TSTP Solution File: GRA007+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRA007+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n016.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 : Thu Aug 31 00:00:06 EDT 2023
% Result : Theorem 0.15s 0.79s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 45
% Syntax : Number of formulae : 119 ( 16 unt; 36 typ; 0 def)
% Number of atoms : 387 ( 118 equ)
% Maximal formula atoms : 37 ( 4 avg)
% Number of connectives : 484 ( 180 ~; 206 |; 71 &)
% ( 4 <=>; 20 =>; 1 <=; 2 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 51 ( 24 >; 27 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 2 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 11 con; 0-4 aty)
% Number of variables : 199 ( 24 sgn; 96 !; 11 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
edge: $i > $o ).
tff(decl_23,type,
head_of: $i > $i ).
tff(decl_24,type,
tail_of: $i > $i ).
tff(decl_25,type,
vertex: $i > $o ).
tff(decl_26,type,
complete: $o ).
tff(decl_27,type,
path: ( $i * $i * $i ) > $o ).
tff(decl_28,type,
empty: $i ).
tff(decl_29,type,
path_cons: ( $i * $i ) > $i ).
tff(decl_30,type,
on_path: ( $i * $i ) > $o ).
tff(decl_31,type,
in_path: ( $i * $i ) > $o ).
tff(decl_32,type,
sequential: ( $i * $i ) > $o ).
tff(decl_33,type,
precedes: ( $i * $i * $i ) > $o ).
tff(decl_34,type,
shortest_path: ( $i * $i * $i ) > $o ).
tff(decl_35,type,
length_of: $i > $i ).
tff(decl_36,type,
less_or_equal: ( $i * $i ) > $o ).
tff(decl_37,type,
triangle: ( $i * $i * $i ) > $o ).
tff(decl_38,type,
edges: $i ).
tff(decl_39,type,
number_of_in: ( $i * $i ) > $i ).
tff(decl_40,type,
sequential_pairs: $i ).
tff(decl_41,type,
n1: $i ).
tff(decl_42,type,
minus: ( $i * $i ) > $i ).
tff(decl_43,type,
triangles: $i ).
tff(decl_44,type,
graph: $i ).
tff(decl_45,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_46,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_47,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
esk4_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_49,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
esk7_1: $i > $i ).
tff(decl_52,type,
esk8_1: $i > $i ).
tff(decl_53,type,
esk9_0: $i ).
tff(decl_54,type,
esk10_0: $i ).
tff(decl_55,type,
esk11_0: $i ).
tff(decl_56,type,
esk12_0: $i ).
tff(decl_57,type,
esk13_0: $i ).
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/benchmark/theBenchmark.p',back_edge) ).
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/benchmark/Axioms/GRA001+0.ax',shortest_path_defn) ).
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/benchmark/Axioms/GRA001+0.ax',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/benchmark/Axioms/GRA001+0.ax',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/benchmark/Axioms/GRA001+0.ax',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/benchmark/Axioms/GRA001+0.ax',complete_properties) ).
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/benchmark/Axioms/GRA001+0.ax',shortest_path_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/benchmark/Axioms/GRA001+0.ax',precedes_defn) ).
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/benchmark/Axioms/GRA001+0.ax',sequential_defn) ).
fof(c_0_9,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_10,plain,
! [X53,X54,X55,X56,X57,X58,X59] :
( ( path(X53,X54,X55)
| ~ shortest_path(X53,X54,X55) )
& ( X53 != X54
| ~ shortest_path(X53,X54,X55) )
& ( ~ path(X53,X54,X56)
| less_or_equal(length_of(X55),length_of(X56))
| ~ shortest_path(X53,X54,X55) )
& ( path(X57,X58,esk6_3(X57,X58,X59))
| ~ path(X57,X58,X59)
| X57 = X58
| shortest_path(X57,X58,X59) )
& ( ~ less_or_equal(length_of(X59),length_of(esk6_3(X57,X58,X59)))
| ~ path(X57,X58,X59)
| X57 = X58
| shortest_path(X57,X58,X59) ) ),
inference(distribute,[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)],[shortest_path_defn])])])])])]) ).
fof(c_0_11,negated_conjecture,
! [X89] :
( complete
& shortest_path(esk9_0,esk10_0,esk13_0)
& precedes(esk11_0,esk12_0,esk13_0)
& ( ~ edge(X89)
| tail_of(X89) != head_of(esk12_0)
| head_of(X89) != tail_of(esk11_0) ) ),
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_12,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_13,plain,
! [X33,X34,X35,X36] :
( ( vertex(X36)
| ~ path(X33,X34,X35)
| ~ in_path(X36,X35) )
& ( on_path(esk4_4(X33,X34,X35,X36),X35)
| ~ path(X33,X34,X35)
| ~ in_path(X36,X35) )
& ( X36 = head_of(esk4_4(X33,X34,X35,X36))
| X36 = tail_of(esk4_4(X33,X34,X35,X36))
| ~ path(X33,X34,X35)
| ~ in_path(X36,X35) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[in_path_properties])])])]) ).
cnf(c_0_14,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
shortest_path(esk9_0,esk10_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X29,X30,X31,X32] :
( ( edge(X32)
| ~ path(X29,X30,X31)
| ~ on_path(X32,X31) )
& ( in_path(head_of(X32),X31)
| ~ path(X29,X30,X31)
| ~ on_path(X32,X31) )
& ( in_path(tail_of(X32),X31)
| ~ path(X29,X30,X31)
| ~ on_path(X32,X31) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[on_path_properties])])]) ).
fof(c_0_17,plain,
! [X46,X47,X48,X49,X50,X51] :
( ( on_path(X49,X46)
| ~ precedes(X49,X50,X46)
| ~ path(X47,X48,X46) )
& ( on_path(X50,X46)
| ~ precedes(X49,X50,X46)
| ~ path(X47,X48,X46) )
& ( ~ sequential(X49,X50)
| ~ sequential(X49,X51)
| ~ precedes(X51,X50,X46)
| ~ precedes(X49,X50,X46)
| ~ path(X47,X48,X46) )
& ( sequential(X49,esk5_3(X46,X49,X50))
| sequential(X49,X50)
| ~ precedes(X49,X50,X46)
| ~ path(X47,X48,X46) )
& ( precedes(esk5_3(X46,X49,X50),X50,X46)
| sequential(X49,X50)
| ~ precedes(X49,X50,X46)
| ~ path(X47,X48,X46) ) ),
inference(distribute,[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_12])])])])])]) ).
fof(c_0_18,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_19,plain,
( vertex(X1)
| ~ path(X2,X3,X4)
| ~ in_path(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
path(esk9_0,esk10_0,esk13_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
( in_path(tail_of(X1),X2)
| ~ path(X3,X4,X2)
| ~ on_path(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( on_path(X1,X2)
| ~ precedes(X1,X3,X2)
| ~ path(X4,X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
precedes(esk11_0,esk12_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_24,plain,
( in_path(head_of(X1),X2)
| ~ path(X3,X4,X2)
| ~ on_path(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
( on_path(X1,X2)
| ~ precedes(X3,X1,X2)
| ~ path(X4,X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_26,plain,
! [X15,X16] :
( ( edge(esk1_2(X15,X16))
| ~ vertex(X15)
| ~ vertex(X16)
| X15 = X16
| ~ complete )
& ( X15 != head_of(esk1_2(X15,X16))
| X16 != tail_of(esk1_2(X15,X16))
| X16 != head_of(esk1_2(X15,X16))
| X15 != tail_of(esk1_2(X15,X16))
| ~ vertex(X15)
| ~ vertex(X16)
| X15 = X16
| ~ complete )
& ( X16 = head_of(esk1_2(X15,X16))
| X15 = head_of(esk1_2(X15,X16))
| ~ vertex(X15)
| ~ vertex(X16)
| X15 = X16
| ~ complete )
& ( X15 = tail_of(esk1_2(X15,X16))
| X15 = head_of(esk1_2(X15,X16))
| ~ vertex(X15)
| ~ vertex(X16)
| X15 = X16
| ~ complete )
& ( X16 = head_of(esk1_2(X15,X16))
| X16 = tail_of(esk1_2(X15,X16))
| ~ vertex(X15)
| ~ vertex(X16)
| X15 = X16
| ~ complete )
& ( X15 = tail_of(esk1_2(X15,X16))
| X16 = tail_of(esk1_2(X15,X16))
| ~ vertex(X15)
| ~ vertex(X16)
| X15 = X16
| ~ complete ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])])]) ).
cnf(c_0_27,negated_conjecture,
( vertex(X1)
| ~ in_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_28,negated_conjecture,
( in_path(tail_of(X1),esk13_0)
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_29,negated_conjecture,
( on_path(esk11_0,esk13_0)
| ~ path(X1,X2,esk13_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,negated_conjecture,
( in_path(head_of(X1),esk13_0)
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_20]) ).
cnf(c_0_31,negated_conjecture,
( on_path(esk12_0,esk13_0)
| ~ path(X1,X2,esk13_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_32,plain,
( X1 = tail_of(esk1_2(X1,X2))
| X2 = tail_of(esk1_2(X1,X2))
| X1 = X2
| ~ vertex(X1)
| ~ vertex(X2)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_34,negated_conjecture,
( vertex(tail_of(X1))
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,negated_conjecture,
on_path(esk11_0,esk13_0),
inference(spm,[status(thm)],[c_0_29,c_0_20]) ).
fof(c_0_36,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_37,plain,
( X1 = head_of(esk1_2(X2,X1))
| X2 = head_of(esk1_2(X2,X1))
| X2 = X1
| ~ vertex(X2)
| ~ vertex(X1)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_38,negated_conjecture,
( vertex(head_of(X1))
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_30]) ).
cnf(c_0_39,negated_conjecture,
on_path(esk12_0,esk13_0),
inference(spm,[status(thm)],[c_0_31,c_0_20]) ).
cnf(c_0_40,plain,
( tail_of(esk1_2(X1,X2)) = X1
| tail_of(esk1_2(X1,X2)) = X2
| X1 = X2
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]) ).
cnf(c_0_41,negated_conjecture,
vertex(tail_of(esk11_0)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
fof(c_0_42,plain,
! [X61,X62,X63,X64,X65,X66] :
( ( tail_of(X66) != tail_of(X63)
| head_of(X66) != head_of(X64)
| ~ shortest_path(X61,X62,X65)
| ~ precedes(X63,X64,X65) )
& ( ~ precedes(X64,X63,X65)
| ~ shortest_path(X61,X62,X65)
| ~ precedes(X63,X64,X65) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])])]) ).
cnf(c_0_43,plain,
( head_of(esk1_2(X1,X2)) = X2
| head_of(esk1_2(X1,X2)) = X1
| X2 = X1
| ~ vertex(X1)
| ~ vertex(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_33])]) ).
cnf(c_0_44,negated_conjecture,
vertex(head_of(esk12_0)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,plain,
( X1 = tail_of(esk1_2(X1,X2))
| X1 = head_of(esk1_2(X1,X2))
| X1 = X2
| ~ vertex(X1)
| ~ vertex(X2)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_46,negated_conjecture,
( tail_of(esk1_2(X1,tail_of(esk11_0))) = tail_of(esk11_0)
| tail_of(esk1_2(X1,tail_of(esk11_0))) = X1
| X1 = tail_of(esk11_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
fof(c_0_47,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]) ).
cnf(c_0_48,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_42]) ).
cnf(c_0_49,negated_conjecture,
( head_of(esk1_2(head_of(esk12_0),X1)) = head_of(esk12_0)
| head_of(esk1_2(head_of(esk12_0),X1)) = X1
| X1 = head_of(esk12_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,plain,
( tail_of(esk1_2(X1,X2)) = X1
| head_of(esk1_2(X1,X2)) = X1
| X1 = X2
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_33])]) ).
cnf(c_0_51,negated_conjecture,
( tail_of(esk1_2(head_of(esk12_0),tail_of(esk11_0))) = head_of(esk12_0)
| tail_of(esk1_2(head_of(esk12_0),tail_of(esk11_0))) = tail_of(esk11_0)
| tail_of(esk11_0) = head_of(esk12_0) ),
inference(spm,[status(thm)],[c_0_46,c_0_44]) ).
fof(c_0_52,plain,
! [X40,X41,X42,X43,X44,X45] :
( ( ~ sequential(X43,X44)
| ~ on_path(X43,X40)
| ~ on_path(X44,X40)
| precedes(X43,X44,X40)
| ~ path(X41,X42,X40) )
& ( ~ sequential(X43,X45)
| ~ precedes(X45,X44,X40)
| ~ on_path(X43,X40)
| ~ on_path(X44,X40)
| precedes(X43,X44,X40)
| ~ path(X41,X42,X40) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])])]) ).
cnf(c_0_53,negated_conjecture,
( head_of(X1) != head_of(X2)
| tail_of(X1) != tail_of(X3)
| ~ precedes(X3,X2,esk13_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_15]) ).
cnf(c_0_54,plain,
( X1 = head_of(esk1_2(X2,X1))
| X1 = tail_of(esk1_2(X2,X1))
| X2 = X1
| ~ vertex(X2)
| ~ vertex(X1)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_55,negated_conjecture,
( ~ edge(X1)
| tail_of(X1) != head_of(esk12_0)
| head_of(X1) != tail_of(esk11_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_56,negated_conjecture,
( head_of(esk1_2(head_of(esk12_0),tail_of(esk11_0))) = tail_of(esk11_0)
| head_of(esk1_2(head_of(esk12_0),tail_of(esk11_0))) = head_of(esk12_0)
| tail_of(esk11_0) = head_of(esk12_0) ),
inference(spm,[status(thm)],[c_0_49,c_0_41]) ).
cnf(c_0_57,negated_conjecture,
( tail_of(esk1_2(head_of(esk12_0),tail_of(esk11_0))) = head_of(esk12_0)
| head_of(esk1_2(head_of(esk12_0),tail_of(esk11_0))) = head_of(esk12_0)
| tail_of(esk11_0) = head_of(esk12_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_41]),c_0_44])]) ).
cnf(c_0_58,plain,
( edge(esk1_2(X1,X2))
| X1 = X2
| ~ vertex(X1)
| ~ vertex(X2)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_59,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_52]) ).
cnf(c_0_60,plain,
( ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_61,negated_conjecture,
( head_of(X1) != head_of(esk12_0)
| tail_of(X1) != tail_of(esk11_0) ),
inference(spm,[status(thm)],[c_0_53,c_0_23]) ).
cnf(c_0_62,plain,
( tail_of(esk1_2(X1,X2)) = X2
| head_of(esk1_2(X1,X2)) = X2
| X2 = X1
| ~ vertex(X1)
| ~ vertex(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_33])]) ).
cnf(c_0_63,negated_conjecture,
( head_of(esk1_2(head_of(esk12_0),tail_of(esk11_0))) = head_of(esk12_0)
| tail_of(esk11_0) = head_of(esk12_0)
| ~ edge(esk1_2(head_of(esk12_0),tail_of(esk11_0))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]) ).
cnf(c_0_64,plain,
( X1 = X2
| edge(esk1_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_33])]) ).
cnf(c_0_65,plain,
( edge(X1)
| ~ path(X2,X3,X4)
| ~ on_path(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_66,negated_conjecture,
( precedes(X1,X2,esk13_0)
| ~ sequential(X1,X2)
| ~ on_path(X2,esk13_0)
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_59,c_0_20]) ).
cnf(c_0_67,negated_conjecture,
( ~ precedes(X1,X2,esk13_0)
| ~ precedes(X2,X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_15]) ).
fof(c_0_68,plain,
! [X38,X39] :
( ( edge(X38)
| ~ sequential(X38,X39) )
& ( edge(X39)
| ~ sequential(X38,X39) )
& ( X38 != X39
| ~ sequential(X38,X39) )
& ( head_of(X38) = tail_of(X39)
| ~ sequential(X38,X39) )
& ( ~ edge(X38)
| ~ edge(X39)
| X38 = X39
| head_of(X38) != tail_of(X39)
| sequential(X38,X39) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sequential_defn])])]) ).
cnf(c_0_69,negated_conjecture,
( head_of(esk1_2(X1,X2)) = X2
| X2 = X1
| head_of(esk1_2(X1,X2)) != head_of(esk12_0)
| X2 != tail_of(esk11_0)
| ~ vertex(X1)
| ~ vertex(X2) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_70,negated_conjecture,
( head_of(esk1_2(head_of(esk12_0),tail_of(esk11_0))) = head_of(esk12_0)
| tail_of(esk11_0) = head_of(esk12_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_41]),c_0_44])]) ).
cnf(c_0_71,negated_conjecture,
( edge(X1)
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_65,c_0_20]) ).
cnf(c_0_72,negated_conjecture,
( precedes(X1,esk11_0,esk13_0)
| ~ sequential(X1,esk11_0)
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_66,c_0_35]) ).
cnf(c_0_73,negated_conjecture,
~ precedes(esk12_0,esk11_0,esk13_0),
inference(spm,[status(thm)],[c_0_67,c_0_23]) ).
cnf(c_0_74,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_75,negated_conjecture,
tail_of(esk11_0) = head_of(esk12_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_44]),c_0_41])]) ).
cnf(c_0_76,negated_conjecture,
edge(esk11_0),
inference(spm,[status(thm)],[c_0_71,c_0_35]) ).
cnf(c_0_77,negated_conjecture,
~ sequential(esk12_0,esk11_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_39]),c_0_73]) ).
cnf(c_0_78,negated_conjecture,
( X1 = esk11_0
| sequential(X1,esk11_0)
| head_of(esk12_0) != head_of(X1)
| ~ edge(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76])]) ).
cnf(c_0_79,negated_conjecture,
edge(esk12_0),
inference(spm,[status(thm)],[c_0_71,c_0_39]) ).
cnf(c_0_80,negated_conjecture,
head_of(esk12_0) != head_of(esk11_0),
inference(er,[status(thm)],[c_0_61]) ).
cnf(c_0_81,negated_conjecture,
esk12_0 = esk11_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79])]) ).
cnf(c_0_82,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRA007+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.00/0.10 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.30 % Computer : n016.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Sun Aug 27 03:45:42 EDT 2023
% 0.11/0.30 % CPUTime :
% 0.15/0.52 start to proof: theBenchmark
% 0.15/0.79 % Version : CSE_E---1.5
% 0.15/0.79 % Problem : theBenchmark.p
% 0.15/0.79 % Proof found
% 0.15/0.79 % SZS status Theorem for theBenchmark.p
% 0.15/0.79 % SZS output start Proof
% See solution above
% 0.69/0.80 % Total time : 0.258000 s
% 0.69/0.80 % SZS output end Proof
% 0.69/0.80 % Total time : 0.261000 s
%------------------------------------------------------------------------------