm,[status(thm)],[c_0_34,c_0_38]) ).

cnf(c_0_48,plain,
    join(X1,X1) = X1,
    inference(spm,[status(thm)],[c_0_40,c_0_45]) ).

cnf(c_0_49,plain,
    converse(join(converse(X1),X2)) = join(X1,converse(X2)),
    inference(spm,[status(thm)],[c_0_46,c_0_15]) ).

cnf(c_0_50,plain,
    join(X1,top) = top,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_34]) ).

cnf(c_0_51,plain,
    join(X1,converse(complement(converse(X1)))) = converse(top),
    inference(spm,[status(thm)],[c_0_49,c_0_34]) ).

cnf(c_0_52,plain,
    join(top,X1) = top,
    inference(spm,[status(thm)],[c_0_29,c_0_50]) ).

cnf(c_0_53,plain,
    converse(top) = top,
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_54,plain,
    join(X1,converse(complement(converse(X1)))) = top,
    inference(rw,[status(thm)],[c_0_51,c_0_53]) ).

cnf(c_0_55,plain,
    join(zero,X1) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_34]),c_0_39]),c_0_45]),c_0_48]),c_0_45]) ).

cnf(c_0_56,plain,
    complement(join(complement(X1),complement(converse(complement(converse(complement(X1))))))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_54]),c_0_39]),c_0_55]) ).

cnf(c_0_57,plain,
    complement(join(X1,complement(converse(complement(converse(X1)))))) = complement(X1),
    inference(spm,[status(thm)],[c_0_56,c_0_45]) ).

cnf(c_0_58,plain,
    join(X1,complement(converse(complement(converse(X1))))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_57]),c_0_37]) ).

cnf(c_0_59,plain,
    join(converse(X1),complement(converse(complement(X1)))) = converse(X1),
    inference(spm,[status(thm)],[c_0_58,c_0_15]) ).

cnf(c_0_60,plain,
    join(X1,converse(complement(converse(complement(X1))))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_58]),c_0_15]),c_0_15]) ).

cnf(c_0_61,plain,
    join(complement(converse(X1)),converse(complement(X1))) = converse(complement(X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_45]),c_0_29]) ).

cnf(c_0_62,plain,
    join(complement(X1),converse(complement(converse(X1)))) = complement(X1),
    inference(spm,[status(thm)],[c_0_60,c_0_45]) ).

cnf(c_0_63,plain,
    converse(complement(converse(X1))) = complement(X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_15]),c_0_62]) ).

fof(c_0_64,negated_conjecture,
    ~ ! [X1,X2] : join(composition(complement(composition(X1,X2)),converse(X2)),complement(X1)) = complement(X1),
    inference(assume_negation,[status(cth)],[goals]) ).

cnf(c_0_65,plain,
    join(complement(X1),composition(X2,complement(composition(converse(X2),X1)))) = complement(X1),
    inference(spm,[status(thm)],[c_0_35,c_0_15]) ).

cnf(c_0_66,plain,
    converse(complement(X1)) = complement(converse(X1)),
    inference(spm,[status(thm)],[c_0_15,c_0_63]) ).

cnf(c_0_67,plain,
    converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

fof(c_0_68,negated_conjecture,
    join(composition(complement(composition(esk1_0,esk2_0)),converse(esk2_0)),complement(esk1_0)) != complement(esk1_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])]) ).

cnf(c_0_69,plain,
    join(X1,composition(X2,complement(composition(converse(X2),complement(X1))))) = X1,
    inference(spm,[status(thm)],[c_0_65,c_0_45]) ).

cnf(c_0_70,plain,
    composition(converse(X1),complement(converse(X2))) = converse(composition(complement(X2),X1)),
    inference(spm,[status(thm)],[c_0_14,c_0_66]) ).

cnf(c_0_71,plain,
    converse(composition(X1,complement(converse(X2)))) = composition(complement(X2),converse(X1)),
    inference(spm,[status(thm)],[c_0_67,c_0_66]) ).

cnf(c_0_72,negated_conjecture,
    join(composition(complement(composition(esk1_0,esk2_0)),converse(esk2_0)),complement(esk1_0)) != complement(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_68]) ).

cnf(c_0_73,plain,
    join(X1,composition(complement(composition(complement(X1),X2)),converse(X2))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_69]),c_0_15]),c_0_70]),c_0_71]) ).

cnf(c_0_74,negated_conjecture,
    join(complement(esk1_0),composition(complement(composition(esk1_0,esk2_0)),converse(esk2_0))) != complement(esk1_0),
    inference(rw,[status(thm)],[c_0_72,c_0_29]) ).

cnf(c_0_75,plain,
    join(complement(X1),composition(complement(composition(X1,X2)),converse(X2))) = complement(X1),
    inference(spm,[status(thm)],[c_0_73,c_0_45]) ).

cnf(c_0_76,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : REL012+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : run_ET %s %d
% 0.12/0.34  % Computer : n005.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Fri Jul  8 10:04:07 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.23/1.41  # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.23/1.41  # Preprocessing time       : 0.014 s
% 0.23/1.41  
% 0.23/1.41  # Proof found!
% 0.23/1.41  # SZS status Theorem
% 0.23/1.41  # SZS output start CNFRefutation
% See solution above
% 0.23/1.41  # Proof object total steps             : 77
% 0.23/1.41  # Proof object clause steps            : 52
% 0.23/1.41  # Proof object formula steps           : 25
% 0.23/1.41  # Proof object conjectures             : 6
% 0.23/1.41  # Proof object clause conjectures      : 3
% 0.23/1.41  # Proof object formula conjectures     : 3
% 0.23/1.41  # Proof object initial clauses used    : 12
% 0.23/1.41  # Proof object initial formulas used   : 12
% 0.23/1.41  # Proof object generating inferences   : 31
% 0.23/1.41  # Proof object simplifying inferences  : 38
% 0.23/1.41  # Training examples: 0 positive, 0 negative
% 0.23/1.41  # Parsed axioms                        : 14
% 0.23/1.41  # Removed by relevancy pruning/SinE    : 0
% 0.23/1.41  # Initial clauses                      : 14
% 0.23/1.41  # Removed in clause preprocessing      : 1
% 0.23/1.41  # Initial clauses in saturation        : 13
% 0.23/1.41  # Processed clauses                    : 2586
% 0.23/1.41  # ...of these trivial                  : 1577
% 0.23/1.41  # ...subsumed                          : 302
% 0.23/1.41  # ...remaining for further processing  : 707
% 0.23/1.41  # Other redundant clauses eliminated   : 0
% 0.23/1.41  # Clauses deleted for lack of memory   : 0
% 0.23/1.41  # Backward-subsumed                    : 0
% 0.23/1.41  # Backward-rewritten                   : 214
% 0.23/1.41  # Generated clauses                    : 68837
% 0.23/1.41  # ...of the previous two non-trivial   : 37754
% 0.23/1.41  # Contextual simplify-reflections      : 0
% 0.23/1.41  # Paramodulations                      : 68837
% 0.23/1.41  # Factorizations                       : 0
% 0.23/1.41  # Equation resolutions                 : 0
% 0.23/1.41  # Current number of processed clauses  : 493
% 0.23/1.41  #    Positive orientable unit clauses  : 486
% 0.23/1.41  #    Positive unorientable unit clauses: 7
% 0.23/1.41  #    Negative unit clauses             : 0
% 0.23/1.41  #    Non-unit-clauses                  : 0
% 0.23/1.41  # Current number of unprocessed clauses: 30374
% 0.23/1.41  # ...number of literals in the above   : 30374
% 0.23/1.41  # Current number of archived formulas  : 0
% 0.23/1.41  # Current number of archived clauses   : 215
% 0.23/1.41  # Clause-clause subsumption calls (NU) : 0
% 0.23/1.41  # Rec. Clause-clause subsumption calls : 0
% 0.23/1.41  # Non-unit clause-clause subsumptions  : 0
% 0.23/1.41  # Unit Clause-clause subsumption calls : 43
% 0.23/1.41  # Rewrite failures with RHS unbound    : 0
% 0.23/1.41  # BW rewrite match attempts            : 2754
% 0.23/1.41  # BW rewrite match successes           : 258
% 0.23/1.41  # Condensation attempts                : 0
% 0.23/1.41  # Condensation successes               : 0
% 0.23/1.41  # Termbank termtop insertions          : 1210235
% 0.23/1.41  
% 0.23/1.41  # -------------------------------------------------
% 0.23/1.41  # User time                : 0.591 s
% 0.23/1.41  # System time              : 0.023 s
% 0.23/1.41  # Total time               : 0.614 s
% 0.23/1.41  # Maximum resident set size: 49016 pages
% 0.23/23.41  eprover: CPU time limit exceeded, terminating
% 0.23/23.42  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.42  eprover: No such file or directory
% 0.23/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.43  eprover: No such file or directory
% 0.23/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.43  eprover: No such file or directory
% 0.23/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.44  eprover: No such file or directory
% 0.23/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.44  eprover: No such file or directory
% 0.23/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.45  eprover: No such file or directory
% 0.23/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.46  eprover: No such file or directory
% 0.23/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.46  eprover: No such file or directory
% 0.23/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.47  eprover: No such file or directory
% 0.23/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.47  eprover: No such file or directory
% 0.23/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.48  eprover: No such file or directory
%------------------------------------------------------------------------------