TSTP Solution File: GRP685+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : GRP685+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n023.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 09:03:18 EDT 2022
% Result : Theorem 0.12s 1.30s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 52 unt; 0 def)
% Number of atoms : 62 ( 61 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 3 |; 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 : 115 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [X1] : ld(X1,mult(X1,X1)) = X1,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',f01) ).
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(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(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(f02,axiom,
! [X1] : rd(mult(X1,X1),X1) = X1,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',f02) ).
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(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(goals,conjecture,
! [X5,X6,X7] :
( rd(mult(X5,ld(X6,X7)),ld(X6,X7)) = rd(mult(X5,X7),X7)
& rd(mult(X5,rd(X6,X7)),rd(X6,X7)) = rd(mult(X5,X7),X7) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals) ).
fof(c_0_8,plain,
! [X2] : ld(X2,mult(X2,X2)) = X2,
inference(variable_rename,[status(thm)],[f01]) ).
fof(c_0_9,plain,
! [X3,X4] : mult(X4,ld(X4,X3)) = ld(X4,mult(X4,X3)),
inference(variable_rename,[status(thm)],[f03]) ).
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(rd(X4,X3),X3) = rd(mult(X4,X3),X3),
inference(variable_rename,[status(thm)],[f04]) ).
fof(c_0_12,plain,
! [X2] : rd(mult(X2,X2),X2) = X2,
inference(variable_rename,[status(thm)],[f02]) ).
fof(c_0_13,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]) ).
fof(c_0_14,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_15,plain,
ld(X1,mult(X1,X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,plain,
mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,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_18,plain,
mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
rd(mult(X1,X1),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,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_13]) ).
cnf(c_0_21,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_14]) ).
cnf(c_0_22,plain,
mult(X1,ld(X1,X1)) = X1,
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_23,plain,
mult(X1,ld(X1,ld(X2,X2))) = mult(rd(rd(X1,X1),X2),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_16]),c_0_18]) ).
cnf(c_0_24,plain,
mult(rd(X1,X1),X1) = X1,
inference(rw,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_25,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_20,c_0_18]),c_0_18]) ).
cnf(c_0_26,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_21,c_0_16]),c_0_16]) ).
cnf(c_0_27,plain,
ld(X1,X1) = mult(rd(rd(X1,X1),X1),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_22]),c_0_23]) ).
cnf(c_0_28,plain,
mult(rd(rd(X1,X1),X1),X1) = rd(X1,X1),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_29,plain,
mult(rd(mult(X1,X2),mult(rd(X3,X4),X4)),mult(rd(X3,X4),X4)) = mult(X1,mult(rd(X2,X4),X4)),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_30,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(mult(X1,ld(X1,rd(X3,X3))),X3),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_31,plain,
ld(X1,X1) = rd(X1,X1),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
mult(rd(mult(X1,X2),X3),X3) = mult(X1,mult(rd(X2,X3),X3)),
inference(spm,[status(thm)],[c_0_29,c_0_24]) ).
cnf(c_0_33,plain,
mult(X1,rd(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_27]),c_0_28]) ).
cnf(c_0_34,plain,
mult(rd(X1,X1),ld(rd(X1,X1),X2)) = mult(mult(X1,ld(X1,rd(X2,X2))),X2),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
mult(X1,ld(X1,rd(X2,X2))) = mult(rd(rd(X1,X1),X2),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_27]),c_0_28]) ).
cnf(c_0_36,plain,
mult(mult(rd(X1,X2),X2),X2) = mult(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_18]),c_0_24]) ).
fof(c_0_37,negated_conjecture,
~ ! [X5,X6,X7] :
( rd(mult(X5,ld(X6,X7)),ld(X6,X7)) = rd(mult(X5,X7),X7)
& rd(mult(X5,rd(X6,X7)),rd(X6,X7)) = rd(mult(X5,X7),X7) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_38,plain,
mult(rd(X1,rd(X2,X3)),rd(X2,X3)) = mult(X1,mult(rd(rd(X1,X1),X3),X3)),
inference(spm,[status(thm)],[c_0_25,c_0_33]) ).
cnf(c_0_39,plain,
mult(X1,mult(rd(rd(X1,X1),X2),X2)) = mult(rd(X1,X2),X2),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,plain,
mult(rd(X1,X1),ld(rd(X1,X1),X2)) = mult(rd(X1,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
fof(c_0_41,negated_conjecture,
( rd(mult(esk1_0,ld(esk2_0,esk3_0)),ld(esk2_0,esk3_0)) != rd(mult(esk1_0,esk3_0),esk3_0)
| rd(mult(esk4_0,rd(esk5_0,esk6_0)),rd(esk5_0,esk6_0)) != rd(mult(esk4_0,esk6_0),esk6_0) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])]) ).
cnf(c_0_42,plain,
mult(rd(X1,rd(X2,X3)),rd(X2,X3)) = mult(rd(X1,X3),X3),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
mult(rd(X1,X1),ld(rd(X1,X1),X1)) = ld(rd(X1,X1),X1),
inference(spm,[status(thm)],[c_0_16,c_0_24]) ).
cnf(c_0_44,plain,
mult(X1,ld(X1,rd(X1,X1))) = rd(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_33]),c_0_27]),c_0_28]) ).
cnf(c_0_45,plain,
mult(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_31]),c_0_33]) ).
cnf(c_0_46,negated_conjecture,
( rd(mult(esk4_0,rd(esk5_0,esk6_0)),rd(esk5_0,esk6_0)) != rd(mult(esk4_0,esk6_0),esk6_0)
| rd(mult(esk1_0,ld(esk2_0,esk3_0)),ld(esk2_0,esk3_0)) != rd(mult(esk1_0,esk3_0),esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_47,plain,
mult(rd(X1,mult(rd(X2,X3),X3)),mult(rd(X2,X3),X3)) = mult(rd(X1,X3),X3),
inference(spm,[status(thm)],[c_0_42,c_0_18]) ).
cnf(c_0_48,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(rd(X1,X1),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_35]),c_0_36]) ).
cnf(c_0_49,plain,
ld(rd(X1,X1),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_34]),c_0_44]),c_0_24]) ).
cnf(c_0_50,plain,
rd(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_45]),c_0_31]),c_0_31]),c_0_33]) ).
cnf(c_0_51,negated_conjecture,
( mult(rd(esk1_0,ld(esk2_0,esk3_0)),ld(esk2_0,esk3_0)) != mult(rd(esk1_0,esk3_0),esk3_0)
| mult(rd(esk4_0,rd(esk5_0,esk6_0)),rd(esk5_0,esk6_0)) != mult(rd(esk4_0,esk6_0),esk6_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_18]),c_0_18]),c_0_18]),c_0_18]) ).
cnf(c_0_52,plain,
mult(rd(X1,mult(X2,X3)),mult(X2,X3)) = mult(rd(X1,X3),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_18]),c_0_36]),c_0_36]) ).
cnf(c_0_53,plain,
mult(X1,ld(X1,X2)) = mult(rd(X1,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_54,negated_conjecture,
mult(rd(esk1_0,ld(esk2_0,esk3_0)),ld(esk2_0,esk3_0)) != mult(rd(esk1_0,esk3_0),esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_42])]) ).
cnf(c_0_55,plain,
mult(rd(X1,ld(X2,X3)),ld(X2,X3)) = mult(rd(X1,X3),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_52]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : GRP685+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.07 % Command : run_ET %s %d
% 0.06/0.26 % Computer : n023.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 600
% 0.06/0.26 % DateTime : Tue Jun 14 06:35:05 EDT 2022
% 0.06/0.26 % CPUTime :
% 0.12/1.30 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.12/1.30 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.12/1.30 # Preprocessing time : 0.008 s
% 0.12/1.30
% 0.12/1.30 # Proof found!
% 0.12/1.30 # SZS status Theorem
% 0.12/1.30 # SZS output start CNFRefutation
% See solution above
% 0.12/1.30 # Proof object total steps : 57
% 0.12/1.30 # Proof object clause steps : 40
% 0.12/1.30 # Proof object formula steps : 17
% 0.12/1.30 # Proof object conjectures : 7
% 0.12/1.30 # Proof object clause conjectures : 4
% 0.12/1.30 # Proof object formula conjectures : 3
% 0.12/1.30 # Proof object initial clauses used : 8
% 0.12/1.30 # Proof object initial formulas used : 8
% 0.12/1.30 # Proof object generating inferences : 17
% 0.12/1.30 # Proof object simplifying inferences : 41
% 0.12/1.30 # Training examples: 0 positive, 0 negative
% 0.12/1.30 # Parsed axioms : 8
% 0.12/1.30 # Removed by relevancy pruning/SinE : 0
% 0.12/1.30 # Initial clauses : 8
% 0.12/1.30 # Removed in clause preprocessing : 0
% 0.12/1.30 # Initial clauses in saturation : 8
% 0.12/1.30 # Processed clauses : 198
% 0.12/1.30 # ...of these trivial : 42
% 0.12/1.30 # ...subsumed : 30
% 0.12/1.30 # ...remaining for further processing : 126
% 0.12/1.30 # Other redundant clauses eliminated : 0
% 0.12/1.30 # Clauses deleted for lack of memory : 0
% 0.12/1.30 # Backward-subsumed : 1
% 0.12/1.30 # Backward-rewritten : 62
% 0.12/1.30 # Generated clauses : 4747
% 0.12/1.30 # ...of the previous two non-trivial : 3196
% 0.12/1.30 # Contextual simplify-reflections : 0
% 0.12/1.30 # Paramodulations : 4747
% 0.12/1.30 # Factorizations : 0
% 0.12/1.30 # Equation resolutions : 0
% 0.12/1.30 # Current number of processed clauses : 63
% 0.12/1.30 # Positive orientable unit clauses : 62
% 0.12/1.30 # Positive unorientable unit clauses: 1
% 0.12/1.30 # Negative unit clauses : 0
% 0.12/1.30 # Non-unit-clauses : 0
% 0.12/1.30 # Current number of unprocessed clauses: 1246
% 0.12/1.30 # ...number of literals in the above : 1246
% 0.12/1.30 # Current number of archived formulas : 0
% 0.12/1.30 # Current number of archived clauses : 63
% 0.12/1.30 # Clause-clause subsumption calls (NU) : 0
% 0.12/1.30 # Rec. Clause-clause subsumption calls : 0
% 0.12/1.30 # Non-unit clause-clause subsumptions : 0
% 0.12/1.30 # Unit Clause-clause subsumption calls : 29
% 0.12/1.30 # Rewrite failures with RHS unbound : 25
% 0.12/1.30 # BW rewrite match attempts : 294
% 0.12/1.30 # BW rewrite match successes : 122
% 0.12/1.30 # Condensation attempts : 0
% 0.12/1.30 # Condensation successes : 0
% 0.12/1.30 # Termbank termtop insertions : 72631
% 0.12/1.30
% 0.12/1.30 # -------------------------------------------------
% 0.12/1.30 # User time : 0.055 s
% 0.12/1.30 # System time : 0.005 s
% 0.12/1.30 # Total time : 0.060 s
% 0.12/1.30 # Maximum resident set size: 5404 pages
%------------------------------------------------------------------------------