%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : REL031+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n020.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 19:19:45 EDT 2022
% Result : Theorem 0.21s 1.40s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 42 unt; 0 def)
% Number of atoms : 51 ( 50 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 10 ( 4 ~; 0 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X1,X2] :
( ( join(composition(converse(X1),X1),one) = one
& join(composition(converse(X2),X2),one) = one )
=> join(composition(converse(composition(X1,X2)),composition(X1,X2)),one) = one ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals) ).
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(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_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
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(composition_distributivity,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
fof(composition_associativity,axiom,
! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_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(c_0_9,negated_conjecture,
~ ! [X1,X2] :
( ( join(composition(converse(X1),X1),one) = one
& join(composition(converse(X2),X2),one) = one )
=> join(composition(converse(composition(X1,X2)),composition(X1,X2)),one) = one ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_10,plain,
! [X3,X4] : converse(composition(X3,X4)) = composition(converse(X4),converse(X3)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_11,plain,
! [X2] : composition(X2,one) = X2,
inference(variable_rename,[status(thm)],[composition_identity]) ).
fof(c_0_12,negated_conjecture,
( join(composition(converse(esk1_0),esk1_0),one) = one
& join(composition(converse(esk2_0),esk2_0),one) = one
& join(composition(converse(composition(esk1_0,esk2_0)),composition(esk1_0,esk2_0)),one) != one ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_13,plain,
! [X3,X4] : join(X3,X4) = join(X4,X3),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_0_14,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X2] : converse(converse(X2)) = X2,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
fof(c_0_17,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_18,negated_conjecture,
join(composition(converse(esk2_0),esk2_0),one) = one,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
composition(converse(one),converse(X1)) = converse(X1),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
join(one,composition(converse(esk2_0),esk2_0)) = one,
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_24,plain,
! [X4,X5,X6] : composition(join(X4,X5),X6) = join(composition(X4,X6),composition(X5,X6)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
fof(c_0_25,plain,
! [X4,X5,X6] : composition(X4,composition(X5,X6)) = composition(composition(X4,X5),X6),
inference(variable_rename,[status(thm)],[composition_associativity]) ).
cnf(c_0_26,plain,
composition(converse(one),X1) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_27,plain,
! [X3,X4] : converse(join(X3,X4)) = join(converse(X3),converse(X4)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
cnf(c_0_28,negated_conjecture,
join(one,join(composition(converse(esk2_0),esk2_0),X1)) = join(one,X1),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_15,c_0_26]) ).
cnf(c_0_32,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,negated_conjecture,
join(one,composition(join(converse(esk2_0),X1),esk2_0)) = join(one,composition(X1,esk2_0)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
join(composition(X1,composition(X2,X3)),composition(X4,X3)) = composition(join(composition(X1,X2),X4),X3),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_26,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
join(composition(converse(esk1_0),esk1_0),one) = one,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_37,negated_conjecture,
join(one,composition(converse(esk2_0),join(esk2_0,converse(X1)))) = join(one,composition(converse(esk2_0),converse(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_32]),c_0_31]),c_0_14]),c_0_31]),c_0_14]),c_0_32]),c_0_21]) ).
cnf(c_0_38,plain,
join(X1,composition(X2,composition(X3,X1))) = composition(join(one,composition(X2,X3)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_19]),c_0_19]) ).
cnf(c_0_39,negated_conjecture,
join(one,composition(converse(esk1_0),esk1_0)) = one,
inference(rw,[status(thm)],[c_0_36,c_0_19]) ).
cnf(c_0_40,negated_conjecture,
join(composition(converse(composition(esk1_0,esk2_0)),composition(esk1_0,esk2_0)),one) != one,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_41,negated_conjecture,
join(one,composition(converse(esk2_0),join(esk2_0,X1))) = join(one,composition(converse(esk2_0),X1)),
inference(spm,[status(thm)],[c_0_37,c_0_21]) ).
cnf(c_0_42,negated_conjecture,
join(X1,composition(converse(esk1_0),composition(esk1_0,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_35]) ).
cnf(c_0_43,negated_conjecture,
join(one,composition(converse(esk2_0),composition(converse(esk1_0),composition(esk1_0,esk2_0)))) != one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_19]),c_0_14]),c_0_30]) ).
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_23]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : REL031+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n020.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 11:45:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.21/1.40 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.21/1.40 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.21/1.40 # Preprocessing time : 0.015 s
% 0.21/1.40
% 0.21/1.40 # Proof found!
% 0.21/1.40 # SZS status Theorem
% 0.21/1.40 # SZS output start CNFRefutation
% See solution above
% 0.21/1.40 # Proof object total steps : 45
% 0.21/1.40 # Proof object clause steps : 26
% 0.21/1.40 # Proof object formula steps : 19
% 0.21/1.40 # Proof object conjectures : 15
% 0.21/1.40 # Proof object clause conjectures : 12
% 0.21/1.40 # Proof object formula conjectures : 3
% 0.21/1.40 # Proof object initial clauses used : 11
% 0.21/1.40 # Proof object initial formulas used : 9
% 0.21/1.40 # Proof object generating inferences : 11
% 0.21/1.40 # Proof object simplifying inferences : 18
% 0.21/1.40 # Training examples: 0 positive, 0 negative
% 0.21/1.40 # Parsed axioms : 14
% 0.21/1.40 # Removed by relevancy pruning/SinE : 3
% 0.21/1.40 # Initial clauses : 13
% 0.21/1.40 # Removed in clause preprocessing : 0
% 0.21/1.40 # Initial clauses in saturation : 13
% 0.21/1.40 # Processed clauses : 163
% 0.21/1.40 # ...of these trivial : 42
% 0.21/1.40 # ...subsumed : 30
% 0.21/1.40 # ...remaining for further processing : 91
% 0.21/1.40 # Other redundant clauses eliminated : 0
% 0.21/1.40 # Clauses deleted for lack of memory : 0
% 0.21/1.40 # Backward-subsumed : 0
% 0.21/1.40 # Backward-rewritten : 12
% 0.21/1.40 # Generated clauses : 1808
% 0.21/1.40 # ...of the previous two non-trivial : 1556
% 0.21/1.40 # Contextual simplify-reflections : 0
% 0.21/1.40 # Paramodulations : 1808
% 0.21/1.40 # Factorizations : 0
% 0.21/1.40 # Equation resolutions : 0
% 0.21/1.40 # Current number of processed clauses : 79
% 0.21/1.40 # Positive orientable unit clauses : 68
% 0.21/1.40 # Positive unorientable unit clauses: 10
% 0.21/1.40 # Negative unit clauses : 1
% 0.21/1.40 # Non-unit-clauses : 0
% 0.21/1.40 # Current number of unprocessed clauses: 1317
% 0.21/1.40 # ...number of literals in the above : 1317
% 0.21/1.40 # Current number of archived formulas : 0
% 0.21/1.40 # Current number of archived clauses : 12
% 0.21/1.40 # Clause-clause subsumption calls (NU) : 0
% 0.21/1.40 # Rec. Clause-clause subsumption calls : 0
% 0.21/1.40 # Non-unit clause-clause subsumptions : 0
% 0.21/1.40 # Unit Clause-clause subsumption calls : 24
% 0.21/1.40 # Rewrite failures with RHS unbound : 0
% 0.21/1.40 # BW rewrite match attempts : 171
% 0.21/1.40 # BW rewrite match successes : 50
% 0.21/1.40 # Condensation attempts : 0
% 0.21/1.40 # Condensation successes : 0
% 0.21/1.40 # Termbank termtop insertions : 30215
% 0.21/1.40
% 0.21/1.40 # -------------------------------------------------
% 0.21/1.40 # User time : 0.050 s
% 0.21/1.40 # System time : 0.003 s
% 0.21/1.40 # Total time : 0.053 s
% 0.21/1.40 # Maximum resident set size: 4660 pages
%------------------------------------------------------------------------------