TSTP Solution File: NUN084+2 by ET---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : NUN084+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n026.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 16:26:07 EDT 2022
% Result : Theorem 0.24s 1.43s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 75 ( 46 unt; 0 def)
% Number of atoms : 169 ( 60 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 144 ( 50 ~; 40 |; 54 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 1 con; 0-2 aty)
% Number of variables : 157 ( 18 sgn 36 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_5a,axiom,
! [X33] :
? [X34] :
( ? [X35] :
( r1(X35)
& r4(X33,X35,X34) )
& ? [X36] :
( r1(X36)
& X34 = X36 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_5a) ).
fof(axiom_3,axiom,
! [X6,X7] :
? [X8] :
! [X9] :
( ( ~ r3(X6,X7,X9)
& X9 != X8 )
| ( r3(X6,X7,X9)
& X9 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_3) ).
fof(axiom_1a,axiom,
! [X14,X15] :
? [X16] :
( ? [X17] :
( ? [X18] :
( r2(X15,X18)
& r3(X14,X18,X17) )
& X17 = X16 )
& ? [X19] :
( r2(X19,X16)
& r3(X14,X15,X19) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1a) ).
fof(axiom_1,axiom,
? [X1] :
! [X2] :
( ( ~ r1(X2)
& X2 != X1 )
| ( r1(X2)
& X2 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1) ).
fof(axiom_2a,axiom,
! [X20,X21] :
? [X22] :
( ? [X23] :
( ? [X24] :
( r2(X21,X24)
& r4(X20,X24,X23) )
& X23 = X22 )
& ? [X25] :
( r3(X25,X20,X22)
& r4(X20,X21,X25) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_2a) ).
fof(axiom_2,axiom,
! [X3] :
? [X4] :
! [X5] :
( ( ~ r2(X3,X5)
& X5 != X4 )
| ( r2(X3,X5)
& X5 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_2) ).
fof(axiom_4,axiom,
! [X10,X11] :
? [X12] :
! [X13] :
( ( ~ r4(X10,X11,X13)
& X13 != X12 )
| ( r4(X10,X11,X13)
& X13 = X12 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_4) ).
fof(axiom_4a,axiom,
! [X30] :
? [X31] :
( ? [X32] :
( r1(X32)
& r3(X30,X32,X31) )
& X31 = X30 ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_4a) ).
fof(xtimesyeqtwo,conjecture,
? [X39,X22,X23] :
( r4(X39,X22,X23)
& ? [X16] :
( X23 = X16
& ? [X17] :
( r2(X17,X16)
& ? [X25] :
( r1(X25)
& r2(X25,X17) ) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',xtimesyeqtwo) ).
fof(c_0_9,plain,
! [X37] :
( r1(esk12_1(X37))
& r4(X37,esk12_1(X37),esk11_1(X37))
& r1(esk13_1(X37))
& esk11_1(X37) = esk13_1(X37) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[axiom_5a])])])]) ).
fof(c_0_10,plain,
! [X10,X11,X13] :
( ( r3(X10,X11,X13)
| ~ r3(X10,X11,X13) )
& ( X13 = esk14_2(X10,X11)
| ~ r3(X10,X11,X13) )
& ( r3(X10,X11,X13)
| X13 != esk14_2(X10,X11) )
& ( X13 = esk14_2(X10,X11)
| X13 != esk14_2(X10,X11) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[axiom_3])])])]) ).
fof(c_0_11,plain,
! [X20,X21] :
( r2(X21,esk17_2(X20,X21))
& r3(X20,esk17_2(X20,X21),esk16_2(X20,X21))
& esk16_2(X20,X21) = esk15_2(X20,X21)
& r2(esk18_2(X20,X21),esk15_2(X20,X21))
& r3(X20,X21,esk18_2(X20,X21)) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[axiom_1a])])])]) ).
fof(c_0_12,plain,
! [X4] :
( ( r1(X4)
| ~ r1(X4) )
& ( X4 = esk5_0
| ~ r1(X4) )
& ( r1(X4)
| X4 != esk5_0 )
& ( X4 = esk5_0
| X4 != esk5_0 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[axiom_1])])])]) ).
cnf(c_0_13,plain,
r1(esk13_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
esk11_1(X1) = esk13_1(X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( X3 = esk14_2(X1,X2)
| ~ r3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
r3(X1,X2,esk18_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( X1 = esk5_0
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
r1(esk11_1(X1)),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
r1(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_20,plain,
! [X26,X27] :
( r2(X27,esk9_2(X26,X27))
& r4(X26,esk9_2(X26,X27),esk8_2(X26,X27))
& esk8_2(X26,X27) = esk7_2(X26,X27)
& r3(esk10_2(X26,X27),X26,esk7_2(X26,X27))
& r4(X26,X27,esk10_2(X26,X27)) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[axiom_2a])])])]) ).
fof(c_0_21,plain,
! [X6,X8] :
( ( r2(X6,X8)
| ~ r2(X6,X8) )
& ( X8 = esk1_1(X6)
| ~ r2(X6,X8) )
& ( r2(X6,X8)
| X8 != esk1_1(X6) )
& ( X8 = esk1_1(X6)
| X8 != esk1_1(X6) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[axiom_2])])])]) ).
cnf(c_0_22,plain,
esk14_2(X1,X2) = esk18_2(X1,X2),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_23,plain,
! [X14,X15,X17] :
( ( r4(X14,X15,X17)
| ~ r4(X14,X15,X17) )
& ( X17 = esk6_2(X14,X15)
| ~ r4(X14,X15,X17) )
& ( r4(X14,X15,X17)
| X17 != esk6_2(X14,X15) )
& ( X17 = esk6_2(X14,X15)
| X17 != esk6_2(X14,X15) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[axiom_4])])])]) ).
cnf(c_0_24,plain,
r4(X1,esk12_1(X1),esk11_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_25,plain,
esk11_1(X1) = esk5_0,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,plain,
esk12_1(X1) = esk5_0,
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_27,plain,
r4(X1,esk9_2(X1,X2),esk8_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
esk8_2(X1,X2) = esk7_2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,plain,
( X2 = esk1_1(X1)
| ~ r2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,plain,
r2(X1,esk9_2(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_31,plain,
( X1 = esk18_2(X2,X3)
| ~ r3(X2,X3,X1) ),
inference(rw,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_32,plain,
r3(esk10_2(X1,X2),X1,esk7_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_33,plain,
( X3 = esk6_2(X1,X2)
| ~ r4(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_34,plain,
r4(X1,esk5_0,esk5_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_35,plain,
r4(X1,X2,esk10_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_36,plain,
r3(X1,esk17_2(X1,X2),esk16_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_37,plain,
esk16_2(X1,X2) = esk15_2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_38,plain,
r2(X1,esk17_2(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_39,plain,
r2(esk18_2(X1,X2),esk15_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_40,plain,
! [X33] :
( r1(esk20_1(X33))
& r3(X33,esk20_1(X33),esk19_1(X33))
& esk19_1(X33) = X33 ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[axiom_4a])])])]) ).
cnf(c_0_41,plain,
r4(X1,esk9_2(X1,X2),esk7_2(X1,X2)),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_42,plain,
esk9_2(X1,X2) = esk1_1(X2),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_43,plain,
esk7_2(X1,X2) = esk18_2(esk10_2(X1,X2),X1),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_44,plain,
esk6_2(X1,esk5_0) = esk5_0,
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_45,plain,
esk6_2(X1,X2) = esk10_2(X1,X2),
inference(spm,[status(thm)],[c_0_33,c_0_35]) ).
cnf(c_0_46,plain,
r3(X1,esk17_2(X1,X2),esk15_2(X1,X2)),
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_47,plain,
esk17_2(X1,X2) = esk1_1(X2),
inference(spm,[status(thm)],[c_0_29,c_0_38]) ).
cnf(c_0_48,plain,
esk15_2(X1,X2) = esk1_1(esk18_2(X1,X2)),
inference(spm,[status(thm)],[c_0_29,c_0_39]) ).
cnf(c_0_49,plain,
r3(X1,esk20_1(X1),esk19_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_50,plain,
esk19_1(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_51,plain,
r1(esk20_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_52,plain,
r4(X1,esk1_1(X2),esk18_2(esk10_2(X1,X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_53,plain,
esk10_2(X1,esk5_0) = esk5_0,
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_54,plain,
r3(X1,esk1_1(X2),esk1_1(esk18_2(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_55,plain,
r3(X1,esk20_1(X1),X1),
inference(rw,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_56,plain,
esk20_1(X1) = esk5_0,
inference(spm,[status(thm)],[c_0_17,c_0_51]) ).
fof(c_0_57,negated_conjecture,
~ ? [X39,X22,X23] :
( r4(X39,X22,X23)
& ? [X16] :
( X23 = X16
& ? [X17] :
( r2(X17,X16)
& ? [X25] :
( r1(X25)
& r2(X25,X17) ) ) ) ),
inference(assume_negation,[status(cth)],[xtimesyeqtwo]) ).
cnf(c_0_58,plain,
r4(X1,esk1_1(esk5_0),esk18_2(esk5_0,X1)),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_59,plain,
esk18_2(X1,esk1_1(X2)) = esk1_1(esk18_2(X1,X2)),
inference(spm,[status(thm)],[c_0_31,c_0_54]) ).
cnf(c_0_60,plain,
r3(X1,esk5_0,X1),
inference(rw,[status(thm)],[c_0_55,c_0_56]) ).
fof(c_0_61,negated_conjecture,
! [X40,X41,X42,X43,X44,X45] :
( ~ r4(X40,X41,X42)
| X42 != X43
| ~ r2(X44,X43)
| ~ r1(X45)
| ~ r2(X45,X44) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])])]) ).
cnf(c_0_62,plain,
r4(esk1_1(X1),esk1_1(esk5_0),esk1_1(esk18_2(esk5_0,X1))),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_63,plain,
esk14_2(X1,esk5_0) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_60]) ).
cnf(c_0_64,negated_conjecture,
( ~ r2(X1,X2)
| ~ r1(X1)
| ~ r2(X2,X3)
| X4 != X3
| ~ r4(X5,X6,X4) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_65,plain,
r4(esk1_1(esk1_1(X1)),esk1_1(esk5_0),esk1_1(esk1_1(esk18_2(esk5_0,X1)))),
inference(spm,[status(thm)],[c_0_62,c_0_59]) ).
cnf(c_0_66,plain,
esk18_2(X1,esk5_0) = X1,
inference(rw,[status(thm)],[c_0_63,c_0_22]) ).
cnf(c_0_67,negated_conjecture,
( ~ r4(X1,X2,X3)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r1(X5) ),
inference(er,[status(thm)],[c_0_64]) ).
cnf(c_0_68,plain,
r4(esk1_1(esk1_1(esk5_0)),esk1_1(esk5_0),esk1_1(esk1_1(esk5_0))),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_69,plain,
( r2(X2,X1)
| X1 != esk1_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_70,negated_conjecture,
( ~ r2(X1,esk1_1(esk1_1(esk5_0)))
| ~ r2(X2,X1)
| ~ r1(X2) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_71,plain,
r2(X1,esk1_1(X1)),
inference(er,[status(thm)],[c_0_69]) ).
cnf(c_0_72,negated_conjecture,
( ~ r2(X1,esk1_1(esk5_0))
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_73,plain,
r1(esk5_0),
inference(rw,[status(thm)],[c_0_18,c_0_25]) ).
cnf(c_0_74,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_71]),c_0_73])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUN084+2 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 2 05:37:27 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.24/1.43 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.43 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.43 # Preprocessing time : 0.016 s
% 0.24/1.43
% 0.24/1.43 # Proof found!
% 0.24/1.43 # SZS status Theorem
% 0.24/1.43 # SZS output start CNFRefutation
% See solution above
% 0.24/1.43 # Proof object total steps : 75
% 0.24/1.43 # Proof object clause steps : 56
% 0.24/1.43 # Proof object formula steps : 19
% 0.24/1.43 # Proof object conjectures : 8
% 0.24/1.43 # Proof object clause conjectures : 5
% 0.24/1.43 # Proof object formula conjectures : 3
% 0.24/1.43 # Proof object initial clauses used : 23
% 0.24/1.43 # Proof object initial formulas used : 9
% 0.24/1.43 # Proof object generating inferences : 20
% 0.24/1.43 # Proof object simplifying inferences : 18
% 0.24/1.43 # Training examples: 0 positive, 0 negative
% 0.24/1.43 # Parsed axioms : 12
% 0.24/1.43 # Removed by relevancy pruning/SinE : 0
% 0.24/1.43 # Initial clauses : 40
% 0.24/1.43 # Removed in clause preprocessing : 12
% 0.24/1.43 # Initial clauses in saturation : 28
% 0.24/1.43 # Processed clauses : 383
% 0.24/1.43 # ...of these trivial : 2
% 0.24/1.43 # ...subsumed : 154
% 0.24/1.43 # ...remaining for further processing : 227
% 0.24/1.43 # Other redundant clauses eliminated : 21
% 0.24/1.43 # Clauses deleted for lack of memory : 0
% 0.24/1.43 # Backward-subsumed : 5
% 0.24/1.43 # Backward-rewritten : 39
% 0.24/1.43 # Generated clauses : 1384
% 0.24/1.43 # ...of the previous two non-trivial : 1197
% 0.24/1.43 # Contextual simplify-reflections : 58
% 0.24/1.43 # Paramodulations : 1344
% 0.24/1.43 # Factorizations : 0
% 0.24/1.43 # Equation resolutions : 40
% 0.24/1.43 # Current number of processed clauses : 180
% 0.24/1.43 # Positive orientable unit clauses : 48
% 0.24/1.43 # Positive unorientable unit clauses: 0
% 0.24/1.43 # Negative unit clauses : 3
% 0.24/1.43 # Non-unit-clauses : 129
% 0.24/1.43 # Current number of unprocessed clauses: 785
% 0.24/1.43 # ...number of literals in the above : 2252
% 0.24/1.43 # Current number of archived formulas : 0
% 0.24/1.43 # Current number of archived clauses : 48
% 0.24/1.43 # Clause-clause subsumption calls (NU) : 6893
% 0.24/1.43 # Rec. Clause-clause subsumption calls : 5733
% 0.24/1.43 # Non-unit clause-clause subsumptions : 188
% 0.24/1.43 # Unit Clause-clause subsumption calls : 150
% 0.24/1.43 # Rewrite failures with RHS unbound : 0
% 0.24/1.43 # BW rewrite match attempts : 91
% 0.24/1.43 # BW rewrite match successes : 17
% 0.24/1.43 # Condensation attempts : 0
% 0.24/1.43 # Condensation successes : 0
% 0.24/1.43 # Termbank termtop insertions : 17116
% 0.24/1.43
% 0.24/1.43 # -------------------------------------------------
% 0.24/1.43 # User time : 0.048 s
% 0.24/1.43 # System time : 0.005 s
% 0.24/1.43 # Total time : 0.053 s
% 0.24/1.43 # Maximum resident set size: 3788 pages
%------------------------------------------------------------------------------