TSTP Solution File: GRA009+1 by E---3.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.2.0
% Problem : GRA009+1 : TPTP v8.2.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n009.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 06:34:40 EDT 2024
% Result : Theorem 3.69s 0.93s
% Output : CNFRefutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 92 ( 14 unt; 0 def)
% Number of atoms : 425 ( 148 equ)
% Maximal formula atoms : 37 ( 4 avg)
% Number of connectives : 543 ( 210 ~; 236 |; 71 &)
% ( 6 <=>; 18 =>; 1 <=; 1 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 2 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 181 ( 11 sgn 81 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/tmp/tmp.y7yps8os9U/E---3.1_1042.p',complete_properties) ).
fof(complete_means_path_and_stuff_means_triangles,conjecture,
( complete
=> ! [X2,X3,X4,X7,X8] :
( ( shortest_path(X2,X3,X4)
& on_path(X7,X4)
& on_path(X8,X4)
& sequential(X7,X8) )
=> ? [X9] : triangle(X7,X8,X9) ) ),
file('/export/starexec/sandbox2/tmp/tmp.y7yps8os9U/E---3.1_1042.p',complete_means_path_and_stuff_means_triangles) ).
fof(sequential_defn,axiom,
! [X7,X8] :
( sequential(X7,X8)
<=> ( edge(X7)
& edge(X8)
& X7 != X8
& head_of(X7) = tail_of(X8) ) ),
file('/export/starexec/sandbox2/tmp/tmp.y7yps8os9U/E---3.1_1042.p',sequential_defn) ).
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/sandbox2/tmp/tmp.y7yps8os9U/E---3.1_1042.p',precedes_defn) ).
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/sandbox2/tmp/tmp.y7yps8os9U/E---3.1_1042.p',shortest_path_defn) ).
fof(triangle_defn,axiom,
! [X7,X8,X9] :
( triangle(X7,X8,X9)
<=> ( edge(X7)
& edge(X8)
& edge(X9)
& sequential(X7,X8)
& sequential(X8,X9)
& sequential(X9,X7) ) ),
file('/export/starexec/sandbox2/tmp/tmp.y7yps8os9U/E---3.1_1042.p',triangle_defn) ).
fof(edge_ends_are_vertices,axiom,
! [X1] :
( edge(X1)
=> ( vertex(head_of(X1))
& vertex(tail_of(X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.y7yps8os9U/E---3.1_1042.p',edge_ends_are_vertices) ).
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/sandbox2/tmp/tmp.y7yps8os9U/E---3.1_1042.p',shortest_path_properties) ).
fof(no_loops,axiom,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.y7yps8os9U/E---3.1_1042.p',no_loops) ).
fof(c_0_9,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]) ).
fof(c_0_10,negated_conjecture,
~ ( complete
=> ! [X2,X3,X4,X7,X8] :
( ( shortest_path(X2,X3,X4)
& on_path(X7,X4)
& on_path(X8,X4)
& sequential(X7,X8) )
=> ? [X9] : triangle(X7,X8,X9) ) ),
inference(assume_negation,[status(cth)],[complete_means_path_and_stuff_means_triangles]) ).
fof(c_0_11,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]) ).
fof(c_0_12,plain,
! [X38,X39] :
( ( edge(esk7_2(X38,X39))
| ~ vertex(X38)
| ~ vertex(X39)
| X38 = X39
| ~ complete )
& ( X38 != head_of(esk7_2(X38,X39))
| X39 != tail_of(esk7_2(X38,X39))
| X39 != head_of(esk7_2(X38,X39))
| X38 != tail_of(esk7_2(X38,X39))
| ~ vertex(X38)
| ~ vertex(X39)
| X38 = X39
| ~ complete )
& ( X39 = head_of(esk7_2(X38,X39))
| X38 = head_of(esk7_2(X38,X39))
| ~ vertex(X38)
| ~ vertex(X39)
| X38 = X39
| ~ complete )
& ( X38 = tail_of(esk7_2(X38,X39))
| X38 = head_of(esk7_2(X38,X39))
| ~ vertex(X38)
| ~ vertex(X39)
| X38 = X39
| ~ complete )
& ( X39 = head_of(esk7_2(X38,X39))
| X39 = tail_of(esk7_2(X38,X39))
| ~ vertex(X38)
| ~ vertex(X39)
| X38 = X39
| ~ complete )
& ( X38 = tail_of(esk7_2(X38,X39))
| X39 = tail_of(esk7_2(X38,X39))
| ~ vertex(X38)
| ~ vertex(X39)
| X38 = X39
| ~ 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_9])])])])])]) ).
fof(c_0_13,negated_conjecture,
! [X18] :
( complete
& shortest_path(esk1_0,esk2_0,esk3_0)
& on_path(esk4_0,esk3_0)
& on_path(esk5_0,esk3_0)
& sequential(esk4_0,esk5_0)
& ~ triangle(esk4_0,esk5_0,X18) ),
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_14,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_15,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_16,plain,
! [X19,X20,X21] :
( ( edge(X19)
| ~ triangle(X19,X20,X21) )
& ( edge(X20)
| ~ triangle(X19,X20,X21) )
& ( edge(X21)
| ~ triangle(X19,X20,X21) )
& ( sequential(X19,X20)
| ~ triangle(X19,X20,X21) )
& ( sequential(X20,X21)
| ~ triangle(X19,X20,X21) )
& ( sequential(X21,X19)
| ~ triangle(X19,X20,X21) )
& ( ~ edge(X19)
| ~ edge(X20)
| ~ edge(X21)
| ~ sequential(X19,X20)
| ~ sequential(X20,X21)
| ~ sequential(X21,X19)
| triangle(X19,X20,X21) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[triangle_defn])])])]) ).
fof(c_0_17,plain,
! [X22,X23] :
( ( edge(X22)
| ~ sequential(X22,X23) )
& ( edge(X23)
| ~ sequential(X22,X23) )
& ( X22 != X23
| ~ sequential(X22,X23) )
& ( head_of(X22) = tail_of(X23)
| ~ sequential(X22,X23) )
& ( ~ edge(X22)
| ~ edge(X23)
| X22 = X23
| head_of(X22) != tail_of(X23)
| sequential(X22,X23) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
cnf(c_0_18,plain,
( X1 = head_of(esk7_2(X2,X1))
| X2 = head_of(esk7_2(X2,X1))
| X2 = X1
| ~ vertex(X2)
| ~ vertex(X1)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_20,plain,
! [X55] :
( ( vertex(head_of(X55))
| ~ edge(X55) )
& ( vertex(tail_of(X55))
| ~ edge(X55) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[edge_ends_are_vertices])])])]) ).
fof(c_0_21,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]) ).
fof(c_0_22,plain,
! [X42,X43,X44,X45,X46,X47] :
( ( ~ sequential(X45,X46)
| ~ on_path(X45,X42)
| ~ on_path(X46,X42)
| precedes(X45,X46,X42)
| ~ path(X43,X44,X42) )
& ( ~ sequential(X45,X47)
| ~ precedes(X47,X46,X42)
| ~ on_path(X45,X42)
| ~ on_path(X46,X42)
| precedes(X45,X46,X42)
| ~ path(X43,X44,X42) ) ),
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_14])])])])]) ).
fof(c_0_23,plain,
! [X24,X25,X26,X27,X28,X29,X30] :
( ( path(X24,X25,X26)
| ~ shortest_path(X24,X25,X26) )
& ( X24 != X25
| ~ shortest_path(X24,X25,X26) )
& ( ~ path(X24,X25,X27)
| less_or_equal(length_of(X26),length_of(X27))
| ~ shortest_path(X24,X25,X26) )
& ( path(X28,X29,esk6_3(X28,X29,X30))
| ~ path(X28,X29,X30)
| X28 = X29
| shortest_path(X28,X29,X30) )
& ( ~ less_or_equal(length_of(X30),length_of(esk6_3(X28,X29,X30)))
| ~ path(X28,X29,X30)
| X28 = X29
| shortest_path(X28,X29,X30) ) ),
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_15])])])])])])]) ).
cnf(c_0_24,plain,
( triangle(X1,X2,X3)
| ~ edge(X1)
| ~ edge(X2)
| ~ edge(X3)
| ~ sequential(X1,X2)
| ~ sequential(X2,X3)
| ~ sequential(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
( edge(X1)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
( head_of(esk7_2(X1,X2)) = X2
| head_of(esk7_2(X1,X2)) = X1
| X2 = X1
| ~ vertex(X1)
| ~ vertex(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]) ).
cnf(c_0_27,plain,
( vertex(head_of(X1))
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_28,plain,
! [X32,X33,X34,X35,X36,X37] :
( ( tail_of(X37) != tail_of(X34)
| head_of(X37) != head_of(X35)
| ~ shortest_path(X32,X33,X36)
| ~ precedes(X34,X35,X36) )
& ( ~ precedes(X35,X34,X36)
| ~ shortest_path(X32,X33,X36)
| ~ precedes(X34,X35,X36) ) ),
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_21])])])])]) ).
cnf(c_0_29,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_22]) ).
cnf(c_0_30,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,negated_conjecture,
~ triangle(esk4_0,esk5_0,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_32,plain,
( triangle(X1,X2,X3)
| ~ sequential(X3,X1)
| ~ sequential(X2,X3)
| ~ sequential(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_24,c_0_25]),c_0_25]),c_0_25]) ).
cnf(c_0_33,negated_conjecture,
sequential(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_34,plain,
( head_of(esk7_2(head_of(X1),X2)) = head_of(X1)
| head_of(esk7_2(head_of(X1),X2)) = X2
| X2 = head_of(X1)
| ~ vertex(X2)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,plain,
( vertex(tail_of(X1))
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_36,plain,
( edge(X1)
| ~ sequential(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_37,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_28]) ).
cnf(c_0_38,negated_conjecture,
shortest_path(esk1_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_39,plain,
( precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3)
| ~ sequential(X1,X2)
| ~ on_path(X2,X3)
| ~ on_path(X1,X3) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_40,negated_conjecture,
( ~ sequential(X1,esk4_0)
| ~ sequential(esk5_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_41,plain,
( X1 = X2
| sequential(X1,X2)
| ~ edge(X1)
| ~ edge(X2)
| head_of(X1) != tail_of(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_42,plain,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
inference(fof_simplification,[status(thm)],[no_loops]) ).
cnf(c_0_43,plain,
( head_of(esk7_2(head_of(X1),tail_of(X2))) = tail_of(X2)
| head_of(esk7_2(head_of(X1),tail_of(X2))) = head_of(X1)
| tail_of(X2) = head_of(X1)
| ~ edge(X1)
| ~ edge(X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_44,negated_conjecture,
edge(esk5_0),
inference(spm,[status(thm)],[c_0_36,c_0_33]) ).
cnf(c_0_45,plain,
( X1 = tail_of(esk7_2(X1,X2))
| X2 = tail_of(esk7_2(X1,X2))
| X1 = X2
| ~ vertex(X1)
| ~ vertex(X2)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_46,negated_conjecture,
( head_of(X1) != head_of(X2)
| tail_of(X1) != tail_of(X3)
| ~ precedes(X3,X2,esk3_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_47,negated_conjecture,
( precedes(X1,X2,esk3_0)
| ~ sequential(X1,X2)
| ~ on_path(X2,esk3_0)
| ~ on_path(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_38]) ).
cnf(c_0_48,negated_conjecture,
( X1 = esk4_0
| head_of(X1) != tail_of(esk4_0)
| ~ sequential(esk5_0,X1)
| ~ edge(esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_36]) ).
cnf(c_0_49,negated_conjecture,
edge(esk4_0),
inference(spm,[status(thm)],[c_0_25,c_0_33]) ).
fof(c_0_50,plain,
! [X41] :
( ~ edge(X41)
| head_of(X41) != tail_of(X41) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])]) ).
cnf(c_0_51,negated_conjecture,
( head_of(esk7_2(head_of(esk5_0),tail_of(X1))) = head_of(esk5_0)
| head_of(esk7_2(head_of(esk5_0),tail_of(X1))) = tail_of(X1)
| tail_of(X1) = head_of(esk5_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_52,plain,
( tail_of(esk7_2(X1,X2)) = X1
| tail_of(esk7_2(X1,X2)) = X2
| X1 = X2
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_19])]) ).
cnf(c_0_53,negated_conjecture,
( head_of(X1) != head_of(X2)
| tail_of(X1) != tail_of(X3)
| ~ sequential(X3,X2)
| ~ on_path(X2,esk3_0)
| ~ on_path(X3,esk3_0) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_54,negated_conjecture,
on_path(esk5_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_55,negated_conjecture,
on_path(esk4_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_56,negated_conjecture,
( X1 = esk4_0
| head_of(X1) != tail_of(esk4_0)
| ~ sequential(esk5_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]) ).
cnf(c_0_57,plain,
( ~ edge(X1)
| head_of(X1) != tail_of(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_58,negated_conjecture,
( head_of(esk7_2(head_of(esk5_0),tail_of(esk4_0))) = tail_of(esk4_0)
| head_of(esk7_2(head_of(esk5_0),tail_of(esk4_0))) = head_of(esk5_0)
| head_of(esk5_0) = tail_of(esk4_0) ),
inference(spm,[status(thm)],[c_0_51,c_0_49]) ).
cnf(c_0_59,plain,
( tail_of(esk7_2(X1,tail_of(X2))) = tail_of(X2)
| tail_of(esk7_2(X1,tail_of(X2))) = X1
| X1 = tail_of(X2)
| ~ vertex(X1)
| ~ edge(X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_35]) ).
cnf(c_0_60,negated_conjecture,
( head_of(X1) != head_of(esk5_0)
| tail_of(X1) != tail_of(esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_33]),c_0_54]),c_0_55])]) ).
cnf(c_0_61,negated_conjecture,
( esk5_0 = X1
| X1 = esk4_0
| head_of(X1) != tail_of(esk4_0)
| tail_of(X1) != head_of(esk5_0)
| ~ edge(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_41]),c_0_44])]) ).
cnf(c_0_62,negated_conjecture,
( head_of(esk7_2(head_of(esk5_0),tail_of(esk4_0))) = tail_of(esk4_0)
| head_of(esk5_0) = tail_of(esk4_0)
| tail_of(esk7_2(head_of(esk5_0),tail_of(esk4_0))) != head_of(esk5_0)
| ~ edge(esk7_2(head_of(esk5_0),tail_of(esk4_0))) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,plain,
( tail_of(esk7_2(head_of(X1),tail_of(X2))) = head_of(X1)
| tail_of(esk7_2(head_of(X1),tail_of(X2))) = tail_of(X2)
| head_of(X1) = tail_of(X2)
| ~ edge(X2)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_27]) ).
cnf(c_0_64,negated_conjecture,
( head_of(esk7_2(head_of(esk5_0),tail_of(esk4_0))) = tail_of(esk4_0)
| head_of(esk5_0) = tail_of(esk4_0)
| tail_of(esk7_2(head_of(esk5_0),tail_of(esk4_0))) != tail_of(esk4_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_58]) ).
cnf(c_0_65,negated_conjecture,
( esk7_2(head_of(esk5_0),tail_of(esk4_0)) = esk4_0
| esk7_2(head_of(esk5_0),tail_of(esk4_0)) = esk5_0
| head_of(esk5_0) = tail_of(esk4_0)
| tail_of(esk7_2(head_of(esk5_0),tail_of(esk4_0))) != head_of(esk5_0)
| ~ edge(esk7_2(head_of(esk5_0),tail_of(esk4_0))) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_66,negated_conjecture,
( tail_of(esk7_2(head_of(X1),tail_of(esk4_0))) = tail_of(esk4_0)
| tail_of(esk7_2(head_of(X1),tail_of(esk4_0))) = head_of(X1)
| head_of(X1) = tail_of(esk4_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_49]) ).
cnf(c_0_67,negated_conjecture,
( head_of(esk5_0) = tail_of(esk4_0)
| tail_of(esk7_2(head_of(esk5_0),tail_of(esk4_0))) != tail_of(esk4_0)
| ~ edge(esk7_2(head_of(esk5_0),tail_of(esk4_0))) ),
inference(spm,[status(thm)],[c_0_57,c_0_64]) ).
cnf(c_0_68,plain,
( edge(esk7_2(X1,X2))
| X1 = X2
| ~ vertex(X1)
| ~ vertex(X2)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_69,plain,
( head_of(X1) = tail_of(X2)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_70,plain,
( ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_71,plain,
( X1 = tail_of(esk7_2(X1,X2))
| X1 = head_of(esk7_2(X1,X2))
| X1 = X2
| ~ vertex(X1)
| ~ vertex(X2)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_72,plain,
( X1 = head_of(esk7_2(X2,X1))
| X1 = tail_of(esk7_2(X2,X1))
| X2 = X1
| ~ vertex(X2)
| ~ vertex(X1)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_73,negated_conjecture,
( esk7_2(head_of(esk5_0),tail_of(esk4_0)) = esk5_0
| esk7_2(head_of(esk5_0),tail_of(esk4_0)) = esk4_0
| head_of(esk5_0) = tail_of(esk4_0)
| ~ edge(esk7_2(head_of(esk5_0),tail_of(esk4_0))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_44])]),c_0_67]) ).
cnf(c_0_74,plain,
( X1 = X2
| edge(esk7_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_19])]) ).
cnf(c_0_75,negated_conjecture,
head_of(esk4_0) = tail_of(esk5_0),
inference(spm,[status(thm)],[c_0_69,c_0_33]) ).
cnf(c_0_76,negated_conjecture,
( ~ precedes(X1,X2,esk3_0)
| ~ precedes(X2,X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_70,c_0_38]) ).
cnf(c_0_77,plain,
( tail_of(esk7_2(X1,X2)) = X1
| head_of(esk7_2(X1,X2)) = X1
| X1 = X2
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_19])]) ).
cnf(c_0_78,plain,
( tail_of(esk7_2(X1,X2)) = X2
| head_of(esk7_2(X1,X2)) = X2
| X2 = X1
| ~ vertex(X1)
| ~ vertex(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_19])]) ).
cnf(c_0_79,negated_conjecture,
( esk7_2(head_of(esk5_0),tail_of(esk4_0)) = esk4_0
| esk7_2(head_of(esk5_0),tail_of(esk4_0)) = esk5_0
| head_of(esk5_0) = tail_of(esk4_0)
| ~ vertex(tail_of(esk4_0))
| ~ vertex(head_of(esk5_0)) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_80,negated_conjecture,
tail_of(esk5_0) != tail_of(esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_75]),c_0_49])]) ).
cnf(c_0_81,negated_conjecture,
( ~ precedes(X1,X2,esk3_0)
| ~ sequential(X2,X1)
| ~ on_path(X1,esk3_0)
| ~ on_path(X2,esk3_0) ),
inference(spm,[status(thm)],[c_0_76,c_0_47]) ).
cnf(c_0_82,negated_conjecture,
( tail_of(esk7_2(head_of(esk5_0),X1)) = head_of(esk5_0)
| head_of(esk5_0) = X1
| tail_of(esk7_2(head_of(esk5_0),X1)) != tail_of(esk4_0)
| ~ vertex(head_of(esk5_0))
| ~ vertex(X1) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_77])]) ).
cnf(c_0_83,negated_conjecture,
( esk7_2(head_of(esk5_0),tail_of(esk4_0)) = esk4_0
| head_of(esk5_0) = tail_of(esk4_0)
| ~ vertex(head_of(esk5_0))
| ~ vertex(tail_of(esk4_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]) ).
cnf(c_0_84,negated_conjecture,
( ~ sequential(X1,X2)
| ~ sequential(X2,X1)
| ~ on_path(X2,esk3_0)
| ~ on_path(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_81,c_0_47]) ).
cnf(c_0_85,negated_conjecture,
( head_of(esk5_0) = tail_of(esk4_0)
| ~ vertex(head_of(esk5_0))
| ~ vertex(tail_of(esk4_0)) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_86,negated_conjecture,
~ sequential(esk5_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_33]),c_0_54]),c_0_55])]) ).
cnf(c_0_87,negated_conjecture,
( head_of(esk5_0) = tail_of(esk4_0)
| ~ vertex(tail_of(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_27]),c_0_44])]) ).
cnf(c_0_88,negated_conjecture,
( esk5_0 = esk4_0
| head_of(esk5_0) != tail_of(esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_41]),c_0_49]),c_0_44])]) ).
cnf(c_0_89,negated_conjecture,
head_of(esk5_0) = tail_of(esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_35]),c_0_49])]) ).
cnf(c_0_90,negated_conjecture,
esk5_0 = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_89])]) ).
cnf(c_0_91,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_90])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRA009+1 : TPTP v8.2.0. Bugfixed v3.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.35 % Computer : n009.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Tue Jun 18 15:03:09 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.20/0.50 Running first-order theorem proving
% 0.20/0.50 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.y7yps8os9U/E---3.1_1042.p
% 3.69/0.93 # Version: 3.2.0
% 3.69/0.93 # Preprocessing class: FSMSSMSSSSSNFFN.
% 3.69/0.93 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.69/0.93 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.69/0.93 # Starting new_bool_3 with 300s (1) cores
% 3.69/0.93 # Starting new_bool_1 with 300s (1) cores
% 3.69/0.93 # Starting sh5l with 300s (1) cores
% 3.69/0.93 # new_bool_3 with pid 1134 completed with status 0
% 3.69/0.93 # Result found by new_bool_3
% 3.69/0.93 # Preprocessing class: FSMSSMSSSSSNFFN.
% 3.69/0.93 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.69/0.93 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.69/0.93 # Starting new_bool_3 with 300s (1) cores
% 3.69/0.93 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 3.69/0.93 # Search class: FGHSF-FFMS31-SFFFFFNN
% 3.69/0.93 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 3.69/0.93 # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 164s (1) cores
% 3.69/0.93 # G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with pid 1139 completed with status 0
% 3.69/0.93 # Result found by G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y
% 3.69/0.93 # Preprocessing class: FSMSSMSSSSSNFFN.
% 3.69/0.93 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.69/0.93 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.69/0.93 # Starting new_bool_3 with 300s (1) cores
% 3.69/0.93 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 3.69/0.93 # Search class: FGHSF-FFMS31-SFFFFFNN
% 3.69/0.93 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 3.69/0.93 # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 164s (1) cores
% 3.69/0.93 # Preprocessing time : 0.002 s
% 3.69/0.93
% 3.69/0.93 # Proof found!
% 3.69/0.93 # SZS status Theorem
% 3.69/0.93 # SZS output start CNFRefutation
% See solution above
% 3.69/0.93 # Parsed axioms : 18
% 3.69/0.93 # Removed by relevancy pruning/SinE : 8
% 3.69/0.93 # Initial clauses : 41
% 3.69/0.93 # Removed in clause preprocessing : 1
% 3.69/0.93 # Initial clauses in saturation : 40
% 3.69/0.93 # Processed clauses : 2627
% 3.69/0.93 # ...of these trivial : 34
% 3.69/0.93 # ...subsumed : 1714
% 3.69/0.93 # ...remaining for further processing : 879
% 3.69/0.93 # Other redundant clauses eliminated : 110
% 3.69/0.93 # Clauses deleted for lack of memory : 0
% 3.69/0.93 # Backward-subsumed : 150
% 3.69/0.93 # Backward-rewritten : 545
% 3.69/0.93 # Generated clauses : 9236
% 3.69/0.93 # ...of the previous two non-redundant : 8667
% 3.69/0.93 # ...aggressively subsumed : 0
% 3.69/0.93 # Contextual simplify-reflections : 288
% 3.69/0.93 # Paramodulations : 9056
% 3.69/0.93 # Factorizations : 31
% 3.69/0.93 # NegExts : 0
% 3.69/0.93 # Equation resolutions : 149
% 3.69/0.93 # Disequality decompositions : 0
% 3.69/0.93 # Total rewrite steps : 4163
% 3.69/0.93 # ...of those cached : 4152
% 3.69/0.93 # Propositional unsat checks : 0
% 3.69/0.93 # Propositional check models : 0
% 3.69/0.93 # Propositional check unsatisfiable : 0
% 3.69/0.93 # Propositional clauses : 0
% 3.69/0.93 # Propositional clauses after purity: 0
% 3.69/0.93 # Propositional unsat core size : 0
% 3.69/0.93 # Propositional preprocessing time : 0.000
% 3.69/0.93 # Propositional encoding time : 0.000
% 3.69/0.93 # Propositional solver time : 0.000
% 3.69/0.93 # Success case prop preproc time : 0.000
% 3.69/0.93 # Success case prop encoding time : 0.000
% 3.69/0.93 # Success case prop solver time : 0.000
% 3.69/0.93 # Current number of processed clauses : 182
% 3.69/0.93 # Positive orientable unit clauses : 7
% 3.69/0.93 # Positive unorientable unit clauses: 0
% 3.69/0.93 # Negative unit clauses : 2
% 3.69/0.93 # Non-unit-clauses : 173
% 3.69/0.93 # Current number of unprocessed clauses: 5323
% 3.69/0.93 # ...number of literals in the above : 54289
% 3.69/0.93 # Current number of archived formulas : 0
% 3.69/0.93 # Current number of archived clauses : 695
% 3.69/0.93 # Clause-clause subsumption calls (NU) : 180005
% 3.69/0.93 # Rec. Clause-clause subsumption calls : 15661
% 3.69/0.93 # Non-unit clause-clause subsumptions : 1697
% 3.69/0.93 # Unit Clause-clause subsumption calls : 244
% 3.69/0.93 # Rewrite failures with RHS unbound : 0
% 3.69/0.93 # BW rewrite match attempts : 3
% 3.69/0.93 # BW rewrite match successes : 3
% 3.69/0.93 # Condensation attempts : 0
% 3.69/0.93 # Condensation successes : 0
% 3.69/0.93 # Termbank termtop insertions : 314841
% 3.69/0.93 # Search garbage collected termcells : 877
% 3.69/0.93
% 3.69/0.93 # -------------------------------------------------
% 3.69/0.93 # User time : 0.410 s
% 3.69/0.93 # System time : 0.010 s
% 3.69/0.93 # Total time : 0.420 s
% 3.69/0.93 # Maximum resident set size: 1872 pages
% 3.69/0.93
% 3.69/0.93 # -------------------------------------------------
% 3.69/0.93 # User time : 0.411 s
% 3.69/0.93 # System time : 0.013 s
% 3.69/0.93 # Total time : 0.424 s
% 3.69/0.93 # Maximum resident set size: 1736 pages
% 3.69/0.93 % E---3.1 exiting
% 3.69/0.93 % E exiting
%------------------------------------------------------------------------------