TSTP Solution File: GRP682+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : GRP682+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n017.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 : Sat Jul 16 09:03:17 EDT 2022
% Result : Theorem 0.24s 1.42s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 66 ( 60 unt; 0 def)
% Number of atoms : 72 ( 71 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 10 ~; 4 |; 2 &)
% ( 0 <=>; 0 =>; 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 138 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f02,axiom,
! [X1] : rd(mult(X1,X1),X1) = X1,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',f02) ).
fof(f04,axiom,
! [X2,X1] : mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',f04) ).
fof(f07,axiom,
! [X2,X1] : ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',f07) ).
fof(f03,axiom,
! [X2,X1] : mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',f03) ).
fof(f01,axiom,
! [X1] : ld(X1,mult(X1,X1)) = X1,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',f01) ).
fof(f05,axiom,
! [X3,X4,X2,X1] : ld(ld(X1,X2),mult(ld(X1,X2),mult(X4,X3))) = mult(ld(X1,mult(X1,X4)),X3),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',f05) ).
fof(f06,axiom,
! [X3,X4,X2,X1] : rd(mult(mult(X1,X2),rd(X4,X3)),rd(X4,X3)) = mult(X1,rd(mult(X2,X3),X3)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',f06) ).
fof(goals,conjecture,
! [X5,X6,X7] :
( ld(ld(X5,X6),mult(ld(X5,X6),X7)) = ld(X5,mult(X5,X7))
& ld(rd(X5,X6),mult(rd(X5,X6),X7)) = ld(X5,mult(X5,X7)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals) ).
fof(c_0_8,plain,
! [X2] : rd(mult(X2,X2),X2) = X2,
inference(variable_rename,[status(thm)],[f02]) ).
fof(c_0_9,plain,
! [X3,X4] : mult(rd(X4,X3),X3) = rd(mult(X4,X3),X3),
inference(variable_rename,[status(thm)],[f04]) ).
fof(c_0_10,plain,
! [X3,X4] : ld(X4,mult(X4,ld(X3,X3))) = rd(mult(rd(X4,X4),X3),X3),
inference(variable_rename,[status(thm)],[f07]) ).
fof(c_0_11,plain,
! [X3,X4] : mult(X4,ld(X4,X3)) = ld(X4,mult(X4,X3)),
inference(variable_rename,[status(thm)],[f03]) ).
fof(c_0_12,plain,
! [X2] : ld(X2,mult(X2,X2)) = X2,
inference(variable_rename,[status(thm)],[f01]) ).
fof(c_0_13,plain,
! [X5,X6,X7,X8] : ld(ld(X8,X7),mult(ld(X8,X7),mult(X6,X5))) = mult(ld(X8,mult(X8,X6)),X5),
inference(variable_rename,[status(thm)],[f05]) ).
cnf(c_0_14,plain,
rd(mult(X1,X1),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
ld(X1,mult(X1,X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
ld(ld(X1,X2),mult(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
mult(rd(X1,X1),X1) = X1,
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
mult(rd(rd(X1,X1),X2),X2) = mult(X1,ld(X1,ld(X2,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_15]),c_0_17]) ).
cnf(c_0_22,plain,
mult(X1,ld(X1,X1)) = X1,
inference(rw,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_23,plain,
mult(ld(X1,X2),ld(ld(X1,X2),mult(X3,X4))) = mult(mult(X1,ld(X1,X3)),X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_17]),c_0_17]) ).
fof(c_0_24,plain,
! [X5,X6,X7,X8] : rd(mult(mult(X8,X7),rd(X6,X5)),rd(X6,X5)) = mult(X8,rd(mult(X7,X5),X5)),
inference(variable_rename,[status(thm)],[f06]) ).
cnf(c_0_25,plain,
rd(X1,X1) = mult(X1,ld(X1,ld(X1,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_20]),c_0_21]) ).
cnf(c_0_26,plain,
mult(X1,ld(X1,ld(X1,X1))) = ld(X1,X1),
inference(spm,[status(thm)],[c_0_17,c_0_22]) ).
cnf(c_0_27,plain,
mult(mult(X1,ld(X1,X2)),ld(mult(X1,ld(X1,X2)),mult(X3,X4))) = mult(mult(X1,ld(X1,X3)),X4),
inference(spm,[status(thm)],[c_0_23,c_0_17]) ).
cnf(c_0_28,plain,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
mult(ld(X1,X1),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_25]),c_0_26]) ).
cnf(c_0_30,plain,
mult(X1,ld(X1,mult(X2,X3))) = mult(mult(X1,ld(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_27,c_0_22]) ).
cnf(c_0_31,plain,
mult(rd(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,mult(rd(X2,X4),X4)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_15]),c_0_15]) ).
cnf(c_0_32,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(mult(X1,ld(X1,ld(X3,X3))),X3),
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_33,plain,
mult(mult(X1,ld(X1,ld(X2,X2))),X2) = mult(X1,ld(X1,X2)),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_34,plain,
mult(rd(X1,rd(X2,X3)),rd(X2,X3)) = mult(ld(X1,X1),mult(rd(X1,X3),X3)),
inference(spm,[status(thm)],[c_0_31,c_0_29]) ).
cnf(c_0_35,plain,
rd(X1,X1) = ld(X1,X1),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_36,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(X1,ld(X1,X3)),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
mult(rd(X1,ld(X1,X1)),ld(X1,X1)) = rd(X1,ld(X1,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_38,plain,
mult(rd(X1,ld(X2,X2)),ld(X2,X2)) = mult(ld(X1,X1),mult(rd(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
mult(X1,ld(X1,ld(X1,X2))) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_36]) ).
cnf(c_0_40,plain,
mult(X1,mult(X1,ld(X1,X2))) = mult(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_17]),c_0_22]) ).
cnf(c_0_41,plain,
rd(X1,ld(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38]),c_0_25]),c_0_39]),c_0_29]),c_0_29]) ).
cnf(c_0_42,plain,
mult(X1,mult(mult(X1,ld(X1,X2)),X3)) = mult(X1,mult(X2,X3)),
inference(spm,[status(thm)],[c_0_40,c_0_30]) ).
cnf(c_0_43,plain,
mult(ld(X1,X1),mult(ld(X1,X1),mult(rd(X1,X2),X2))) = mult(rd(X1,X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_41]),c_0_38]) ).
cnf(c_0_44,plain,
mult(ld(X1,X2),mult(mult(X1,ld(X1,X3)),X4)) = mult(ld(X1,X2),mult(X3,X4)),
inference(spm,[status(thm)],[c_0_42,c_0_36]) ).
cnf(c_0_45,plain,
mult(rd(ld(X1,X1),X2),X2) = mult(X1,ld(X1,ld(X2,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_25]),c_0_26]) ).
cnf(c_0_46,plain,
mult(X1,ld(X1,ld(ld(X1,X2),X3))) = ld(ld(X1,X2),X3),
inference(spm,[status(thm)],[c_0_36,c_0_39]) ).
fof(c_0_47,negated_conjecture,
~ ! [X5,X6,X7] :
( ld(ld(X5,X6),mult(ld(X5,X6),X7)) = ld(X5,mult(X5,X7))
& ld(rd(X5,X6),mult(rd(X5,X6),X7)) = ld(X5,mult(X5,X7)) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_48,plain,
ld(ld(X1,X1),mult(rd(X1,X2),X2)) = mult(ld(X1,X1),mult(rd(X1,X2),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_43]),c_0_17]),c_0_36]),c_0_30]),c_0_44]) ).
cnf(c_0_49,plain,
ld(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_35]),c_0_29]),c_0_46]) ).
cnf(c_0_50,plain,
ld(ld(X1,X2),mult(X1,ld(X1,X3))) = ld(ld(X1,X2),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_36]),c_0_36]),c_0_46]) ).
cnf(c_0_51,plain,
mult(ld(X1,X2),mult(X1,ld(X1,X3))) = mult(ld(X1,X2),X3),
inference(spm,[status(thm)],[c_0_40,c_0_36]) ).
fof(c_0_52,negated_conjecture,
( ld(ld(esk1_0,esk2_0),mult(ld(esk1_0,esk2_0),esk3_0)) != ld(esk1_0,mult(esk1_0,esk3_0))
| ld(rd(esk4_0,esk5_0),mult(rd(esk4_0,esk5_0),esk6_0)) != ld(esk4_0,mult(esk4_0,esk6_0)) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])])]) ).
cnf(c_0_53,plain,
ld(ld(X1,X1),ld(X2,X2)) = mult(ld(X1,X1),ld(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_45]),c_0_49]),c_0_50]),c_0_49]),c_0_51]) ).
cnf(c_0_54,plain,
mult(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
inference(spm,[status(thm)],[c_0_22,c_0_49]) ).
cnf(c_0_55,negated_conjecture,
( ld(rd(esk4_0,esk5_0),mult(rd(esk4_0,esk5_0),esk6_0)) != ld(esk4_0,mult(esk4_0,esk6_0))
| ld(ld(esk1_0,esk2_0),mult(ld(esk1_0,esk2_0),esk3_0)) != ld(esk1_0,mult(esk1_0,esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_56,plain,
mult(ld(X1,X1),mult(rd(X1,X2),X2)) = mult(rd(X1,X2),X2),
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_38,c_0_53]),c_0_54]),c_0_54]),c_0_38]),c_0_38]),c_0_43]) ).
cnf(c_0_57,negated_conjecture,
( mult(ld(esk1_0,esk2_0),ld(ld(esk1_0,esk2_0),esk3_0)) != mult(esk1_0,ld(esk1_0,esk3_0))
| mult(rd(esk4_0,esk5_0),ld(rd(esk4_0,esk5_0),esk6_0)) != mult(esk4_0,ld(esk4_0,esk6_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_17]),c_0_17]),c_0_17]),c_0_17]) ).
cnf(c_0_58,plain,
mult(mult(X1,ld(X1,X2)),ld(mult(X1,ld(X1,X2)),X3)) = mult(X1,ld(X1,X3)),
inference(spm,[status(thm)],[c_0_36,c_0_17]) ).
cnf(c_0_59,plain,
mult(rd(mult(X1,X2),X3),X3) = mult(X1,mult(rd(X2,X3),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_34]),c_0_56]) ).
cnf(c_0_60,negated_conjecture,
( mult(mult(esk1_0,ld(esk1_0,ld(esk3_0,esk3_0))),esk3_0) != mult(esk1_0,ld(esk1_0,esk3_0))
| mult(rd(esk4_0,esk5_0),ld(rd(esk4_0,esk5_0),esk6_0)) != mult(esk4_0,ld(esk4_0,esk6_0)) ),
inference(rw,[status(thm)],[c_0_57,c_0_32]) ).
cnf(c_0_61,plain,
mult(mult(X1,X2),ld(mult(X1,X2),X3)) = mult(X1,ld(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_17]),c_0_40]),c_0_40]) ).
cnf(c_0_62,plain,
mult(rd(X1,X2),X2) = mult(X1,ld(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_22]),c_0_45]),c_0_40]) ).
cnf(c_0_63,negated_conjecture,
mult(rd(esk4_0,esk5_0),ld(rd(esk4_0,esk5_0),esk6_0)) != mult(esk4_0,ld(esk4_0,esk6_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_33])]) ).
cnf(c_0_64,plain,
mult(rd(X1,X2),ld(rd(X1,X2),X3)) = mult(X1,ld(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_61]) ).
cnf(c_0_65,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP682+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jun 14 03:45:08 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.24/1.42 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.42 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.42 # Preprocessing time : 0.014 s
% 0.24/1.42
% 0.24/1.42 # Proof found!
% 0.24/1.42 # SZS status Theorem
% 0.24/1.42 # SZS output start CNFRefutation
% See solution above
% 0.24/1.42 # Proof object total steps : 66
% 0.24/1.42 # Proof object clause steps : 49
% 0.24/1.42 # Proof object formula steps : 17
% 0.24/1.42 # Proof object conjectures : 8
% 0.24/1.42 # Proof object clause conjectures : 5
% 0.24/1.42 # Proof object formula conjectures : 3
% 0.24/1.42 # Proof object initial clauses used : 8
% 0.24/1.42 # Proof object initial formulas used : 8
% 0.24/1.42 # Proof object generating inferences : 26
% 0.24/1.42 # Proof object simplifying inferences : 55
% 0.24/1.42 # Training examples: 0 positive, 0 negative
% 0.24/1.42 # Parsed axioms : 8
% 0.24/1.42 # Removed by relevancy pruning/SinE : 0
% 0.24/1.42 # Initial clauses : 8
% 0.24/1.42 # Removed in clause preprocessing : 0
% 0.24/1.42 # Initial clauses in saturation : 8
% 0.24/1.42 # Processed clauses : 319
% 0.24/1.42 # ...of these trivial : 88
% 0.24/1.42 # ...subsumed : 45
% 0.24/1.42 # ...remaining for further processing : 186
% 0.24/1.42 # Other redundant clauses eliminated : 0
% 0.24/1.42 # Clauses deleted for lack of memory : 0
% 0.24/1.42 # Backward-subsumed : 1
% 0.24/1.42 # Backward-rewritten : 73
% 0.24/1.42 # Generated clauses : 12568
% 0.24/1.42 # ...of the previous two non-trivial : 9059
% 0.24/1.42 # Contextual simplify-reflections : 0
% 0.24/1.42 # Paramodulations : 12568
% 0.24/1.42 # Factorizations : 0
% 0.24/1.42 # Equation resolutions : 0
% 0.24/1.42 # Current number of processed clauses : 112
% 0.24/1.42 # Positive orientable unit clauses : 104
% 0.24/1.42 # Positive unorientable unit clauses: 8
% 0.24/1.42 # Negative unit clauses : 0
% 0.24/1.42 # Non-unit-clauses : 0
% 0.24/1.42 # Current number of unprocessed clauses: 5709
% 0.24/1.42 # ...number of literals in the above : 5709
% 0.24/1.42 # Current number of archived formulas : 0
% 0.24/1.42 # Current number of archived clauses : 74
% 0.24/1.42 # Clause-clause subsumption calls (NU) : 0
% 0.24/1.42 # Rec. Clause-clause subsumption calls : 0
% 0.24/1.42 # Non-unit clause-clause subsumptions : 0
% 0.24/1.42 # Unit Clause-clause subsumption calls : 62
% 0.24/1.42 # Rewrite failures with RHS unbound : 4
% 0.24/1.42 # BW rewrite match attempts : 468
% 0.24/1.42 # BW rewrite match successes : 105
% 0.24/1.42 # Condensation attempts : 0
% 0.24/1.42 # Condensation successes : 0
% 0.24/1.42 # Termbank termtop insertions : 198655
% 0.24/1.42
% 0.24/1.42 # -------------------------------------------------
% 0.24/1.42 # User time : 0.226 s
% 0.24/1.42 # System time : 0.007 s
% 0.24/1.42 # Total time : 0.233 s
% 0.24/1.42 # Maximum resident set size: 10424 pages
%------------------------------------------------------------------------------