%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRA008+2 : TPTP v9.2.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:22:56 PM UTC 2026
% Result : Theorem 6.94s 4.80s
% Output : CNFRefutation 6.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 54 ( 12 unt; 0 def)
% Number of atoms : 202 ( 54 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 257 ( 109 ~; 100 |; 38 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 2 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-4 aty)
% Number of variables : 128 ( 5 sgn 47 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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(c_0_5,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_6,lemma,
! [X161,X162,X163,X164,X165] :
( ( edge(esk9_4(X161,X162,X163,X164))
| ~ shortest_path(X161,X162,X165)
| ~ precedes(X163,X164,X165)
| ~ complete )
& ( tail_of(esk9_4(X161,X162,X163,X164)) = head_of(X164)
| ~ shortest_path(X161,X162,X165)
| ~ precedes(X163,X164,X165)
| ~ complete )
& ( head_of(esk9_4(X161,X162,X163,X164)) = tail_of(X163)
| ~ shortest_path(X161,X162,X165)
| ~ precedes(X163,X164,X165)
| ~ 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_7,negated_conjecture,
! [X172] :
( 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,X172) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_8,plain,
! [X115,X116] :
( ( edge(X115)
| ~ sequential(X115,X116) )
& ( edge(X116)
| ~ sequential(X115,X116) )
& ( X115 != X116
| ~ sequential(X115,X116) )
& ( head_of(X115) = tail_of(X116)
| ~ sequential(X115,X116) )
& ( ~ edge(X115)
| ~ edge(X116)
| X115 = X116
| head_of(X115) != tail_of(X116)
| sequential(X115,X116) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sequential_defn])])]) ).
cnf(c_0_9,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_6]) ).
cnf(c_0_10,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,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_12,plain,
( edge(X1)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
sequential(esk12_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,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_6]) ).
cnf(c_0_15,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_9,c_0_10])]) ).
cnf(c_0_16,negated_conjecture,
shortest_path(esk10_0,esk11_0,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,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_6]) ).
fof(c_0_18,plain,
! [X138,X139,X140,X141,X142,X143] :
( ( tail_of(X143) != tail_of(X140)
| head_of(X143) != head_of(X141)
| ~ shortest_path(X138,X139,X142)
| ~ precedes(X140,X141,X142) )
& ( ~ precedes(X141,X140,X142)
| ~ shortest_path(X138,X139,X142)
| ~ precedes(X140,X141,X142) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
fof(c_0_19,plain,
! [X144,X145,X146] :
( ( edge(X144)
| ~ triangle(X144,X145,X146) )
& ( edge(X145)
| ~ triangle(X144,X145,X146) )
& ( edge(X146)
| ~ triangle(X144,X145,X146) )
& ( sequential(X144,X145)
| ~ triangle(X144,X145,X146) )
& ( sequential(X145,X146)
| ~ triangle(X144,X145,X146) )
& ( sequential(X146,X144)
| ~ triangle(X144,X145,X146) )
& ( ~ edge(X144)
| ~ edge(X145)
| ~ edge(X146)
| ~ sequential(X144,X145)
| ~ sequential(X145,X146)
| ~ sequential(X146,X144)
| triangle(X144,X145,X146) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[triangle_defn])])]) ).
cnf(c_0_20,plain,
( X1 = X2
| sequential(X1,X2)
| ~ edge(X1)
| ~ edge(X2)
| head_of(X1) != tail_of(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
edge(esk12_0),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_22,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_14,c_0_10])]) ).
cnf(c_0_23,negated_conjecture,
( edge(esk9_4(esk10_0,esk11_0,X1,X2))
| ~ precedes(X1,X2,esk14_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_24,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_17,c_0_10])]) ).
cnf(c_0_25,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_18]) ).
cnf(c_0_26,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_19]) ).
cnf(c_0_27,negated_conjecture,
( X1 = esk12_0
| sequential(X1,esk12_0)
| tail_of(esk12_0) != head_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,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_22,c_0_16]) ).
cnf(c_0_29,negated_conjecture,
( X1 = esk9_4(esk10_0,esk11_0,X2,X3)
| sequential(X1,esk9_4(esk10_0,esk11_0,X2,X3))
| tail_of(esk9_4(esk10_0,esk11_0,X2,X3)) != head_of(X1)
| ~ precedes(X2,X3,esk14_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_30,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_24,c_0_16]) ).
cnf(c_0_31,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_25,c_0_16]) ).
cnf(c_0_32,negated_conjecture,
precedes(esk12_0,esk13_0,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_33,negated_conjecture,
~ triangle(esk12_0,esk13_0,X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_34,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_26,c_0_12]),c_0_12]),c_0_12]) ).
cnf(c_0_35,negated_conjecture,
( esk9_4(esk10_0,esk11_0,X1,X2) = esk12_0
| sequential(esk9_4(esk10_0,esk11_0,X1,X2),esk12_0)
| tail_of(esk12_0) != tail_of(X1)
| ~ precedes(X1,X2,esk14_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_23]) ).
cnf(c_0_36,negated_conjecture,
( X1 = esk9_4(esk10_0,esk11_0,X2,X3)
| sequential(X1,esk9_4(esk10_0,esk11_0,X2,X3))
| head_of(X3) != head_of(X1)
| ~ precedes(X2,X3,esk14_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,plain,
( edge(X1)
| ~ sequential(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_38,negated_conjecture,
( head_of(X1) != head_of(esk13_0)
| tail_of(X1) != tail_of(esk12_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,negated_conjecture,
( ~ sequential(X1,esk12_0)
| ~ sequential(esk13_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_13])]) ).
cnf(c_0_40,negated_conjecture,
( esk9_4(esk10_0,esk11_0,esk12_0,esk13_0) = esk12_0
| sequential(esk9_4(esk10_0,esk11_0,esk12_0,esk13_0),esk12_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_32]) ).
cnf(c_0_41,negated_conjecture,
( X1 = esk9_4(esk10_0,esk11_0,esk12_0,esk13_0)
| sequential(X1,esk9_4(esk10_0,esk11_0,esk12_0,esk13_0))
| head_of(esk13_0) != head_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_32]) ).
cnf(c_0_42,negated_conjecture,
edge(esk13_0),
inference(spm,[status(thm)],[c_0_37,c_0_13]) ).
cnf(c_0_43,negated_conjecture,
( head_of(esk9_4(esk10_0,esk11_0,X1,X2)) != head_of(esk13_0)
| head_of(X2) != tail_of(esk12_0)
| ~ precedes(X1,X2,esk14_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_30]) ).
cnf(c_0_44,negated_conjecture,
( esk9_4(esk10_0,esk11_0,esk12_0,esk13_0) = esk12_0
| ~ sequential(esk13_0,esk9_4(esk10_0,esk11_0,esk12_0,esk13_0)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,negated_conjecture,
( esk9_4(esk10_0,esk11_0,esk12_0,esk13_0) = esk13_0
| sequential(esk13_0,esk9_4(esk10_0,esk11_0,esk12_0,esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_41]),c_0_42])]) ).
cnf(c_0_46,negated_conjecture,
( tail_of(X1) != head_of(esk13_0)
| head_of(X2) != tail_of(esk12_0)
| ~ precedes(X1,X2,esk14_0) ),
inference(spm,[status(thm)],[c_0_43,c_0_28]) ).
cnf(c_0_47,plain,
( head_of(X1) = tail_of(X2)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_48,negated_conjecture,
( esk9_4(esk10_0,esk11_0,esk12_0,esk13_0) = esk13_0
| esk9_4(esk10_0,esk11_0,esk12_0,esk13_0) = esk12_0 ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
tail_of(esk12_0) != head_of(esk13_0),
inference(spm,[status(thm)],[c_0_46,c_0_32]) ).
cnf(c_0_50,negated_conjecture,
tail_of(esk13_0) = head_of(esk12_0),
inference(spm,[status(thm)],[c_0_47,c_0_13]) ).
cnf(c_0_51,negated_conjecture,
esk9_4(esk10_0,esk11_0,esk12_0,esk13_0) = esk12_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_48]),c_0_32])]),c_0_49]) ).
cnf(c_0_52,negated_conjecture,
tail_of(esk12_0) != head_of(esk12_0),
inference(spm,[status(thm)],[c_0_38,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_51]),c_0_32])]),c_0_52]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA008+2 : TPTP v9.2.1. Bugfixed v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n009.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:07:26 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 6.94/4.80 % Version : CSE_E---1.7
% 6.94/4.80 % Problem : theBenchmark.p
% 6.94/4.80 % SZS status Theorem for theBenchmark.p
% 6.94/4.80 % SZS output start CNFRefutation
% See solution above
% 6.94/4.83 % Total time : 3.370s
%------------------------------------------------------------------------------