TSTP Solution File: GRA008+1 by E-SAT---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : GRA008+1 : TPTP v8.2.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n010.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 May 20 20:41:22 EDT 2024
% Result : Theorem 1.11s 0.61s
% Output : CNFRefutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 99 ( 16 unt; 0 def)
% Number of atoms : 454 ( 144 equ)
% Maximal formula atoms : 37 ( 4 avg)
% Number of connectives : 572 ( 217 ~; 245 |; 78 &)
% ( 7 <=>; 22 =>; 1 <=; 2 <~>)
% 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 : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 209 ( 25 sgn 97 !; 10 ?)
% 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/benchmark/Axioms/GRA001+0.ax',complete_properties) ).
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(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(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(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(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(no_loops,axiom,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',no_loops) ).
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(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/benchmark/Axioms/GRA001+0.ax',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/benchmark/Axioms/GRA001+0.ax',shortest_path_defn) ).
fof(c_0_10,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_11,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_12,plain,
! [X51,X52] :
( ( edge(esk8_2(X51,X52))
| ~ vertex(X51)
| ~ vertex(X52)
| X51 = X52
| ~ complete )
& ( X51 != head_of(esk8_2(X51,X52))
| X52 != tail_of(esk8_2(X51,X52))
| X52 != head_of(esk8_2(X51,X52))
| X51 != tail_of(esk8_2(X51,X52))
| ~ vertex(X51)
| ~ vertex(X52)
| X51 = X52
| ~ complete )
& ( X52 = head_of(esk8_2(X51,X52))
| X51 = head_of(esk8_2(X51,X52))
| ~ vertex(X51)
| ~ vertex(X52)
| X51 = X52
| ~ complete )
& ( X51 = tail_of(esk8_2(X51,X52))
| X51 = head_of(esk8_2(X51,X52))
| ~ vertex(X51)
| ~ vertex(X52)
| X51 = X52
| ~ complete )
& ( X52 = head_of(esk8_2(X51,X52))
| X52 = tail_of(esk8_2(X51,X52))
| ~ vertex(X51)
| ~ vertex(X52)
| X51 = X52
| ~ complete )
& ( X51 = tail_of(esk8_2(X51,X52))
| X52 = tail_of(esk8_2(X51,X52))
| ~ vertex(X51)
| ~ vertex(X52)
| X51 = X52
| ~ 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_10])])])])])]) ).
fof(c_0_13,negated_conjecture,
! [X18] :
( complete
& shortest_path(esk1_0,esk2_0,esk5_0)
& precedes(esk3_0,esk4_0,esk5_0)
& sequential(esk3_0,esk4_0)
& ~ triangle(esk3_0,esk4_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_11])])])])]) ).
fof(c_0_14,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_15,plain,
( X1 = head_of(esk8_2(X2,X1))
| X2 = head_of(esk8_2(X2,X1))
| X2 = X1
| ~ vertex(X2)
| ~ vertex(X1)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_17,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_18,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_19,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_14])])])]) ).
cnf(c_0_20,plain,
( head_of(esk8_2(X1,X2)) = X2
| head_of(esk8_2(X1,X2)) = X1
| X2 = X1
| ~ vertex(X1)
| ~ vertex(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]) ).
cnf(c_0_21,plain,
( vertex(head_of(X1))
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,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_23,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_18]) ).
cnf(c_0_24,plain,
( edge(X1)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( head_of(esk8_2(head_of(X1),X2)) = head_of(X1)
| head_of(esk8_2(head_of(X1),X2)) = X2
| X2 = head_of(X1)
| ~ vertex(X2)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( vertex(tail_of(X1))
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
( edge(X1)
| ~ sequential(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,negated_conjecture,
sequential(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_29,plain,
! [X37,X38,X39,X40,X41,X42] :
( ( tail_of(X42) != tail_of(X39)
| head_of(X42) != head_of(X40)
| ~ shortest_path(X37,X38,X41)
| ~ precedes(X39,X40,X41) )
& ( ~ precedes(X40,X39,X41)
| ~ shortest_path(X37,X38,X41)
| ~ precedes(X39,X40,X41) ) ),
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_22])])])])]) ).
cnf(c_0_30,negated_conjecture,
~ triangle(esk3_0,esk4_0,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_31,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_23,c_0_24]),c_0_24]),c_0_24]) ).
fof(c_0_32,plain,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
inference(fof_simplification,[status(thm)],[no_loops]) ).
cnf(c_0_33,plain,
( head_of(esk8_2(head_of(X1),tail_of(X2))) = tail_of(X2)
| head_of(esk8_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_25,c_0_26]) ).
cnf(c_0_34,negated_conjecture,
edge(esk4_0),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,plain,
( X1 = tail_of(esk8_2(X1,X2))
| X2 = tail_of(esk8_2(X1,X2))
| X1 = X2
| ~ vertex(X1)
| ~ vertex(X2)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_36,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_29]) ).
cnf(c_0_37,negated_conjecture,
shortest_path(esk1_0,esk2_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_38,negated_conjecture,
( ~ sequential(X1,esk3_0)
| ~ sequential(esk4_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_28])]) ).
cnf(c_0_39,plain,
( X1 = X2
| sequential(X1,X2)
| ~ edge(X1)
| ~ edge(X2)
| head_of(X1) != tail_of(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_40,negated_conjecture,
edge(esk3_0),
inference(spm,[status(thm)],[c_0_24,c_0_28]) ).
fof(c_0_41,plain,
! [X54] :
( ~ edge(X54)
| head_of(X54) != tail_of(X54) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])]) ).
cnf(c_0_42,negated_conjecture,
( head_of(esk8_2(head_of(esk4_0),tail_of(X1))) = head_of(esk4_0)
| head_of(esk8_2(head_of(esk4_0),tail_of(X1))) = tail_of(X1)
| tail_of(X1) = head_of(esk4_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_43,plain,
( tail_of(esk8_2(X1,X2)) = X1
| tail_of(esk8_2(X1,X2)) = X2
| X1 = X2
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_16])]) ).
cnf(c_0_44,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_36,c_0_37]) ).
cnf(c_0_45,negated_conjecture,
precedes(esk3_0,esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_46,negated_conjecture,
( X1 = esk3_0
| head_of(X1) != tail_of(esk3_0)
| ~ sequential(esk4_0,X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]),c_0_27]) ).
cnf(c_0_47,plain,
( ~ edge(X1)
| head_of(X1) != tail_of(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,negated_conjecture,
( head_of(esk8_2(head_of(esk4_0),tail_of(esk3_0))) = tail_of(esk3_0)
| head_of(esk8_2(head_of(esk4_0),tail_of(esk3_0))) = head_of(esk4_0)
| head_of(esk4_0) = tail_of(esk3_0) ),
inference(spm,[status(thm)],[c_0_42,c_0_40]) ).
cnf(c_0_49,plain,
( tail_of(esk8_2(X1,tail_of(X2))) = tail_of(X2)
| tail_of(esk8_2(X1,tail_of(X2))) = X1
| X1 = tail_of(X2)
| ~ vertex(X1)
| ~ edge(X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_26]) ).
cnf(c_0_50,negated_conjecture,
( head_of(X1) != head_of(esk4_0)
| tail_of(X1) != tail_of(esk3_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
fof(c_0_51,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_52,negated_conjecture,
( esk4_0 = X1
| X1 = esk3_0
| head_of(X1) != tail_of(esk3_0)
| tail_of(X1) != head_of(esk4_0)
| ~ edge(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_39]),c_0_34])]) ).
cnf(c_0_53,negated_conjecture,
( head_of(esk8_2(head_of(esk4_0),tail_of(esk3_0))) = tail_of(esk3_0)
| head_of(esk4_0) = tail_of(esk3_0)
| tail_of(esk8_2(head_of(esk4_0),tail_of(esk3_0))) != head_of(esk4_0)
| ~ edge(esk8_2(head_of(esk4_0),tail_of(esk3_0))) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,plain,
( tail_of(esk8_2(head_of(X1),tail_of(X2))) = head_of(X1)
| tail_of(esk8_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_49,c_0_21]) ).
cnf(c_0_55,negated_conjecture,
( head_of(esk8_2(head_of(esk4_0),tail_of(esk3_0))) = tail_of(esk3_0)
| head_of(esk4_0) = tail_of(esk3_0)
| tail_of(esk8_2(head_of(esk4_0),tail_of(esk3_0))) != tail_of(esk3_0) ),
inference(spm,[status(thm)],[c_0_50,c_0_48]) ).
fof(c_0_56,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_57,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_58,plain,
! [X30,X31,X32,X33,X34,X35] :
( ( on_path(X33,X30)
| ~ precedes(X33,X34,X30)
| ~ path(X31,X32,X30) )
& ( on_path(X34,X30)
| ~ precedes(X33,X34,X30)
| ~ path(X31,X32,X30) )
& ( ~ sequential(X33,X34)
| ~ sequential(X33,X35)
| ~ precedes(X35,X34,X30)
| ~ precedes(X33,X34,X30)
| ~ path(X31,X32,X30) )
& ( sequential(X33,esk6_3(X30,X33,X34))
| sequential(X33,X34)
| ~ precedes(X33,X34,X30)
| ~ path(X31,X32,X30) )
& ( precedes(esk6_3(X30,X33,X34),X34,X30)
| sequential(X33,X34)
| ~ precedes(X33,X34,X30)
| ~ path(X31,X32,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_51])])])])])])]) ).
cnf(c_0_59,negated_conjecture,
( esk8_2(head_of(esk4_0),tail_of(esk3_0)) = esk3_0
| esk8_2(head_of(esk4_0),tail_of(esk3_0)) = esk4_0
| head_of(esk4_0) = tail_of(esk3_0)
| tail_of(esk8_2(head_of(esk4_0),tail_of(esk3_0))) != head_of(esk4_0)
| ~ edge(esk8_2(head_of(esk4_0),tail_of(esk3_0))) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_60,negated_conjecture,
( tail_of(esk8_2(head_of(X1),tail_of(esk3_0))) = tail_of(esk3_0)
| tail_of(esk8_2(head_of(X1),tail_of(esk3_0))) = head_of(X1)
| head_of(X1) = tail_of(esk3_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_40]) ).
cnf(c_0_61,negated_conjecture,
( head_of(esk4_0) = tail_of(esk3_0)
| tail_of(esk8_2(head_of(esk4_0),tail_of(esk3_0))) != tail_of(esk3_0)
| ~ edge(esk8_2(head_of(esk4_0),tail_of(esk3_0))) ),
inference(spm,[status(thm)],[c_0_47,c_0_55]) ).
cnf(c_0_62,plain,
( edge(esk8_2(X1,X2))
| X1 = X2
| ~ vertex(X1)
| ~ vertex(X2)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_63,plain,
( head_of(X1) = tail_of(X2)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_64,plain,
! [X24,X25,X26,X27,X28,X29] :
( ( ~ sequential(X27,X28)
| ~ on_path(X27,X24)
| ~ on_path(X28,X24)
| precedes(X27,X28,X24)
| ~ path(X25,X26,X24) )
& ( ~ sequential(X27,X29)
| ~ precedes(X29,X28,X24)
| ~ on_path(X27,X24)
| ~ on_path(X28,X24)
| precedes(X27,X28,X24)
| ~ path(X25,X26,X24) ) ),
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_56])])])])]) ).
fof(c_0_65,plain,
! [X43,X44,X45,X46,X47,X48,X49] :
( ( path(X43,X44,X45)
| ~ shortest_path(X43,X44,X45) )
& ( X43 != X44
| ~ shortest_path(X43,X44,X45) )
& ( ~ path(X43,X44,X46)
| less_or_equal(length_of(X45),length_of(X46))
| ~ shortest_path(X43,X44,X45) )
& ( path(X47,X48,esk7_3(X47,X48,X49))
| ~ path(X47,X48,X49)
| X47 = X48
| shortest_path(X47,X48,X49) )
& ( ~ less_or_equal(length_of(X49),length_of(esk7_3(X47,X48,X49)))
| ~ path(X47,X48,X49)
| X47 = X48
| shortest_path(X47,X48,X49) ) ),
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_57])])])])])])]) ).
cnf(c_0_66,plain,
( on_path(X1,X2)
| ~ precedes(X1,X3,X2)
| ~ path(X4,X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_67,plain,
( on_path(X1,X2)
| ~ precedes(X3,X1,X2)
| ~ path(X4,X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_68,plain,
( X1 = tail_of(esk8_2(X1,X2))
| X1 = head_of(esk8_2(X1,X2))
| X1 = X2
| ~ vertex(X1)
| ~ vertex(X2)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_69,plain,
( X1 = head_of(esk8_2(X2,X1))
| X1 = tail_of(esk8_2(X2,X1))
| X2 = X1
| ~ vertex(X2)
| ~ vertex(X1)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_70,negated_conjecture,
( esk8_2(head_of(esk4_0),tail_of(esk3_0)) = esk4_0
| esk8_2(head_of(esk4_0),tail_of(esk3_0)) = esk3_0
| head_of(esk4_0) = tail_of(esk3_0)
| ~ edge(esk8_2(head_of(esk4_0),tail_of(esk3_0))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_34])]),c_0_61]) ).
cnf(c_0_71,plain,
( X1 = X2
| edge(esk8_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_16])]) ).
cnf(c_0_72,negated_conjecture,
head_of(esk3_0) = tail_of(esk4_0),
inference(spm,[status(thm)],[c_0_63,c_0_28]) ).
cnf(c_0_73,plain,
( ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_74,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_64]) ).
cnf(c_0_75,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_76,negated_conjecture,
( on_path(esk3_0,esk5_0)
| ~ path(X1,X2,esk5_0) ),
inference(spm,[status(thm)],[c_0_66,c_0_45]) ).
cnf(c_0_77,negated_conjecture,
( on_path(esk4_0,esk5_0)
| ~ path(X1,X2,esk5_0) ),
inference(spm,[status(thm)],[c_0_67,c_0_45]) ).
cnf(c_0_78,plain,
( tail_of(esk8_2(X1,X2)) = X1
| head_of(esk8_2(X1,X2)) = X1
| X1 = X2
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_16])]) ).
cnf(c_0_79,plain,
( tail_of(esk8_2(X1,X2)) = X2
| head_of(esk8_2(X1,X2)) = X2
| X2 = X1
| ~ vertex(X1)
| ~ vertex(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_16])]) ).
cnf(c_0_80,negated_conjecture,
( esk8_2(head_of(esk4_0),tail_of(esk3_0)) = esk3_0
| esk8_2(head_of(esk4_0),tail_of(esk3_0)) = esk4_0
| head_of(esk4_0) = tail_of(esk3_0)
| ~ vertex(tail_of(esk3_0))
| ~ vertex(head_of(esk4_0)) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_81,negated_conjecture,
tail_of(esk4_0) != tail_of(esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_72]),c_0_40])]) ).
cnf(c_0_82,negated_conjecture,
( ~ precedes(X1,X2,esk5_0)
| ~ precedes(X2,X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_73,c_0_37]) ).
cnf(c_0_83,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_74,c_0_75]) ).
cnf(c_0_84,negated_conjecture,
( on_path(esk3_0,esk5_0)
| ~ shortest_path(X1,X2,esk5_0) ),
inference(spm,[status(thm)],[c_0_76,c_0_75]) ).
cnf(c_0_85,negated_conjecture,
( on_path(esk4_0,esk5_0)
| ~ shortest_path(X1,X2,esk5_0) ),
inference(spm,[status(thm)],[c_0_77,c_0_75]) ).
cnf(c_0_86,negated_conjecture,
( tail_of(esk8_2(head_of(esk4_0),X1)) = head_of(esk4_0)
| head_of(esk4_0) = X1
| tail_of(esk8_2(head_of(esk4_0),X1)) != tail_of(esk3_0)
| ~ vertex(head_of(esk4_0))
| ~ vertex(X1) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_78])]) ).
cnf(c_0_87,negated_conjecture,
( esk8_2(head_of(esk4_0),tail_of(esk3_0)) = esk3_0
| head_of(esk4_0) = tail_of(esk3_0)
| ~ vertex(head_of(esk4_0))
| ~ vertex(tail_of(esk3_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]) ).
cnf(c_0_88,negated_conjecture,
~ precedes(esk4_0,esk3_0,esk5_0),
inference(spm,[status(thm)],[c_0_82,c_0_45]) ).
cnf(c_0_89,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_83,c_0_37]) ).
cnf(c_0_90,negated_conjecture,
on_path(esk3_0,esk5_0),
inference(spm,[status(thm)],[c_0_84,c_0_37]) ).
cnf(c_0_91,negated_conjecture,
on_path(esk4_0,esk5_0),
inference(spm,[status(thm)],[c_0_85,c_0_37]) ).
cnf(c_0_92,negated_conjecture,
( head_of(esk4_0) = tail_of(esk3_0)
| ~ vertex(head_of(esk4_0))
| ~ vertex(tail_of(esk3_0)) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_93,negated_conjecture,
~ sequential(esk4_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90]),c_0_91])]) ).
cnf(c_0_94,negated_conjecture,
( head_of(esk4_0) = tail_of(esk3_0)
| ~ vertex(tail_of(esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_21]),c_0_34])]) ).
cnf(c_0_95,negated_conjecture,
( esk4_0 = esk3_0
| head_of(esk4_0) != tail_of(esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_39]),c_0_40]),c_0_34])]) ).
cnf(c_0_96,negated_conjecture,
head_of(esk4_0) = tail_of(esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_26]),c_0_40])]) ).
cnf(c_0_97,negated_conjecture,
esk4_0 = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_96])]) ).
cnf(c_0_98,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_97])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA008+1 : TPTP v8.2.0. Bugfixed v3.2.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n010.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 : Sat May 18 12:53:08 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.21/0.47 Running first-order model finding
% 0.21/0.47 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.11/0.61 # Version: 3.1.0
% 1.11/0.61 # Preprocessing class: FSMSSMSSSSSNFFN.
% 1.11/0.61 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.11/0.61 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.11/0.61 # Starting new_bool_3 with 300s (1) cores
% 1.11/0.61 # Starting new_bool_1 with 300s (1) cores
% 1.11/0.61 # Starting sh5l with 300s (1) cores
% 1.11/0.61 # new_bool_3 with pid 5467 completed with status 0
% 1.11/0.61 # Result found by new_bool_3
% 1.11/0.61 # Preprocessing class: FSMSSMSSSSSNFFN.
% 1.11/0.61 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.11/0.61 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.11/0.61 # Starting new_bool_3 with 300s (1) cores
% 1.11/0.61 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.11/0.61 # Search class: FGHSF-FFMS31-SFFFFFNN
% 1.11/0.61 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.11/0.61 # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 164s (1) cores
% 1.11/0.61 # G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with pid 5470 completed with status 0
% 1.11/0.61 # Result found by G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y
% 1.11/0.61 # Preprocessing class: FSMSSMSSSSSNFFN.
% 1.11/0.61 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.11/0.61 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.11/0.61 # Starting new_bool_3 with 300s (1) cores
% 1.11/0.61 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.11/0.61 # Search class: FGHSF-FFMS31-SFFFFFNN
% 1.11/0.61 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.11/0.61 # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 164s (1) cores
% 1.11/0.61 # Preprocessing time : 0.002 s
% 1.11/0.61
% 1.11/0.61 # Proof found!
% 1.11/0.61 # SZS status Theorem
% 1.11/0.61 # SZS output start CNFRefutation
% See solution above
% 1.11/0.61 # Parsed axioms : 18
% 1.11/0.61 # Removed by relevancy pruning/SinE : 8
% 1.11/0.61 # Initial clauses : 40
% 1.11/0.61 # Removed in clause preprocessing : 1
% 1.11/0.61 # Initial clauses in saturation : 39
% 1.11/0.61 # Processed clauses : 757
% 1.11/0.61 # ...of these trivial : 7
% 1.11/0.61 # ...subsumed : 330
% 1.11/0.61 # ...remaining for further processing : 420
% 1.11/0.61 # Other redundant clauses eliminated : 44
% 1.11/0.61 # Clauses deleted for lack of memory : 0
% 1.11/0.61 # Backward-subsumed : 36
% 1.11/0.61 # Backward-rewritten : 213
% 1.11/0.61 # Generated clauses : 2031
% 1.11/0.61 # ...of the previous two non-redundant : 1925
% 1.11/0.61 # ...aggressively subsumed : 0
% 1.11/0.61 # Contextual simplify-reflections : 55
% 1.11/0.61 # Paramodulations : 1950
% 1.11/0.61 # Factorizations : 24
% 1.11/0.61 # NegExts : 0
% 1.11/0.61 # Equation resolutions : 57
% 1.11/0.61 # Disequality decompositions : 0
% 1.11/0.61 # Total rewrite steps : 965
% 1.11/0.61 # ...of those cached : 953
% 1.11/0.61 # Propositional unsat checks : 0
% 1.11/0.61 # Propositional check models : 0
% 1.11/0.61 # Propositional check unsatisfiable : 0
% 1.11/0.61 # Propositional clauses : 0
% 1.11/0.61 # Propositional clauses after purity: 0
% 1.11/0.61 # Propositional unsat core size : 0
% 1.11/0.61 # Propositional preprocessing time : 0.000
% 1.11/0.61 # Propositional encoding time : 0.000
% 1.11/0.61 # Propositional solver time : 0.000
% 1.11/0.61 # Success case prop preproc time : 0.000
% 1.11/0.61 # Success case prop encoding time : 0.000
% 1.11/0.61 # Success case prop solver time : 0.000
% 1.11/0.61 # Current number of processed clauses : 169
% 1.11/0.61 # Positive orientable unit clauses : 7
% 1.11/0.61 # Positive unorientable unit clauses: 0
% 1.11/0.61 # Negative unit clauses : 2
% 1.11/0.61 # Non-unit-clauses : 160
% 1.11/0.61 # Current number of unprocessed clauses: 1000
% 1.11/0.61 # ...number of literals in the above : 7254
% 1.11/0.61 # Current number of archived formulas : 0
% 1.11/0.61 # Current number of archived clauses : 249
% 1.11/0.61 # Clause-clause subsumption calls (NU) : 38561
% 1.11/0.61 # Rec. Clause-clause subsumption calls : 6831
% 1.11/0.61 # Non-unit clause-clause subsumptions : 266
% 1.11/0.61 # Unit Clause-clause subsumption calls : 308
% 1.11/0.61 # Rewrite failures with RHS unbound : 0
% 1.11/0.61 # BW rewrite match attempts : 4
% 1.11/0.61 # BW rewrite match successes : 4
% 1.11/0.61 # Condensation attempts : 0
% 1.11/0.61 # Condensation successes : 0
% 1.11/0.61 # Termbank termtop insertions : 63457
% 1.11/0.61 # Search garbage collected termcells : 878
% 1.11/0.61
% 1.11/0.61 # -------------------------------------------------
% 1.11/0.61 # User time : 0.120 s
% 1.11/0.61 # System time : 0.003 s
% 1.11/0.61 # Total time : 0.123 s
% 1.11/0.61 # Maximum resident set size: 1864 pages
% 1.11/0.61
% 1.11/0.61 # -------------------------------------------------
% 1.11/0.61 # User time : 0.124 s
% 1.11/0.61 # System time : 0.004 s
% 1.11/0.61 # Total time : 0.127 s
% 1.11/0.61 # Maximum resident set size: 1756 pages
% 1.11/0.61 % E---3.1 exiting
%------------------------------------------------------------------------------