%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRA008+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:31:30 PM UTC 2026
% Result : Theorem 0.15s 5.49s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 80 ( 16 unt; 0 def)
% Number of atoms : 331 ( 113 equ)
% Maximal formula atoms : 37 ( 4 avg)
% Number of connectives : 418 ( 167 ~; 173 |; 58 &)
% ( 4 <=>; 15 =>; 0 <=; 1 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 2 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 161 ( 7 sgn 60 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sequential_is_triangle,conjecture,
( complete
=> ! [X2,X3,X7,X8,X4] :
( ( sequential(X7,X8)
& precedes(X7,X8,X4)
& shortest_path(X2,X3,X4) )
=> ? [X9] : triangle(X7,X8,X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_is_triangle) ).
fof(shortest_path_properties,axiom,
! [X2,X3,X7,X8,X4] :
( ( precedes(X7,X8,X4)
& shortest_path(X2,X3,X4) )
=> ( ~ precedes(X8,X7,X4)
& ~ ? [X9] :
( head_of(X9) = head_of(X8)
& tail_of(X9) = tail_of(X7) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',shortest_path_properties) ).
fof(back_edge,lemma,
( complete
=> ! [X2,X3,X7,X8,X4] :
( ( precedes(X7,X8,X4)
& shortest_path(X2,X3,X4) )
=> ? [X9] :
( head_of(X9) = tail_of(X7)
& tail_of(X9) = head_of(X8)
& edge(X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',back_edge) ).
fof(complete_properties,axiom,
( complete
=> ! [X2,X3] :
( ( X2 != X3
& vertex(X3)
& vertex(X2) )
=> ? [X1] :
( ( ( X3 = tail_of(X1)
& X2 = head_of(X1) )
<~> ( X2 = tail_of(X1)
& X3 = head_of(X1) ) )
& edge(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',complete_properties) ).
fof(edge_ends_are_vertices,axiom,
! [X1] :
( edge(X1)
=> ( vertex(tail_of(X1))
& vertex(head_of(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',edge_ends_are_vertices) ).
fof(sequential_defn,axiom,
! [X7,X8] :
( sequential(X7,X8)
<=> ( head_of(X7) = tail_of(X8)
& X7 != X8
& edge(X8)
& edge(X7) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',sequential_defn) ).
fof(triangle_defn,axiom,
! [X7,X8,X9] :
( triangle(X7,X8,X9)
<=> ( sequential(X9,X7)
& sequential(X8,X9)
& sequential(X7,X8)
& edge(X9)
& edge(X8)
& edge(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangle_defn) ).
fof(no_loops,axiom,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',no_loops) ).
fof(c_0_8,negated_conjecture,
~ ( complete
=> ! [X2,X3,X7,X8,X4] :
( ( sequential(X7,X8)
& precedes(X7,X8,X4)
& shortest_path(X2,X3,X4) )
=> ? [X9] : triangle(X7,X8,X9) ) ),
inference(assume_negation,[status(cth)],[sequential_is_triangle]) ).
fof(c_0_9,plain,
! [X2,X3,X7,X8,X4] :
( ( precedes(X7,X8,X4)
& shortest_path(X2,X3,X4) )
=> ( ~ precedes(X8,X7,X4)
& ~ ? [X9] :
( head_of(X9) = head_of(X8)
& tail_of(X9) = tail_of(X7) ) ) ),
inference(fof_simplification,[status(thm)],[shortest_path_properties]) ).
fof(c_0_10,lemma,
! [X43,X44,X45,X46,X47] :
( ( ~ complete
| ~ precedes(X45,X46,X47)
| ~ shortest_path(X43,X44,X47)
| head_of(esk7_4(X43,X44,X45,X46)) = tail_of(X45) )
& ( ~ complete
| ~ precedes(X45,X46,X47)
| ~ shortest_path(X43,X44,X47)
| tail_of(esk7_4(X43,X44,X45,X46)) = head_of(X46) )
& ( ~ complete
| ~ precedes(X45,X46,X47)
| ~ shortest_path(X43,X44,X47)
| edge(esk7_4(X43,X44,X45,X46)) ) ),
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)],[back_edge])])])])])])]) ).
fof(c_0_11,negated_conjecture,
! [X18] :
( ~ triangle(esk3_0,esk4_0,X18)
& sequential(esk3_0,esk4_0)
& precedes(esk3_0,esk4_0,esk5_0)
& shortest_path(esk1_0,esk2_0,esk5_0)
& complete ),
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_8])])])])]) ).
fof(c_0_12,plain,
! [X37,X38,X39,X40,X41,X42] :
( ( ~ precedes(X39,X40,X41)
| ~ shortest_path(X37,X38,X41)
| ~ precedes(X40,X39,X41) )
& ( ~ precedes(X39,X40,X41)
| ~ shortest_path(X37,X38,X41)
| head_of(X42) != head_of(X40)
| tail_of(X42) != tail_of(X39) ) ),
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_9])])])])]) ).
cnf(c_0_13,lemma,
( ~ complete
| ~ precedes(X3,X4,X5)
| ~ shortest_path(X1,X2,X5)
| head_of(esk7_4(X1,X2,X3,X4)) = tail_of(X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,lemma,
( ~ complete
| ~ precedes(X3,X4,X5)
| ~ shortest_path(X1,X2,X5)
| edge(esk7_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( ~ precedes(X2,X3,X6)
| ~ shortest_path(X4,X5,X6)
| head_of(X1) != head_of(X3)
| tail_of(X1) != tail_of(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
shortest_path(esk1_0,esk2_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_18,plain,
( complete
=> ! [X2,X3] :
( ( X2 != X3
& vertex(X3)
& vertex(X2) )
=> ? [X1] :
( ~ ( ( X3 = tail_of(X1)
& X2 = head_of(X1) )
<=> ( X2 = tail_of(X1)
& X3 = head_of(X1) ) )
& edge(X1) ) ) ),
inference(fof_simplification,[status(thm)],[complete_properties]) ).
fof(c_0_19,plain,
! [X53] :
( ( ~ edge(X53)
| vertex(tail_of(X53)) )
& ( ~ edge(X53)
| vertex(head_of(X53)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[edge_ends_are_vertices])])])]) ).
cnf(c_0_20,lemma,
( ~ precedes(X3,X4,X5)
| ~ shortest_path(X1,X2,X5)
| head_of(esk7_4(X1,X2,X3,X4)) = tail_of(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]) ).
cnf(c_0_21,lemma,
( ~ precedes(X3,X4,X5)
| ~ shortest_path(X1,X2,X5)
| edge(esk7_4(X1,X2,X3,X4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_14])]) ).
cnf(c_0_22,lemma,
( ~ complete
| ~ precedes(X3,X4,X5)
| ~ shortest_path(X1,X2,X5)
| tail_of(esk7_4(X1,X2,X3,X4)) = head_of(X4) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23,negated_conjecture,
( ~ precedes(X3,X2,esk5_0)
| tail_of(X1) != tail_of(X3)
| head_of(X1) != head_of(X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,negated_conjecture,
precedes(esk3_0,esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_25,plain,
! [X49,X50] :
( ( ~ complete
| X49 = X50
| ~ vertex(X50)
| ~ vertex(X49)
| X50 = tail_of(esk8_2(X49,X50))
| X49 = tail_of(esk8_2(X49,X50)) )
& ( ~ complete
| X49 = X50
| ~ vertex(X50)
| ~ vertex(X49)
| X50 = tail_of(esk8_2(X49,X50))
| X50 = head_of(esk8_2(X49,X50)) )
& ( ~ complete
| X49 = X50
| ~ vertex(X50)
| ~ vertex(X49)
| X49 = head_of(esk8_2(X49,X50))
| X49 = tail_of(esk8_2(X49,X50)) )
& ( ~ complete
| X49 = X50
| ~ vertex(X50)
| ~ vertex(X49)
| X49 = head_of(esk8_2(X49,X50))
| X50 = head_of(esk8_2(X49,X50)) )
& ( ~ complete
| X49 = X50
| ~ vertex(X50)
| ~ vertex(X49)
| X49 != tail_of(esk8_2(X49,X50))
| X50 != head_of(esk8_2(X49,X50))
| X50 != tail_of(esk8_2(X49,X50))
| X49 != head_of(esk8_2(X49,X50)) )
& ( ~ complete
| X49 = X50
| ~ vertex(X50)
| ~ vertex(X49)
| edge(esk8_2(X49,X50)) ) ),
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_18])])])])])]) ).
cnf(c_0_26,plain,
( ~ edge(X1)
| vertex(head_of(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,negated_conjecture,
( ~ precedes(X1,X2,esk5_0)
| head_of(esk7_4(esk1_0,esk2_0,X1,X2)) = tail_of(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_28,negated_conjecture,
( ~ precedes(X1,X2,esk5_0)
| edge(esk7_4(esk1_0,esk2_0,X1,X2)) ),
inference(spm,[status(thm)],[c_0_21,c_0_17]) ).
cnf(c_0_29,lemma,
( ~ precedes(X3,X4,X5)
| ~ shortest_path(X1,X2,X5)
| tail_of(esk7_4(X1,X2,X3,X4)) = head_of(X4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_14])]) ).
cnf(c_0_30,negated_conjecture,
( tail_of(X1) != tail_of(esk3_0)
| head_of(X1) != head_of(esk4_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,plain,
( ~ complete
| ~ vertex(X1)
| ~ vertex(X2)
| X2 = X1
| X2 = head_of(esk8_2(X2,X1))
| X1 = head_of(esk8_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,negated_conjecture,
( ~ precedes(X1,X2,esk5_0)
| vertex(tail_of(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_33,plain,
( ~ edge(X1)
| vertex(tail_of(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_34,negated_conjecture,
( ~ precedes(X1,X2,esk5_0)
| tail_of(esk7_4(esk1_0,esk2_0,X1,X2)) = head_of(X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_17]) ).
cnf(c_0_35,negated_conjecture,
( ~ precedes(X1,X2,esk5_0)
| tail_of(X1) != head_of(esk4_0)
| tail_of(esk7_4(esk1_0,esk2_0,X1,X2)) != tail_of(esk3_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_36,plain,
( ~ vertex(X2)
| ~ vertex(X1)
| X2 = X1
| head_of(esk8_2(X1,X2)) = X1
| head_of(esk8_2(X1,X2)) = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_14])]) ).
cnf(c_0_37,negated_conjecture,
vertex(tail_of(esk3_0)),
inference(spm,[status(thm)],[c_0_32,c_0_24]) ).
cnf(c_0_38,negated_conjecture,
( ~ precedes(X2,X1,esk5_0)
| vertex(head_of(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_28]) ).
cnf(c_0_39,negated_conjecture,
( ~ precedes(X2,X1,esk5_0)
| tail_of(X2) != head_of(esk4_0)
| head_of(X1) != tail_of(esk3_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_34]) ).
cnf(c_0_40,negated_conjecture,
( ~ vertex(X1)
| X1 = tail_of(esk3_0)
| head_of(esk8_2(tail_of(esk3_0),X1)) = X1
| head_of(esk8_2(tail_of(esk3_0),X1)) = tail_of(esk3_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
vertex(head_of(esk4_0)),
inference(spm,[status(thm)],[c_0_38,c_0_24]) ).
cnf(c_0_42,negated_conjecture,
head_of(esk4_0) != tail_of(esk3_0),
inference(spm,[status(thm)],[c_0_39,c_0_24]) ).
fof(c_0_43,plain,
! [X7,X8] :
( sequential(X7,X8)
<=> ( head_of(X7) = tail_of(X8)
& X7 != X8
& edge(X8)
& edge(X7) ) ),
inference(fof_simplification,[status(thm)],[sequential_defn]) ).
cnf(c_0_44,plain,
( ~ complete
| ~ vertex(X2)
| ~ vertex(X1)
| X1 = X2
| X1 = head_of(esk8_2(X1,X2))
| X1 = tail_of(esk8_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_45,negated_conjecture,
( head_of(esk8_2(tail_of(esk3_0),head_of(esk4_0))) = tail_of(esk3_0)
| head_of(esk8_2(tail_of(esk3_0),head_of(esk4_0))) = head_of(esk4_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
fof(c_0_46,plain,
! [X19,X20,X21] :
( ( triangle(X19,X20,X21)
| ~ sequential(X21,X19)
| ~ sequential(X20,X21)
| ~ sequential(X19,X20)
| ~ edge(X21)
| ~ edge(X20)
| ~ edge(X19) )
& ( ~ triangle(X19,X20,X21)
| sequential(X21,X19) )
& ( ~ triangle(X19,X20,X21)
| sequential(X20,X21) )
& ( ~ triangle(X19,X20,X21)
| sequential(X19,X20) )
& ( ~ triangle(X19,X20,X21)
| edge(X21) )
& ( ~ triangle(X19,X20,X21)
| edge(X20) )
& ( ~ triangle(X19,X20,X21)
| edge(X19) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[triangle_defn])])])]) ).
fof(c_0_47,plain,
! [X22,X23] :
( ( sequential(X22,X23)
| head_of(X22) != tail_of(X23)
| X22 = X23
| ~ edge(X23)
| ~ edge(X22) )
& ( ~ sequential(X22,X23)
| head_of(X22) = tail_of(X23) )
& ( ~ sequential(X22,X23)
| X22 != X23 )
& ( ~ sequential(X22,X23)
| edge(X23) )
& ( ~ sequential(X22,X23)
| edge(X22) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])])]) ).
cnf(c_0_48,plain,
( ~ vertex(X1)
| ~ vertex(X2)
| X1 = X2
| head_of(esk8_2(X1,X2)) = X1
| tail_of(esk8_2(X1,X2)) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_14])]) ).
cnf(c_0_49,negated_conjecture,
( tail_of(esk8_2(tail_of(esk3_0),head_of(esk4_0))) != tail_of(esk3_0)
| head_of(esk8_2(tail_of(esk3_0),head_of(esk4_0))) = tail_of(esk3_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_45]) ).
cnf(c_0_50,plain,
( ~ complete
| ~ vertex(X1)
| ~ vertex(X2)
| X2 = X1
| X1 = tail_of(esk8_2(X2,X1))
| X1 = head_of(esk8_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_51,plain,
( ~ sequential(X3,X1)
| ~ sequential(X2,X3)
| ~ sequential(X1,X2)
| ~ edge(X3)
| ~ edge(X2)
| ~ edge(X1)
| triangle(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_52,plain,
( ~ sequential(X1,X2)
| edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_53,plain,
( head_of(X1) != tail_of(X2)
| ~ edge(X2)
| ~ edge(X1)
| sequential(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_54,negated_conjecture,
head_of(esk8_2(tail_of(esk3_0),head_of(esk4_0))) = tail_of(esk3_0),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_45]),c_0_41]),c_0_37])]),c_0_42]),c_0_49]) ).
cnf(c_0_55,plain,
( ~ complete
| ~ vertex(X2)
| ~ vertex(X1)
| X1 = X2
| edge(esk8_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_56,plain,
( ~ vertex(X2)
| ~ vertex(X1)
| X2 = X1
| head_of(esk8_2(X1,X2)) = X2
| tail_of(esk8_2(X1,X2)) = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_14])]) ).
cnf(c_0_57,negated_conjecture,
~ triangle(esk3_0,esk4_0,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_58,plain,
( ~ sequential(X1,X2)
| ~ sequential(X2,X3)
| ~ sequential(X3,X1)
| triangle(X1,X2,X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_51,c_0_52]),c_0_52]),c_0_52]) ).
cnf(c_0_59,negated_conjecture,
sequential(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_60,negated_conjecture,
( ~ edge(X1)
| ~ edge(esk8_2(tail_of(esk3_0),head_of(esk4_0)))
| tail_of(X1) != tail_of(esk3_0)
| sequential(esk8_2(tail_of(esk3_0),head_of(esk4_0)),X1)
| esk8_2(tail_of(esk3_0),head_of(esk4_0)) = X1 ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_61,plain,
( ~ vertex(X1)
| ~ vertex(X2)
| edge(esk8_2(X1,X2))
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_14])]) ).
cnf(c_0_62,negated_conjecture,
tail_of(esk8_2(tail_of(esk3_0),head_of(esk4_0))) = head_of(esk4_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_54]),c_0_37]),c_0_41])]),c_0_42]) ).
fof(c_0_63,plain,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
inference(fof_simplification,[status(thm)],[no_loops]) ).
cnf(c_0_64,negated_conjecture,
( ~ sequential(esk4_0,X1)
| ~ sequential(X1,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59])]) ).
cnf(c_0_65,negated_conjecture,
( ~ edge(X1)
| tail_of(X1) != tail_of(esk3_0)
| sequential(esk8_2(tail_of(esk3_0),head_of(esk4_0)),X1)
| esk8_2(tail_of(esk3_0),head_of(esk4_0)) = X1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_41]),c_0_37])]),c_0_42]) ).
cnf(c_0_66,negated_conjecture,
edge(esk3_0),
inference(spm,[status(thm)],[c_0_52,c_0_59]) ).
cnf(c_0_67,negated_conjecture,
( ~ edge(X1)
| ~ edge(esk8_2(tail_of(esk3_0),head_of(esk4_0)))
| head_of(esk4_0) != head_of(X1)
| sequential(X1,esk8_2(tail_of(esk3_0),head_of(esk4_0)))
| X1 = esk8_2(tail_of(esk3_0),head_of(esk4_0)) ),
inference(spm,[status(thm)],[c_0_53,c_0_62]) ).
cnf(c_0_68,plain,
( ~ sequential(X2,X1)
| edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_69,plain,
! [X52] :
( head_of(X52) != tail_of(X52)
| ~ edge(X52) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_63])])]) ).
cnf(c_0_70,plain,
( ~ sequential(X1,X2)
| head_of(X1) = tail_of(X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_71,negated_conjecture,
( ~ sequential(esk4_0,esk8_2(tail_of(esk3_0),head_of(esk4_0)))
| esk8_2(tail_of(esk3_0),head_of(esk4_0)) = esk3_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66])]) ).
cnf(c_0_72,negated_conjecture,
( ~ edge(X1)
| head_of(esk4_0) != head_of(X1)
| sequential(X1,esk8_2(tail_of(esk3_0),head_of(esk4_0)))
| X1 = esk8_2(tail_of(esk3_0),head_of(esk4_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_61]),c_0_41]),c_0_37])]),c_0_42]) ).
cnf(c_0_73,negated_conjecture,
edge(esk4_0),
inference(spm,[status(thm)],[c_0_68,c_0_59]) ).
cnf(c_0_74,plain,
( head_of(X1) != tail_of(X1)
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_75,negated_conjecture,
head_of(esk3_0) = tail_of(esk4_0),
inference(spm,[status(thm)],[c_0_70,c_0_59]) ).
cnf(c_0_76,negated_conjecture,
( esk8_2(tail_of(esk3_0),head_of(esk4_0)) = esk3_0
| esk8_2(tail_of(esk3_0),head_of(esk4_0)) = esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73])]) ).
cnf(c_0_77,negated_conjecture,
tail_of(esk4_0) != tail_of(esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_66])]) ).
cnf(c_0_78,negated_conjecture,
esk8_2(tail_of(esk3_0),head_of(esk4_0)) = esk3_0,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_76]),c_0_41]),c_0_37])]),c_0_77]),c_0_42]) ).
cnf(c_0_79,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_78]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA008+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/5.37 % Computer : n026.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sun Sep 20 18:25:14 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.49 % Version: 3.5.1
% 0.15/5.49 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.49 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.49 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.49 % Starting sh5l with 300s (1) cores
% 0.15/5.49 % new_bool_1 with pid 335083 completed with status 0
% 0.15/5.49 % Result found by new_bool_1
% 0.15/5.49 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.49 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.49 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/5.49 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/5.49 % Search class: FGHSF-FFMS32-SFFFFFNN
% 0.15/5.49 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/5.49 % Starting SubtermCWHack with 31s (1) cores
% 0.15/5.49 % SubtermCWHack with pid 335085 completed with status 0
% 0.15/5.49 % Result found by SubtermCWHack
% 0.15/5.49 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.49 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.49 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/5.49 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/5.49 % Search class: FGHSF-FFMS32-SFFFFFNN
% 0.15/5.49 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/5.49 % Starting SubtermCWHack with 31s (1) cores
% 0.15/5.49 % Preprocessing time : 0.002 s
% 0.15/5.49
% 0.15/5.49 % Proof found!
% 0.15/5.49 % SZS status Theorem
% 0.15/5.49 % SZS output start CNFRefutation
% See solution above
% 0.15/5.49 % Parsed axioms : 19
% 0.15/5.49 % Removed by relevancy pruning/SinE : 9
% 0.15/5.49 % Initial clauses : 38
% 0.15/5.49 % Removed in clause preprocessing : 1
% 0.15/5.49 % Initial clauses in saturation : 37
% 0.15/5.49 % Processed clauses : 287
% 0.15/5.49 % ...of these trivial : 0
% 0.15/5.49 % ...subsumed : 105
% 0.15/5.49 % ...remaining for further processing : 182
% 0.15/5.49 % Other redundant clauses eliminated : 5
% 0.15/5.49 % Clauses deleted for lack of memory : 0
% 0.15/5.49 % Backward-subsumed : 9
% 0.15/5.49 % Backward-rewritten : 14
% 0.15/5.49 % Generated clauses : 729
% 0.15/5.49 % ...of the previous two non-redundant : 575
% 0.15/5.49 % ...aggressively subsumed : 0
% 0.15/5.49 % Contextual simplify-reflections : 18
% 0.15/5.49 % Paramodulations : 701
% 0.15/5.49 % Factorizations : 20
% 0.15/5.49 % NegExts : 0
% 0.15/5.49 % Equation resolutions : 8
% 0.15/5.49 % Disequality decompositions : 0
% 0.15/5.49 % Total rewrite steps : 531
% 0.15/5.49 % ...of those cached : 518
% 0.15/5.49 % Propositional unsat checks : 0
% 0.15/5.49 % Propositional check models : 0
% 0.15/5.49 % Propositional check unsatisfiable : 0
% 0.15/5.49 % Propositional clauses : 0
% 0.15/5.49 % Propositional clauses after purity: 0
% 0.15/5.49 % Propositional unsat core size : 0
% 0.15/5.49 % Propositional preprocessing time : 0.000
% 0.15/5.49 % Propositional encoding time : 0.000
% 0.15/5.49 % Propositional solver time : 0.000
% 0.15/5.49 % Success case prop preproc time : 0.000
% 0.15/5.49 % Success case prop encoding time : 0.000
% 0.15/5.49 % Success case prop solver time : 0.000
% 0.15/5.49 % Current number of processed clauses : 158
% 0.15/5.49 % Positive orientable unit clauses : 13
% 0.15/5.49 % Positive unorientable unit clauses: 0
% 0.15/5.49 % Negative unit clauses : 5
% 0.15/5.49 % Non-unit-clauses : 140
% 0.15/5.49 % Current number of unprocessed clauses: 314
% 0.15/5.49 % ...number of literals in the above : 1720
% 0.15/5.49 % Current number of archived formulas : 0
% 0.15/5.49 % Current number of archived clauses : 23
% 0.15/5.49 % Clause-clause subsumption calls (NU) : 3265
% 0.15/5.49 % Rec. Clause-clause subsumption calls : 1017
% 0.15/5.49 % Non-unit clause-clause subsumptions : 94
% 0.15/5.49 % Unit Clause-clause subsumption calls : 105
% 0.15/5.49 % Rewrite failures with RHS unbound : 0
% 0.15/5.49 % BW rewrite match attempts : 5
% 0.15/5.49 % BW rewrite match successes : 5
% 0.15/5.49 % Condensation attempts : 0
% 0.15/5.49 % Condensation successes : 0
% 0.15/5.49 % Termbank termtop insertions : 23515
% 0.15/5.49 % Search garbage collected termcells : 838
% 0.15/5.49
% 0.15/5.49 % -------------------------------------------------
% 0.15/5.49 % User time : 0.042 s
% 0.15/5.49 % System time : 0.003 s
% 0.15/5.49 % Total time : 0.045 s
% 0.15/5.49 % Maximum resident set size: 3928 pages
% 0.15/5.49
% 0.15/5.49 % -------------------------------------------------
% 0.15/5.49 % User time : 0.046 s
% 0.15/5.49 % System time : 0.006 s
% 0.15/5.49 % Total time : 0.052 s
% 0.15/5.49 % Maximum resident set size: 4864 pages
% 0.15/5.49 % E exiting
%------------------------------------------------------------------------------