TSTP Solution File: GRA007+2 by E---3.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.2.0
% Problem : GRA007+2 : TPTP v8.2.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n007.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 : 300s
% DateTime : Mon Jun 24 06:34:39 EDT 2024
% Result : Theorem 2.00s 0.75s
% Output : CNFRefutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 85 ( 16 unt; 0 def)
% Number of atoms : 395 ( 121 equ)
% Maximal formula atoms : 37 ( 4 avg)
% Number of connectives : 491 ( 181 ~; 204 |; 76 &)
% ( 6 <=>; 21 =>; 1 <=; 2 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 2 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-4 aty)
% Number of variables : 204 ( 24 sgn 102 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(shortest_path_defn,axiom,
! [X2,X3,X10] :
( shortest_path(X2,X3,X10)
<=> ( path(X2,X3,X10)
& X2 != X3
& ! [X4] :
( path(X2,X3,X4)
=> less_or_equal(length_of(X10),length_of(X4)) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZWPRWwaib4/E---3.1_23979.p',shortest_path_defn) ).
fof(back_edge,conjecture,
( complete
=> ! [X2,X3,X7,X8,X4] :
( ( shortest_path(X2,X3,X4)
& precedes(X7,X8,X4) )
=> ? [X9] :
( edge(X9)
& tail_of(X9) = head_of(X8)
& head_of(X9) = tail_of(X7) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZWPRWwaib4/E---3.1_23979.p',back_edge) ).
fof(precedes_properties,axiom,
! [X4,X2,X3] :
( path(X2,X3,X4)
=> ! [X7,X8] :
( precedes(X7,X8,X4)
=> ( on_path(X7,X4)
& on_path(X8,X4)
& ( sequential(X7,X8)
<~> ? [X9] :
( sequential(X7,X9)
& precedes(X9,X8,X4) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZWPRWwaib4/E---3.1_23979.p',precedes_properties) ).
fof(in_path_properties,axiom,
! [X2,X3,X4,X6] :
( ( path(X2,X3,X4)
& in_path(X6,X4) )
=> ( vertex(X6)
& ? [X1] :
( on_path(X1,X4)
& ( X6 = head_of(X1)
| X6 = tail_of(X1) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZWPRWwaib4/E---3.1_23979.p',in_path_properties) ).
fof(on_path_properties,axiom,
! [X2,X3,X4,X1] :
( ( path(X2,X3,X4)
& on_path(X1,X4) )
=> ( edge(X1)
& in_path(head_of(X1),X4)
& in_path(tail_of(X1),X4) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZWPRWwaib4/E---3.1_23979.p',on_path_properties) ).
fof(complete_properties,axiom,
( complete
=> ! [X2,X3] :
( ( vertex(X2)
& vertex(X3)
& X2 != X3 )
=> ? [X1] :
( edge(X1)
& ( ( X2 = head_of(X1)
& X3 = tail_of(X1) )
<~> ( X3 = head_of(X1)
& X2 = tail_of(X1) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZWPRWwaib4/E---3.1_23979.p',complete_properties) ).
fof(precedes_defn,axiom,
! [X4,X2,X3] :
( path(X2,X3,X4)
=> ! [X7,X8] :
( precedes(X7,X8,X4)
<= ( on_path(X7,X4)
& on_path(X8,X4)
& ( sequential(X7,X8)
| ? [X9] :
( sequential(X7,X9)
& precedes(X9,X8,X4) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZWPRWwaib4/E---3.1_23979.p',precedes_defn) ).
fof(shortest_path_properties,axiom,
! [X2,X3,X7,X8,X4] :
( ( shortest_path(X2,X3,X4)
& precedes(X7,X8,X4) )
=> ( ~ ? [X9] :
( tail_of(X9) = tail_of(X7)
& head_of(X9) = head_of(X8) )
& ~ precedes(X8,X7,X4) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZWPRWwaib4/E---3.1_23979.p',shortest_path_properties) ).
fof(sequential_defn,axiom,
! [X7,X8] :
( sequential(X7,X8)
<=> ( edge(X7)
& edge(X8)
& X7 != X8
& head_of(X7) = tail_of(X8) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZWPRWwaib4/E---3.1_23979.p',sequential_defn) ).
fof(c_0_9,plain,
! [X2,X3,X10] :
( shortest_path(X2,X3,X10)
<=> ( path(X2,X3,X10)
& X2 != X3
& ! [X4] :
( path(X2,X3,X4)
=> less_or_equal(length_of(X10),length_of(X4)) ) ) ),
inference(fof_simplification,[status(thm)],[shortest_path_defn]) ).
fof(c_0_10,negated_conjecture,
~ ( complete
=> ! [X2,X3,X7,X8,X4] :
( ( shortest_path(X2,X3,X4)
& precedes(X7,X8,X4) )
=> ? [X9] :
( edge(X9)
& tail_of(X9) = head_of(X8)
& head_of(X9) = tail_of(X7) ) ) ),
inference(assume_negation,[status(cth)],[back_edge]) ).
fof(c_0_11,plain,
! [X69,X70,X71,X72,X73,X74,X75] :
( ( path(X69,X70,X71)
| ~ shortest_path(X69,X70,X71) )
& ( X69 != X70
| ~ shortest_path(X69,X70,X71) )
& ( ~ path(X69,X70,X72)
| less_or_equal(length_of(X71),length_of(X72))
| ~ shortest_path(X69,X70,X71) )
& ( path(X73,X74,esk10_3(X73,X74,X75))
| ~ path(X73,X74,X75)
| X73 = X74
| shortest_path(X73,X74,X75) )
& ( ~ less_or_equal(length_of(X75),length_of(esk10_3(X73,X74,X75)))
| ~ path(X73,X74,X75)
| X73 = X74
| shortest_path(X73,X74,X75) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])])])]) ).
fof(c_0_12,negated_conjecture,
! [X18] :
( complete
& shortest_path(esk1_0,esk2_0,esk5_0)
& precedes(esk3_0,esk4_0,esk5_0)
& ( ~ edge(X18)
| tail_of(X18) != head_of(esk4_0)
| head_of(X18) != tail_of(esk3_0) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])]) ).
fof(c_0_13,plain,
! [X4,X2,X3] :
( path(X2,X3,X4)
=> ! [X7,X8] :
( precedes(X7,X8,X4)
=> ( on_path(X7,X4)
& on_path(X8,X4)
& ~ ( sequential(X7,X8)
<=> ? [X9] :
( sequential(X7,X9)
& precedes(X9,X8,X4) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[precedes_properties]) ).
fof(c_0_14,plain,
! [X77,X78,X79,X80] :
( ( vertex(X80)
| ~ path(X77,X78,X79)
| ~ in_path(X80,X79) )
& ( on_path(esk11_4(X77,X78,X79,X80),X79)
| ~ path(X77,X78,X79)
| ~ in_path(X80,X79) )
& ( X80 = head_of(esk11_4(X77,X78,X79,X80))
| X80 = tail_of(esk11_4(X77,X78,X79,X80))
| ~ path(X77,X78,X79)
| ~ in_path(X80,X79) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[in_path_properties])])])])]) ).
cnf(c_0_15,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
shortest_path(esk1_0,esk2_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X49,X50,X51,X52] :
( ( edge(X52)
| ~ path(X49,X50,X51)
| ~ on_path(X52,X51) )
& ( in_path(head_of(X52),X51)
| ~ path(X49,X50,X51)
| ~ on_path(X52,X51) )
& ( in_path(tail_of(X52),X51)
| ~ path(X49,X50,X51)
| ~ on_path(X52,X51) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[on_path_properties])])])]) ).
fof(c_0_18,plain,
! [X62,X63,X64,X65,X66,X67] :
( ( on_path(X65,X62)
| ~ precedes(X65,X66,X62)
| ~ path(X63,X64,X62) )
& ( on_path(X66,X62)
| ~ precedes(X65,X66,X62)
| ~ path(X63,X64,X62) )
& ( ~ sequential(X65,X66)
| ~ sequential(X65,X67)
| ~ precedes(X67,X66,X62)
| ~ precedes(X65,X66,X62)
| ~ path(X63,X64,X62) )
& ( sequential(X65,esk9_3(X62,X65,X66))
| sequential(X65,X66)
| ~ precedes(X65,X66,X62)
| ~ path(X63,X64,X62) )
& ( precedes(esk9_3(X62,X65,X66),X66,X62)
| sequential(X65,X66)
| ~ precedes(X65,X66,X62)
| ~ path(X63,X64,X62) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])])])])]) ).
fof(c_0_19,plain,
( complete
=> ! [X2,X3] :
( ( vertex(X2)
& vertex(X3)
& X2 != X3 )
=> ? [X1] :
( edge(X1)
& ~ ( ( X2 = head_of(X1)
& X3 = tail_of(X1) )
<=> ( X3 = head_of(X1)
& X2 = tail_of(X1) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[complete_properties]) ).
cnf(c_0_20,plain,
( vertex(X1)
| ~ path(X2,X3,X4)
| ~ in_path(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,negated_conjecture,
path(esk1_0,esk2_0,esk5_0),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( in_path(tail_of(X1),X2)
| ~ path(X3,X4,X2)
| ~ on_path(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( on_path(X1,X2)
| ~ precedes(X1,X3,X2)
| ~ path(X4,X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
precedes(esk3_0,esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_25,plain,
( in_path(head_of(X1),X2)
| ~ path(X3,X4,X2)
| ~ on_path(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
( on_path(X1,X2)
| ~ precedes(X3,X1,X2)
| ~ path(X4,X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_27,plain,
! [X35,X36] :
( ( edge(esk6_2(X35,X36))
| ~ vertex(X35)
| ~ vertex(X36)
| X35 = X36
| ~ complete )
& ( X35 != head_of(esk6_2(X35,X36))
| X36 != tail_of(esk6_2(X35,X36))
| X36 != head_of(esk6_2(X35,X36))
| X35 != tail_of(esk6_2(X35,X36))
| ~ vertex(X35)
| ~ vertex(X36)
| X35 = X36
| ~ complete )
& ( X36 = head_of(esk6_2(X35,X36))
| X35 = head_of(esk6_2(X35,X36))
| ~ vertex(X35)
| ~ vertex(X36)
| X35 = X36
| ~ complete )
& ( X35 = tail_of(esk6_2(X35,X36))
| X35 = head_of(esk6_2(X35,X36))
| ~ vertex(X35)
| ~ vertex(X36)
| X35 = X36
| ~ complete )
& ( X36 = head_of(esk6_2(X35,X36))
| X36 = tail_of(esk6_2(X35,X36))
| ~ vertex(X35)
| ~ vertex(X36)
| X35 = X36
| ~ complete )
& ( X35 = tail_of(esk6_2(X35,X36))
| X36 = tail_of(esk6_2(X35,X36))
| ~ vertex(X35)
| ~ vertex(X36)
| X35 = X36
| ~ complete ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])])]) ).
cnf(c_0_28,negated_conjecture,
( vertex(X1)
| ~ in_path(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_29,negated_conjecture,
( in_path(tail_of(X1),esk5_0)
| ~ on_path(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_30,negated_conjecture,
( on_path(esk3_0,esk5_0)
| ~ path(X1,X2,esk5_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,negated_conjecture,
( in_path(head_of(X1),esk5_0)
| ~ on_path(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_21]) ).
cnf(c_0_32,negated_conjecture,
( on_path(esk4_0,esk5_0)
| ~ path(X1,X2,esk5_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_33,plain,
( X1 = tail_of(esk6_2(X1,X2))
| X2 = tail_of(esk6_2(X1,X2))
| X1 = X2
| ~ vertex(X1)
| ~ vertex(X2)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_35,negated_conjecture,
( vertex(tail_of(X1))
| ~ on_path(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,negated_conjecture,
on_path(esk3_0,esk5_0),
inference(spm,[status(thm)],[c_0_30,c_0_21]) ).
fof(c_0_37,plain,
! [X4,X2,X3] :
( path(X2,X3,X4)
=> ! [X7,X8] :
( ( on_path(X7,X4)
& on_path(X8,X4)
& ( sequential(X7,X8)
| ? [X9] :
( sequential(X7,X9)
& precedes(X9,X8,X4) ) ) )
=> precedes(X7,X8,X4) ) ),
inference(fof_simplification,[status(thm)],[precedes_defn]) ).
fof(c_0_38,plain,
! [X2,X3,X7,X8,X4] :
( ( shortest_path(X2,X3,X4)
& precedes(X7,X8,X4) )
=> ( ~ ? [X9] :
( tail_of(X9) = tail_of(X7)
& head_of(X9) = head_of(X8) )
& ~ precedes(X8,X7,X4) ) ),
inference(fof_simplification,[status(thm)],[shortest_path_properties]) ).
cnf(c_0_39,plain,
( X1 = head_of(esk6_2(X2,X1))
| X2 = head_of(esk6_2(X2,X1))
| X2 = X1
| ~ vertex(X2)
| ~ vertex(X1)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_40,negated_conjecture,
( vertex(head_of(X1))
| ~ on_path(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_31]) ).
cnf(c_0_41,negated_conjecture,
on_path(esk4_0,esk5_0),
inference(spm,[status(thm)],[c_0_32,c_0_21]) ).
cnf(c_0_42,plain,
( tail_of(esk6_2(X1,X2)) = X1
| tail_of(esk6_2(X1,X2)) = X2
| X1 = X2
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).
cnf(c_0_43,negated_conjecture,
vertex(tail_of(esk3_0)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_44,plain,
! [X56,X57,X58,X59,X60,X61] :
( ( ~ sequential(X59,X60)
| ~ on_path(X59,X56)
| ~ on_path(X60,X56)
| precedes(X59,X60,X56)
| ~ path(X57,X58,X56) )
& ( ~ sequential(X59,X61)
| ~ precedes(X61,X60,X56)
| ~ on_path(X59,X56)
| ~ on_path(X60,X56)
| precedes(X59,X60,X56)
| ~ path(X57,X58,X56) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])])]) ).
fof(c_0_45,plain,
! [X23,X24,X25,X26,X27,X28] :
( ( tail_of(X28) != tail_of(X25)
| head_of(X28) != head_of(X26)
| ~ shortest_path(X23,X24,X27)
| ~ precedes(X25,X26,X27) )
& ( ~ precedes(X26,X25,X27)
| ~ shortest_path(X23,X24,X27)
| ~ precedes(X25,X26,X27) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])])])]) ).
cnf(c_0_46,plain,
( head_of(esk6_2(X1,X2)) = X2
| head_of(esk6_2(X1,X2)) = X1
| X2 = X1
| ~ vertex(X1)
| ~ vertex(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_34])]) ).
cnf(c_0_47,negated_conjecture,
vertex(head_of(esk4_0)),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,plain,
( X1 = tail_of(esk6_2(X1,X2))
| X1 = head_of(esk6_2(X1,X2))
| X1 = X2
| ~ vertex(X1)
| ~ vertex(X2)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_49,negated_conjecture,
( tail_of(esk6_2(X1,tail_of(esk3_0))) = tail_of(esk3_0)
| tail_of(esk6_2(X1,tail_of(esk3_0))) = X1
| X1 = tail_of(esk3_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,plain,
( precedes(X1,X2,X3)
| ~ sequential(X1,X2)
| ~ on_path(X1,X3)
| ~ on_path(X2,X3)
| ~ path(X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_51,plain,
( ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_52,plain,
( tail_of(X1) != tail_of(X2)
| head_of(X1) != head_of(X3)
| ~ shortest_path(X4,X5,X6)
| ~ precedes(X2,X3,X6) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_53,negated_conjecture,
( head_of(esk6_2(head_of(esk4_0),X1)) = head_of(esk4_0)
| head_of(esk6_2(head_of(esk4_0),X1)) = X1
| X1 = head_of(esk4_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_54,plain,
( tail_of(esk6_2(X1,X2)) = X1
| head_of(esk6_2(X1,X2)) = X1
| X1 = X2
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_34])]) ).
cnf(c_0_55,negated_conjecture,
( tail_of(esk6_2(head_of(esk4_0),tail_of(esk3_0))) = head_of(esk4_0)
| tail_of(esk6_2(head_of(esk4_0),tail_of(esk3_0))) = tail_of(esk3_0)
| tail_of(esk3_0) = head_of(esk4_0) ),
inference(spm,[status(thm)],[c_0_49,c_0_47]) ).
cnf(c_0_56,negated_conjecture,
( precedes(X1,X2,esk5_0)
| ~ sequential(X1,X2)
| ~ on_path(X2,esk5_0)
| ~ on_path(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_50,c_0_21]) ).
cnf(c_0_57,negated_conjecture,
( ~ precedes(X1,X2,esk5_0)
| ~ precedes(X2,X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_51,c_0_16]) ).
fof(c_0_58,plain,
! [X7,X8] :
( sequential(X7,X8)
<=> ( edge(X7)
& edge(X8)
& X7 != X8
& head_of(X7) = tail_of(X8) ) ),
inference(fof_simplification,[status(thm)],[sequential_defn]) ).
cnf(c_0_59,plain,
( edge(X1)
| ~ path(X2,X3,X4)
| ~ on_path(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_60,negated_conjecture,
( head_of(X1) != head_of(X2)
| tail_of(X1) != tail_of(X3)
| ~ precedes(X3,X2,esk5_0) ),
inference(spm,[status(thm)],[c_0_52,c_0_16]) ).
cnf(c_0_61,plain,
( X1 = head_of(esk6_2(X2,X1))
| X1 = tail_of(esk6_2(X2,X1))
| X2 = X1
| ~ vertex(X2)
| ~ vertex(X1)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_62,negated_conjecture,
( ~ edge(X1)
| tail_of(X1) != head_of(esk4_0)
| head_of(X1) != tail_of(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_63,negated_conjecture,
( head_of(esk6_2(head_of(esk4_0),tail_of(esk3_0))) = tail_of(esk3_0)
| head_of(esk6_2(head_of(esk4_0),tail_of(esk3_0))) = head_of(esk4_0)
| tail_of(esk3_0) = head_of(esk4_0) ),
inference(spm,[status(thm)],[c_0_53,c_0_43]) ).
cnf(c_0_64,negated_conjecture,
( tail_of(esk6_2(head_of(esk4_0),tail_of(esk3_0))) = head_of(esk4_0)
| head_of(esk6_2(head_of(esk4_0),tail_of(esk3_0))) = head_of(esk4_0)
| tail_of(esk3_0) = head_of(esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_43]),c_0_47])]) ).
cnf(c_0_65,plain,
( edge(esk6_2(X1,X2))
| X1 = X2
| ~ vertex(X1)
| ~ vertex(X2)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_66,negated_conjecture,
( precedes(X1,esk3_0,esk5_0)
| ~ sequential(X1,esk3_0)
| ~ on_path(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_56,c_0_36]) ).
cnf(c_0_67,negated_conjecture,
~ precedes(esk4_0,esk3_0,esk5_0),
inference(spm,[status(thm)],[c_0_57,c_0_24]) ).
fof(c_0_68,plain,
! [X21,X22] :
( ( edge(X21)
| ~ sequential(X21,X22) )
& ( edge(X22)
| ~ sequential(X21,X22) )
& ( X21 != X22
| ~ sequential(X21,X22) )
& ( head_of(X21) = tail_of(X22)
| ~ sequential(X21,X22) )
& ( ~ edge(X21)
| ~ edge(X22)
| X21 = X22
| head_of(X21) != tail_of(X22)
| sequential(X21,X22) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])])]) ).
cnf(c_0_69,negated_conjecture,
( edge(X1)
| ~ on_path(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_59,c_0_21]) ).
cnf(c_0_70,negated_conjecture,
( head_of(X1) != head_of(esk4_0)
| tail_of(X1) != tail_of(esk3_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_24]) ).
cnf(c_0_71,plain,
( tail_of(esk6_2(X1,X2)) = X2
| head_of(esk6_2(X1,X2)) = X2
| X2 = X1
| ~ vertex(X1)
| ~ vertex(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_34])]) ).
cnf(c_0_72,negated_conjecture,
( head_of(esk6_2(head_of(esk4_0),tail_of(esk3_0))) = head_of(esk4_0)
| tail_of(esk3_0) = head_of(esk4_0)
| ~ edge(esk6_2(head_of(esk4_0),tail_of(esk3_0))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).
cnf(c_0_73,plain,
( X1 = X2
| edge(esk6_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_34])]) ).
cnf(c_0_74,negated_conjecture,
~ sequential(esk4_0,esk3_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_41]),c_0_67]) ).
cnf(c_0_75,plain,
( X1 = X2
| sequential(X1,X2)
| ~ edge(X1)
| ~ edge(X2)
| head_of(X1) != tail_of(X2) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_76,negated_conjecture,
edge(esk3_0),
inference(spm,[status(thm)],[c_0_69,c_0_36]) ).
cnf(c_0_77,negated_conjecture,
edge(esk4_0),
inference(spm,[status(thm)],[c_0_69,c_0_41]) ).
cnf(c_0_78,negated_conjecture,
( head_of(esk6_2(X1,X2)) = X2
| X2 = X1
| head_of(esk6_2(X1,X2)) != head_of(esk4_0)
| X2 != tail_of(esk3_0)
| ~ vertex(X1)
| ~ vertex(X2) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_79,negated_conjecture,
( head_of(esk6_2(head_of(esk4_0),tail_of(esk3_0))) = head_of(esk4_0)
| tail_of(esk3_0) = head_of(esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_43]),c_0_47])]) ).
cnf(c_0_80,negated_conjecture,
( esk4_0 = esk3_0
| tail_of(esk3_0) != head_of(esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]),c_0_77])]) ).
cnf(c_0_81,negated_conjecture,
tail_of(esk3_0) = head_of(esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_47]),c_0_43])]) ).
cnf(c_0_82,negated_conjecture,
head_of(esk4_0) != head_of(esk3_0),
inference(er,[status(thm)],[c_0_70]) ).
cnf(c_0_83,negated_conjecture,
esk4_0 = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81])]) ).
cnf(c_0_84,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_83])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRA007+2 : TPTP v8.2.0. Bugfixed v3.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Jun 18 16:38:24 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.22/0.49 Running first-order theorem proving
% 0.22/0.49 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.ZWPRWwaib4/E---3.1_23979.p
% 2.00/0.75 # Version: 3.2.0
% 2.00/0.75 # Preprocessing class: FSMSSMSSSSSNFFN.
% 2.00/0.75 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.00/0.75 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.00/0.75 # Starting new_bool_3 with 300s (1) cores
% 2.00/0.75 # Starting new_bool_1 with 300s (1) cores
% 2.00/0.75 # Starting sh5l with 300s (1) cores
% 2.00/0.75 # sh5l with pid 24060 completed with status 0
% 2.00/0.75 # Result found by sh5l
% 2.00/0.75 # Preprocessing class: FSMSSMSSSSSNFFN.
% 2.00/0.75 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.00/0.75 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.00/0.75 # Starting new_bool_3 with 300s (1) cores
% 2.00/0.75 # Starting new_bool_1 with 300s (1) cores
% 2.00/0.75 # Starting sh5l with 300s (1) cores
% 2.00/0.75 # SinE strategy is gf500_gu_R04_F100_L20000
% 2.00/0.75 # Search class: FGHSF-FFMS32-SFFFFFNN
% 2.00/0.75 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 2.00/0.75 # Starting G-E--_301_C18_F1_URBAN_S0Y with 181s (1) cores
% 2.00/0.75 # G-E--_301_C18_F1_URBAN_S0Y with pid 24068 completed with status 0
% 2.00/0.75 # Result found by G-E--_301_C18_F1_URBAN_S0Y
% 2.00/0.75 # Preprocessing class: FSMSSMSSSSSNFFN.
% 2.00/0.75 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.00/0.75 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.00/0.75 # Starting new_bool_3 with 300s (1) cores
% 2.00/0.75 # Starting new_bool_1 with 300s (1) cores
% 2.00/0.75 # Starting sh5l with 300s (1) cores
% 2.00/0.75 # SinE strategy is gf500_gu_R04_F100_L20000
% 2.00/0.75 # Search class: FGHSF-FFMS32-SFFFFFNN
% 2.00/0.75 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 2.00/0.75 # Starting G-E--_301_C18_F1_URBAN_S0Y with 181s (1) cores
% 2.00/0.75 # Preprocessing time : 0.002 s
% 2.00/0.75
% 2.00/0.75 # Proof found!
% 2.00/0.75 # SZS status Theorem
% 2.00/0.75 # SZS output start CNFRefutation
% See solution above
% 2.00/0.75 # Parsed axioms : 19
% 2.00/0.75 # Removed by relevancy pruning/SinE : 0
% 2.00/0.75 # Initial clauses : 64
% 2.00/0.75 # Removed in clause preprocessing : 1
% 2.00/0.75 # Initial clauses in saturation : 63
% 2.00/0.75 # Processed clauses : 975
% 2.00/0.75 # ...of these trivial : 79
% 2.00/0.75 # ...subsumed : 203
% 2.00/0.75 # ...remaining for further processing : 693
% 2.00/0.75 # Other redundant clauses eliminated : 71
% 2.00/0.75 # Clauses deleted for lack of memory : 0
% 2.00/0.75 # Backward-subsumed : 37
% 2.00/0.75 # Backward-rewritten : 314
% 2.00/0.75 # Generated clauses : 6219
% 2.00/0.75 # ...of the previous two non-redundant : 5827
% 2.00/0.75 # ...aggressively subsumed : 0
% 2.00/0.75 # Contextual simplify-reflections : 65
% 2.00/0.75 # Paramodulations : 6053
% 2.00/0.75 # Factorizations : 54
% 2.00/0.75 # NegExts : 0
% 2.00/0.75 # Equation resolutions : 112
% 2.00/0.75 # Disequality decompositions : 0
% 2.00/0.75 # Total rewrite steps : 1589
% 2.00/0.75 # ...of those cached : 1572
% 2.00/0.75 # Propositional unsat checks : 0
% 2.00/0.75 # Propositional check models : 0
% 2.00/0.75 # Propositional check unsatisfiable : 0
% 2.00/0.75 # Propositional clauses : 0
% 2.00/0.75 # Propositional clauses after purity: 0
% 2.00/0.75 # Propositional unsat core size : 0
% 2.00/0.75 # Propositional preprocessing time : 0.000
% 2.00/0.75 # Propositional encoding time : 0.000
% 2.00/0.75 # Propositional solver time : 0.000
% 2.00/0.75 # Success case prop preproc time : 0.000
% 2.00/0.75 # Success case prop encoding time : 0.000
% 2.00/0.75 # Success case prop solver time : 0.000
% 2.00/0.75 # Current number of processed clauses : 340
% 2.00/0.75 # Positive orientable unit clauses : 15
% 2.00/0.75 # Positive unorientable unit clauses: 0
% 2.00/0.75 # Negative unit clauses : 2
% 2.00/0.75 # Non-unit-clauses : 323
% 2.00/0.75 # Current number of unprocessed clauses: 4743
% 2.00/0.75 # ...number of literals in the above : 33780
% 2.00/0.75 # Current number of archived formulas : 0
% 2.00/0.75 # Current number of archived clauses : 351
% 2.00/0.75 # Clause-clause subsumption calls (NU) : 36544
% 2.00/0.75 # Rec. Clause-clause subsumption calls : 6461
% 2.00/0.75 # Non-unit clause-clause subsumptions : 287
% 2.00/0.75 # Unit Clause-clause subsumption calls : 618
% 2.00/0.75 # Rewrite failures with RHS unbound : 0
% 2.00/0.75 # BW rewrite match attempts : 4
% 2.00/0.75 # BW rewrite match successes : 4
% 2.00/0.75 # Condensation attempts : 0
% 2.00/0.75 # Condensation successes : 0
% 2.00/0.75 # Termbank termtop insertions : 166583
% 2.00/0.75 # Search garbage collected termcells : 1276
% 2.00/0.75
% 2.00/0.75 # -------------------------------------------------
% 2.00/0.75 # User time : 0.238 s
% 2.00/0.75 # System time : 0.008 s
% 2.00/0.75 # Total time : 0.247 s
% 2.00/0.75 # Maximum resident set size: 2008 pages
% 2.00/0.75
% 2.00/0.75 # -------------------------------------------------
% 2.00/0.75 # User time : 0.240 s
% 2.00/0.75 # System time : 0.010 s
% 2.00/0.75 # Total time : 0.250 s
% 2.00/0.75 # Maximum resident set size: 1736 pages
% 2.00/0.75 % E---3.1 exiting
% 2.00/0.75 % E exiting
%------------------------------------------------------------------------------