TSTP Solution File: REL004+2 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : REL004+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n022.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 19:18:54 EDT 2022
% Result : Theorem 0.23s 1.41s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 12
% Syntax : Number of formulae : 84 ( 84 unt; 0 def)
% Number of atoms : 84 ( 83 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 124 ( 13 sgn 40 !; 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(composition_identity,axiom,
! [X1] : composition(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_identity) ).
fof(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
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(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(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(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_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(goals,conjecture,
! [X1] : converse(complement(X1)) = complement(converse(X1)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',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] : composition(X2,one) = X2,
inference(variable_rename,[status(thm)],[composition_identity]) ).
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,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_16,plain,
! [X2] : converse(converse(X2)) = X2,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
cnf(c_0_17,plain,
composition(converse(one),converse(X1)) = converse(X1),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_19,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_20,plain,
! [X3,X4] : join(X3,X4) = join(X4,X3),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_0_21,plain,
composition(converse(one),X1) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_22,plain,
! [X3,X4] : converse(join(X3,X4)) = join(converse(X3),converse(X4)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
cnf(c_0_23,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_15,c_0_21]) ).
fof(c_0_26,plain,
! [X2] : top = join(X2,complement(X2)),
inference(variable_rename,[status(thm)],[def_top]) ).
cnf(c_0_27,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_28,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_29,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_21,c_0_25]) ).
cnf(c_0_31,plain,
top = join(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
join(converse(X1),X2) = converse(join(X1,converse(X2))),
inference(spm,[status(thm)],[c_0_27,c_0_18]) ).
cnf(c_0_33,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_25]),c_0_30]) ).
cnf(c_0_35,plain,
converse(join(X1,converse(complement(converse(X1))))) = top,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
join(complement(X1),join(complement(X1),X2)) = join(complement(X1),X2),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(spm,[status(thm)],[c_0_18,c_0_35]) ).
fof(c_0_38,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_39,plain,
converse(join(top,converse(complement(X1)))) = converse(top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_24]),c_0_32]) ).
fof(c_0_40,plain,
! [X2] : zero = meet(X2,complement(X2)),
inference(variable_rename,[status(thm)],[def_zero]) ).
fof(c_0_41,plain,
! [X3,X4] : meet(X3,X4) = complement(join(complement(X3),complement(X4))),
inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_0_42,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_43,plain,
converse(join(X1,converse(X2))) = join(X2,converse(X1)),
inference(spm,[status(thm)],[c_0_24,c_0_32]) ).
cnf(c_0_44,plain,
converse(top) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_37]),c_0_18]) ).
cnf(c_0_45,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_46,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_47,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[c_0_42,c_0_24]) ).
cnf(c_0_48,plain,
join(X1,join(X2,complement(join(X1,X2)))) = top,
inference(spm,[status(thm)],[c_0_31,c_0_33]) ).
cnf(c_0_49,plain,
converse(join(top,converse(X1))) = join(X1,top),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_31]),c_0_24]) ).
cnf(c_0_51,plain,
zero = complement(join(complement(X1),complement(complement(X1)))),
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_47]),c_0_24]) ).
cnf(c_0_53,plain,
join(X1,top) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_54,plain,
complement(top) = zero,
inference(rw,[status(thm)],[c_0_51,c_0_31]) ).
cnf(c_0_55,plain,
join(X1,zero) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).
cnf(c_0_56,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_47,c_0_31]),c_0_54]),c_0_34]),c_0_24]) ).
cnf(c_0_57,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_55]) ).
cnf(c_0_58,plain,
join(complement(complement(X1)),complement(join(complement(X1),complement(composition(converse(X2),complement(composition(X2,X1))))))) = X1,
inference(spm,[status(thm)],[c_0_47,c_0_29]) ).
cnf(c_0_59,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_60,plain,
join(X1,complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_58]),c_0_24]) ).
cnf(c_0_61,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_24]),c_0_33]) ).
cnf(c_0_62,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(rw,[status(thm)],[c_0_37,c_0_44]) ).
cnf(c_0_63,plain,
join(complement(X1),complement(join(X1,X2))) = complement(X1),
inference(spm,[status(thm)],[c_0_52,c_0_59]) ).
cnf(c_0_64,plain,
converse(join(X1,converse(complement(join(complement(converse(X1)),X2))))) = converse(X1),
inference(spm,[status(thm)],[c_0_32,c_0_52]) ).
cnf(c_0_65,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_24,c_0_33]) ).
cnf(c_0_66,plain,
join(X1,X1) = X1,
inference(rw,[status(thm)],[c_0_60,c_0_59]) ).
cnf(c_0_67,plain,
join(X1,join(X2,converse(complement(converse(X1))))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_53]) ).
cnf(c_0_68,plain,
join(complement(X1),complement(converse(join(X2,converse(X1))))) = complement(X1),
inference(spm,[status(thm)],[c_0_63,c_0_43]) ).
cnf(c_0_69,plain,
join(X1,converse(complement(join(complement(converse(X1)),X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_64]),c_0_18]) ).
cnf(c_0_70,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_71,plain,
complement(join(complement(X1),complement(join(X2,converse(complement(converse(complement(X1)))))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_67]),c_0_54]),c_0_57]) ).
cnf(c_0_72,plain,
join(complement(converse(X1)),complement(converse(join(X2,X1)))) = complement(converse(X1)),
inference(spm,[status(thm)],[c_0_68,c_0_18]) ).
cnf(c_0_73,plain,
join(X1,converse(complement(join(X2,complement(converse(X1)))))) = X1,
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_74,plain,
complement(join(complement(X1),complement(converse(complement(converse(complement(X1))))))) = X1,
inference(spm,[status(thm)],[c_0_71,c_0_57]) ).
cnf(c_0_75,plain,
join(complement(converse(X1)),complement(converse(join(X1,X2)))) = complement(converse(X1)),
inference(spm,[status(thm)],[c_0_72,c_0_24]) ).
cnf(c_0_76,plain,
converse(join(X1,converse(complement(converse(complement(X1)))))) = complement(converse(complement(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_24]),c_0_32]) ).
fof(c_0_77,negated_conjecture,
~ ! [X1] : converse(complement(X1)) = complement(converse(X1)),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_78,plain,
converse(join(complement(X1),converse(complement(converse(X1))))) = complement(converse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_59]),c_0_24]),c_0_32]) ).
fof(c_0_79,negated_conjecture,
converse(complement(esk1_0)) != complement(converse(esk1_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_77])])]) ).
cnf(c_0_80,plain,
converse(complement(converse(X1))) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_18]),c_0_24]),c_0_32]),c_0_78]) ).
cnf(c_0_81,negated_conjecture,
converse(complement(esk1_0)) != complement(converse(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_82,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_80]),c_0_66]) ).
cnf(c_0_83,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL004+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 07:48:56 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.23/1.41 # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a 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 : 84
% 0.23/1.41 # Proof object clause steps : 59
% 0.23/1.41 # Proof object formula steps : 25
% 0.23/1.41 # Proof object conjectures : 5
% 0.23/1.41 # Proof object clause conjectures : 2
% 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 : 37
% 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 : 17
% 0.23/1.41 # Removed by relevancy pruning/SinE : 0
% 0.23/1.41 # Initial clauses : 17
% 0.23/1.41 # Removed in clause preprocessing : 1
% 0.23/1.41 # Initial clauses in saturation : 16
% 0.23/1.41 # Processed clauses : 894
% 0.23/1.41 # ...of these trivial : 307
% 0.23/1.41 # ...subsumed : 303
% 0.23/1.41 # ...remaining for further processing : 284
% 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 : 130
% 0.23/1.41 # Generated clauses : 42380
% 0.23/1.41 # ...of the previous two non-trivial : 36777
% 0.23/1.41 # Contextual simplify-reflections : 0
% 0.23/1.41 # Paramodulations : 42380
% 0.23/1.41 # Factorizations : 0
% 0.23/1.41 # Equation resolutions : 0
% 0.23/1.41 # Current number of processed clauses : 154
% 0.23/1.41 # Positive orientable unit clauses : 103
% 0.23/1.41 # Positive unorientable unit clauses: 51
% 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: 20877
% 0.23/1.41 # ...number of literals in the above : 20877
% 0.23/1.41 # Current number of archived formulas : 0
% 0.23/1.41 # Current number of archived clauses : 131
% 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 : 1452
% 0.23/1.41 # Rewrite failures with RHS unbound : 0
% 0.23/1.41 # BW rewrite match attempts : 2118
% 0.23/1.41 # BW rewrite match successes : 556
% 0.23/1.41 # Condensation attempts : 0
% 0.23/1.41 # Condensation successes : 0
% 0.23/1.41 # Termbank termtop insertions : 1383422
% 0.23/1.41
% 0.23/1.41 # -------------------------------------------------
% 0.23/1.41 # User time : 0.629 s
% 0.23/1.41 # System time : 0.026 s
% 0.23/1.41 # Total time : 0.655 s
% 0.23/1.41 # Maximum resident set size: 55088 pages
%------------------------------------------------------------------------------