TSTP Solution File: GRA008+2 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRA008+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n022.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 00:00:07 EDT 2023
% Result : Theorem 1.08s 1.17s
% Output : CNFRefutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 49
% Syntax : Number of formulae : 137 ( 18 unt; 37 typ; 0 def)
% Number of atoms : 453 ( 137 equ)
% Maximal formula atoms : 37 ( 4 avg)
% Number of connectives : 575 ( 222 ~; 244 |; 81 &)
% ( 5 <=>; 21 =>; 0 <=; 2 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 55 ( 25 >; 30 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 2 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 11 con; 0-4 aty)
% Number of variables : 233 ( 15 sgn; 100 !; 10 ?; 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_4: ( $i * $i * $i * $i ) > $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 ).
tff(decl_58,type,
esk14_0: $i ).
fof(sequential_is_triangle,conjecture,
( complete
=> ! [X2,X3,X7,X8,X4] :
( ( shortest_path(X2,X3,X4)
& precedes(X7,X8,X4)
& sequential(X7,X8) )
=> ? [X9] : triangle(X7,X8,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_is_triangle) ).
fof(back_edge,lemma,
( 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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/GRA001+0.ax',precedes_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/sandbox2/benchmark/Axioms/GRA001+0.ax',complete_properties) ).
fof(edge_ends_are_vertices,axiom,
! [X1] :
( edge(X1)
=> ( vertex(head_of(X1))
& vertex(tail_of(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',edge_ends_are_vertices) ).
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/sandbox2/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/sandbox2/benchmark/Axioms/GRA001+0.ax',on_path_properties) ).
fof(no_loops,axiom,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',no_loops) ).
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/benchmark/Axioms/GRA001+0.ax',shortest_path_properties) ).
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/benchmark/theBenchmark.p',triangle_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/sandbox2/benchmark/Axioms/GRA001+0.ax',sequential_defn) ).
fof(c_0_12,negated_conjecture,
~ ( complete
=> ! [X2,X3,X7,X8,X4] :
( ( shortest_path(X2,X3,X4)
& precedes(X7,X8,X4)
& sequential(X7,X8) )
=> ? [X9] : triangle(X7,X8,X9) ) ),
inference(assume_negation,[status(cth)],[sequential_is_triangle]) ).
fof(c_0_13,lemma,
! [X84,X85,X86,X87,X88] :
( ( edge(esk9_4(X84,X85,X86,X87))
| ~ shortest_path(X84,X85,X88)
| ~ precedes(X86,X87,X88)
| ~ complete )
& ( tail_of(esk9_4(X84,X85,X86,X87)) = head_of(X87)
| ~ shortest_path(X84,X85,X88)
| ~ precedes(X86,X87,X88)
| ~ complete )
& ( head_of(esk9_4(X84,X85,X86,X87)) = tail_of(X86)
| ~ shortest_path(X84,X85,X88)
| ~ precedes(X86,X87,X88)
| ~ complete ) ),
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)],[back_edge])])])])])]) ).
fof(c_0_14,negated_conjecture,
! [X95] :
( complete
& shortest_path(esk10_0,esk11_0,esk14_0)
& precedes(esk12_0,esk13_0,esk14_0)
& sequential(esk12_0,esk13_0)
& ~ triangle(esk12_0,esk13_0,X95) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
cnf(c_0_15,lemma,
( head_of(esk9_4(X1,X2,X3,X4)) = tail_of(X3)
| ~ shortest_path(X1,X2,X5)
| ~ precedes(X3,X4,X5)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,lemma,
( edge(esk9_4(X1,X2,X3,X4))
| ~ shortest_path(X1,X2,X5)
| ~ precedes(X3,X4,X5)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,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_19,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]) ).
cnf(c_0_20,lemma,
( tail_of(esk9_4(X1,X2,X3,X4)) = head_of(X4)
| ~ shortest_path(X1,X2,X5)
| ~ precedes(X3,X4,X5)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_21,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_22,plain,
! [X14] :
( ( vertex(head_of(X14))
| ~ edge(X14) )
& ( vertex(tail_of(X14))
| ~ edge(X14) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[edge_ends_are_vertices])])]) ).
cnf(c_0_23,lemma,
( head_of(esk9_4(X1,X2,X3,X4)) = tail_of(X3)
| ~ shortest_path(X1,X2,X5)
| ~ precedes(X3,X4,X5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]) ).
cnf(c_0_24,negated_conjecture,
shortest_path(esk10_0,esk11_0,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,lemma,
( edge(esk9_4(X1,X2,X3,X4))
| ~ shortest_path(X1,X2,X5)
| ~ precedes(X3,X4,X5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_16])]) ).
fof(c_0_26,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_27,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_28,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_29,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_19])])])])])]) ).
fof(c_0_30,plain,
! [X13] :
( ~ edge(X13)
| head_of(X13) != tail_of(X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[no_loops])]) ).
cnf(c_0_31,lemma,
( tail_of(esk9_4(X1,X2,X3,X4)) = head_of(X4)
| ~ shortest_path(X1,X2,X5)
| ~ precedes(X3,X4,X5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_16])]) ).
fof(c_0_32,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_33,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_21])])])])]) ).
cnf(c_0_34,plain,
( vertex(head_of(X1))
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_35,negated_conjecture,
( head_of(esk9_4(esk10_0,esk11_0,X1,X2)) = tail_of(X1)
| ~ precedes(X1,X2,esk14_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_36,negated_conjecture,
( edge(esk9_4(esk10_0,esk11_0,X1,X2))
| ~ precedes(X1,X2,esk14_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_37,plain,
( vertex(X1)
| ~ path(X2,X3,X4)
| ~ in_path(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_38,negated_conjecture,
path(esk10_0,esk11_0,esk14_0),
inference(spm,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_39,plain,
( in_path(head_of(X1),X2)
| ~ path(X3,X4,X2)
| ~ on_path(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_40,plain,
( on_path(X1,X2)
| ~ precedes(X3,X1,X2)
| ~ path(X4,X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_41,negated_conjecture,
precedes(esk12_0,esk13_0,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_42,plain,
( ~ edge(X1)
| head_of(X1) != tail_of(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_43,negated_conjecture,
( tail_of(esk9_4(esk10_0,esk11_0,X1,X2)) = head_of(X2)
| ~ precedes(X1,X2,esk14_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_24]) ).
fof(c_0_44,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_32])])])]) ).
cnf(c_0_45,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_33]) ).
cnf(c_0_46,negated_conjecture,
( vertex(tail_of(X1))
| ~ precedes(X1,X2,esk14_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_47,negated_conjecture,
( vertex(X1)
| ~ in_path(X1,esk14_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_48,negated_conjecture,
( in_path(head_of(X1),esk14_0)
| ~ on_path(X1,esk14_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_38]) ).
cnf(c_0_49,negated_conjecture,
( on_path(esk13_0,esk14_0)
| ~ path(X1,X2,esk14_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_50,negated_conjecture,
( head_of(esk9_4(esk10_0,esk11_0,X1,X2)) != head_of(X2)
| ~ precedes(X1,X2,esk14_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_36]) ).
cnf(c_0_51,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_44]) ).
cnf(c_0_52,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_45,c_0_16])]) ).
cnf(c_0_53,negated_conjecture,
vertex(tail_of(esk12_0)),
inference(spm,[status(thm)],[c_0_46,c_0_41]) ).
cnf(c_0_54,negated_conjecture,
( vertex(head_of(X1))
| ~ on_path(X1,esk14_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_55,negated_conjecture,
on_path(esk13_0,esk14_0),
inference(spm,[status(thm)],[c_0_49,c_0_38]) ).
cnf(c_0_56,negated_conjecture,
( tail_of(X1) != head_of(X2)
| ~ precedes(X1,X2,esk14_0) ),
inference(spm,[status(thm)],[c_0_50,c_0_35]) ).
fof(c_0_57,plain,
! [X67,X68,X69] :
( ( edge(X67)
| ~ triangle(X67,X68,X69) )
& ( edge(X68)
| ~ triangle(X67,X68,X69) )
& ( edge(X69)
| ~ triangle(X67,X68,X69) )
& ( sequential(X67,X68)
| ~ triangle(X67,X68,X69) )
& ( sequential(X68,X69)
| ~ triangle(X67,X68,X69) )
& ( sequential(X69,X67)
| ~ triangle(X67,X68,X69) )
& ( ~ edge(X67)
| ~ edge(X68)
| ~ edge(X69)
| ~ sequential(X67,X68)
| ~ sequential(X68,X69)
| ~ sequential(X69,X67)
| triangle(X67,X68,X69) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[triangle_defn])])]) ).
fof(c_0_58,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_59,negated_conjecture,
( head_of(X1) != head_of(X2)
| tail_of(X1) != tail_of(X3)
| ~ precedes(X3,X2,esk14_0) ),
inference(spm,[status(thm)],[c_0_51,c_0_24]) ).
cnf(c_0_60,negated_conjecture,
( tail_of(esk1_2(X1,tail_of(esk12_0))) = tail_of(esk12_0)
| tail_of(esk1_2(X1,tail_of(esk12_0))) = X1
| X1 = tail_of(esk12_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_61,negated_conjecture,
vertex(head_of(esk13_0)),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_62,negated_conjecture,
tail_of(esk12_0) != head_of(esk13_0),
inference(spm,[status(thm)],[c_0_56,c_0_41]) ).
cnf(c_0_63,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_57]) ).
cnf(c_0_64,plain,
( edge(X1)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_65,plain,
( edge(esk1_2(X1,X2))
| X1 = X2
| ~ vertex(X1)
| ~ vertex(X2)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_66,plain,
( edge(X1)
| ~ sequential(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_67,negated_conjecture,
sequential(esk12_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_68,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_33]) ).
cnf(c_0_69,negated_conjecture,
( head_of(X1) != head_of(esk13_0)
| tail_of(X1) != tail_of(esk12_0) ),
inference(spm,[status(thm)],[c_0_59,c_0_41]) ).
cnf(c_0_70,negated_conjecture,
( tail_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = head_of(esk13_0)
| tail_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = tail_of(esk12_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]) ).
cnf(c_0_71,negated_conjecture,
~ triangle(esk12_0,esk13_0,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_72,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_63,c_0_64]),c_0_64]),c_0_64]) ).
cnf(c_0_73,plain,
( X1 = X2
| sequential(X1,X2)
| ~ edge(X1)
| ~ edge(X2)
| head_of(X1) != tail_of(X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_74,plain,
( X1 = X2
| edge(esk1_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_16])]) ).
cnf(c_0_75,negated_conjecture,
edge(esk13_0),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_76,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_33]) ).
cnf(c_0_77,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_68,c_0_16])]) ).
cnf(c_0_78,negated_conjecture,
( tail_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = head_of(esk13_0)
| head_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) != head_of(esk13_0) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_79,negated_conjecture,
( ~ sequential(X1,esk12_0)
| ~ sequential(esk13_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_67])]) ).
cnf(c_0_80,plain,
( esk1_2(X1,X2) = X3
| X1 = X2
| sequential(esk1_2(X1,X2),X3)
| tail_of(X3) != head_of(esk1_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1)
| ~ edge(X3) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_81,negated_conjecture,
edge(esk12_0),
inference(spm,[status(thm)],[c_0_64,c_0_67]) ).
cnf(c_0_82,negated_conjecture,
( esk13_0 = X1
| sequential(esk13_0,X1)
| tail_of(X1) != head_of(esk13_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_75]) ).
cnf(c_0_83,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_76,c_0_16])]) ).
cnf(c_0_84,negated_conjecture,
( head_of(esk1_2(head_of(esk13_0),X1)) = head_of(esk13_0)
| head_of(esk1_2(head_of(esk13_0),X1)) = X1
| X1 = head_of(esk13_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_61]) ).
cnf(c_0_85,negated_conjecture,
( head_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) != head_of(esk13_0)
| ~ edge(esk1_2(head_of(esk13_0),tail_of(esk12_0))) ),
inference(spm,[status(thm)],[c_0_42,c_0_78]) ).
cnf(c_0_86,negated_conjecture,
( esk1_2(X1,X2) = esk12_0
| X1 = X2
| head_of(esk1_2(X1,X2)) != tail_of(esk12_0)
| ~ sequential(esk13_0,esk1_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81])]) ).
cnf(c_0_87,negated_conjecture,
( head_of(esk1_2(X1,X2)) = X1
| esk1_2(X1,X2) = esk13_0
| X1 = X2
| sequential(esk13_0,esk1_2(X1,X2))
| X1 != head_of(esk13_0)
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_74]) ).
cnf(c_0_88,negated_conjecture,
( head_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = tail_of(esk12_0)
| head_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = head_of(esk13_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_53]),c_0_62]) ).
cnf(c_0_89,negated_conjecture,
head_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) != head_of(esk13_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_74]),c_0_53]),c_0_61])]),c_0_62]) ).
cnf(c_0_90,plain,
( head_of(X1) = tail_of(X2)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_91,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_33]) ).
cnf(c_0_92,negated_conjecture,
( head_of(esk1_2(X1,X2)) = X1
| esk1_2(X1,X2) = esk13_0
| esk1_2(X1,X2) = esk12_0
| X1 = X2
| head_of(esk1_2(X1,X2)) != tail_of(esk12_0)
| X1 != head_of(esk13_0)
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_93,negated_conjecture,
head_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = tail_of(esk12_0),
inference(sr,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_94,negated_conjecture,
tail_of(esk13_0) = head_of(esk12_0),
inference(spm,[status(thm)],[c_0_90,c_0_67]) ).
cnf(c_0_95,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_91,c_0_16])]) ).
cnf(c_0_96,negated_conjecture,
( esk1_2(head_of(esk13_0),tail_of(esk12_0)) = esk12_0
| esk1_2(head_of(esk13_0),tail_of(esk12_0)) = esk13_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_53]),c_0_61])]),c_0_62]) ).
cnf(c_0_97,negated_conjecture,
tail_of(esk12_0) != head_of(esk12_0),
inference(spm,[status(thm)],[c_0_69,c_0_94]) ).
cnf(c_0_98,negated_conjecture,
esk1_2(head_of(esk13_0),tail_of(esk12_0)) = esk12_0,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_94]),c_0_61]),c_0_53])]),c_0_97]),c_0_62]) ).
cnf(c_0_99,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_98]),c_0_97]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRA008+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 03:29:10 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.59 start to proof: theBenchmark
% 1.08/1.17 % Version : CSE_E---1.5
% 1.08/1.17 % Problem : theBenchmark.p
% 1.08/1.17 % Proof found
% 1.08/1.17 % SZS status Theorem for theBenchmark.p
% 1.08/1.17 % SZS output start Proof
% See solution above
% 1.08/1.18 % Total time : 0.571000 s
% 1.08/1.18 % SZS output end Proof
% 1.08/1.18 % Total time : 0.575000 s
%------------------------------------------------------------------------------