%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRA004+1 : TPTP v9.2.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n006.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 04:22:55 PM UTC 2026
% Result : Theorem 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 14 unt; 0 def)
% Number of atoms : 231 ( 58 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 286 ( 112 ~; 102 |; 53 &)
% ( 3 <=>; 14 =>; 1 <=; 1 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 142 ( 18 sgn 83 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(shortest_path_properties,axiom,
! [X2,X3,X7,X8,X4] :
( ( shortest_path(X2,X3,X4)
& precedes(X7,X8,X4) )
=> ( ~ ? [X9] :
( tail_of(X9) = tail_of(X7)
& head_of(X9) = head_of(X8) )
& ~ precedes(X8,X7,X4) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',shortest_path_properties) ).
fof(shortest_path_properties_lemma,conjecture,
! [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) )
& head_of(X8) != tail_of(X7)
& head_of(X8) != head_of(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_properties_lemma) ).
fof(precedes_properties,axiom,
! [X4,X2,X3] :
( path(X2,X3,X4)
=> ! [X7,X8] :
( precedes(X7,X8,X4)
=> ( on_path(X7,X4)
& on_path(X8,X4)
& ( sequential(X7,X8)
<~> ? [X9] :
( sequential(X7,X9)
& precedes(X9,X8,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',precedes_properties) ).
fof(shortest_path_defn,axiom,
! [X2,X3,X10] :
( shortest_path(X2,X3,X10)
<=> ( path(X2,X3,X10)
& X2 != X3
& ! [X4] :
( path(X2,X3,X4)
=> less_or_equal(length_of(X10),length_of(X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',shortest_path_defn) ).
fof(on_path_properties,axiom,
! [X2,X3,X4,X1] :
( ( path(X2,X3,X4)
& on_path(X1,X4) )
=> ( edge(X1)
& in_path(head_of(X1),X4)
& in_path(tail_of(X1),X4) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',on_path_properties) ).
fof(precedes_defn,axiom,
! [X4,X2,X3] :
( path(X2,X3,X4)
=> ! [X7,X8] :
( precedes(X7,X8,X4)
<= ( on_path(X7,X4)
& on_path(X8,X4)
& ( sequential(X7,X8)
| ? [X9] :
( sequential(X7,X9)
& precedes(X9,X8,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',precedes_defn) ).
fof(sequential_defn,axiom,
! [X7,X8] :
( sequential(X7,X8)
<=> ( edge(X7)
& edge(X8)
& X7 != X8
& head_of(X7) = tail_of(X8) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',sequential_defn) ).
fof(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,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_9,negated_conjecture,
~ ! [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) )
& head_of(X8) != tail_of(X7)
& head_of(X8) != head_of(X7) ) ),
inference(assume_negation,[status(cth)],[shortest_path_properties_lemma]) ).
fof(c_0_10,plain,
! [X132,X133,X134,X135,X136,X137] :
( ( tail_of(X137) != tail_of(X134)
| head_of(X137) != head_of(X135)
| ~ shortest_path(X132,X133,X136)
| ~ precedes(X134,X135,X136) )
& ( ~ precedes(X135,X134,X136)
| ~ shortest_path(X132,X133,X136)
| ~ precedes(X134,X135,X136) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_11,negated_conjecture,
( shortest_path(esk9_0,esk10_0,esk13_0)
& precedes(esk11_0,esk12_0,esk13_0)
& ( tail_of(esk14_0) = tail_of(esk11_0)
| head_of(esk12_0) = tail_of(esk11_0)
| head_of(esk12_0) = head_of(esk11_0) )
& ( head_of(esk14_0) = head_of(esk12_0)
| head_of(esk12_0) = tail_of(esk11_0)
| head_of(esk12_0) = head_of(esk11_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_12,plain,
! [X4,X2,X3] :
( path(X2,X3,X4)
=> ! [X7,X8] :
( precedes(X7,X8,X4)
=> ( on_path(X7,X4)
& on_path(X8,X4)
& ~ ( sequential(X7,X8)
<=> ? [X9] :
( sequential(X7,X9)
& precedes(X9,X8,X4) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[precedes_properties]) ).
cnf(c_0_13,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_10]) ).
cnf(c_0_14,negated_conjecture,
shortest_path(esk9_0,esk10_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,plain,
! [X124,X125,X126,X127,X128,X129,X130] :
( ( path(X124,X125,X126)
| ~ shortest_path(X124,X125,X126) )
& ( X124 != X125
| ~ shortest_path(X124,X125,X126) )
& ( ~ path(X124,X125,X127)
| less_or_equal(length_of(X126),length_of(X127))
| ~ shortest_path(X124,X125,X126) )
& ( path(X128,X129,esk6_3(X128,X129,X130))
| ~ path(X128,X129,X130)
| X128 = X129
| shortest_path(X128,X129,X130) )
& ( ~ less_or_equal(length_of(X130),length_of(esk6_3(X128,X129,X130)))
| ~ path(X128,X129,X130)
| X128 = X129
| shortest_path(X128,X129,X130) ) ),
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_16,plain,
! [X117,X118,X119,X120,X121,X122] :
( ( on_path(X120,X117)
| ~ precedes(X120,X121,X117)
| ~ path(X118,X119,X117) )
& ( on_path(X121,X117)
| ~ precedes(X120,X121,X117)
| ~ path(X118,X119,X117) )
& ( ~ sequential(X120,X121)
| ~ sequential(X120,X122)
| ~ precedes(X122,X121,X117)
| ~ precedes(X120,X121,X117)
| ~ path(X118,X119,X117) )
& ( sequential(X120,esk5_3(X117,X120,X121))
| sequential(X120,X121)
| ~ precedes(X120,X121,X117)
| ~ path(X118,X119,X117) )
& ( precedes(esk5_3(X117,X120,X121),X121,X117)
| sequential(X120,X121)
| ~ precedes(X120,X121,X117)
| ~ path(X118,X119,X117) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])])])]) ).
cnf(c_0_17,negated_conjecture,
( head_of(X1) != head_of(X2)
| tail_of(X1) != tail_of(X3)
| ~ precedes(X3,X2,esk13_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
precedes(esk11_0,esk12_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_19,plain,
! [X100,X101,X102,X103] :
( ( edge(X103)
| ~ path(X100,X101,X102)
| ~ on_path(X103,X102) )
& ( in_path(head_of(X103),X102)
| ~ path(X100,X101,X102)
| ~ on_path(X103,X102) )
& ( in_path(tail_of(X103),X102)
| ~ path(X100,X101,X102)
| ~ on_path(X103,X102) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[on_path_properties])])]) ).
cnf(c_0_20,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( on_path(X1,X2)
| ~ precedes(X1,X3,X2)
| ~ path(X4,X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( head_of(X1) != head_of(esk12_0)
| tail_of(X1) != tail_of(esk11_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_23,plain,
! [X4,X2,X3] :
( path(X2,X3,X4)
=> ! [X7,X8] :
( ( on_path(X7,X4)
& on_path(X8,X4)
& ( sequential(X7,X8)
| ? [X9] :
( sequential(X7,X9)
& precedes(X9,X8,X4) ) ) )
=> precedes(X7,X8,X4) ) ),
inference(fof_simplification,[status(thm)],[precedes_defn]) ).
cnf(c_0_24,plain,
( edge(X1)
| ~ path(X2,X3,X4)
| ~ on_path(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
path(esk9_0,esk10_0,esk13_0),
inference(spm,[status(thm)],[c_0_20,c_0_14]) ).
cnf(c_0_26,negated_conjecture,
( on_path(esk11_0,esk13_0)
| ~ path(X1,X2,esk13_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_27,negated_conjecture,
( tail_of(esk14_0) = tail_of(esk11_0)
| head_of(esk12_0) = tail_of(esk11_0)
| head_of(esk12_0) = head_of(esk11_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_28,negated_conjecture,
head_of(esk11_0) != head_of(esk12_0),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
( head_of(esk14_0) = head_of(esk12_0)
| head_of(esk12_0) = tail_of(esk11_0)
| head_of(esk12_0) = head_of(esk11_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,plain,
( on_path(X1,X2)
| ~ precedes(X3,X1,X2)
| ~ path(X4,X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_31,plain,
! [X111,X112,X113,X114,X115,X116] :
( ( ~ sequential(X114,X115)
| ~ on_path(X114,X111)
| ~ on_path(X115,X111)
| precedes(X114,X115,X111)
| ~ path(X112,X113,X111) )
& ( ~ sequential(X114,X116)
| ~ precedes(X116,X115,X111)
| ~ on_path(X114,X111)
| ~ on_path(X115,X111)
| precedes(X114,X115,X111)
| ~ path(X112,X113,X111) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).
fof(c_0_32,plain,
! [X109,X110] :
( ( edge(X109)
| ~ sequential(X109,X110) )
& ( edge(X110)
| ~ sequential(X109,X110) )
& ( X109 != X110
| ~ sequential(X109,X110) )
& ( head_of(X109) = tail_of(X110)
| ~ sequential(X109,X110) )
& ( ~ edge(X109)
| ~ edge(X110)
| X109 = X110
| head_of(X109) != tail_of(X110)
| sequential(X109,X110) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sequential_defn])])]) ).
cnf(c_0_33,negated_conjecture,
( edge(X1)
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_34,negated_conjecture,
on_path(esk11_0,esk13_0),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_35,negated_conjecture,
( tail_of(esk14_0) = tail_of(esk11_0)
| tail_of(esk11_0) = head_of(esk12_0) ),
inference(sr,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_36,negated_conjecture,
( tail_of(esk11_0) = head_of(esk12_0)
| head_of(esk14_0) = head_of(esk12_0) ),
inference(sr,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_37,negated_conjecture,
( on_path(esk12_0,esk13_0)
| ~ path(X1,X2,esk13_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_18]) ).
cnf(c_0_38,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_31]) ).
cnf(c_0_39,plain,
( ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_40,plain,
( X1 = X2
| sequential(X1,X2)
| ~ edge(X1)
| ~ edge(X2)
| head_of(X1) != tail_of(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,negated_conjecture,
edge(esk11_0),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_42,negated_conjecture,
tail_of(esk11_0) = head_of(esk12_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_35]),c_0_36]) ).
cnf(c_0_43,negated_conjecture,
on_path(esk12_0,esk13_0),
inference(spm,[status(thm)],[c_0_37,c_0_25]) ).
cnf(c_0_44,negated_conjecture,
( precedes(X1,X2,esk13_0)
| ~ sequential(X1,X2)
| ~ on_path(X2,esk13_0)
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_25]) ).
cnf(c_0_45,negated_conjecture,
( ~ precedes(X1,X2,esk13_0)
| ~ precedes(X2,X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_14]) ).
cnf(c_0_46,negated_conjecture,
( X1 = esk11_0
| sequential(X1,esk11_0)
| head_of(esk12_0) != head_of(X1)
| ~ edge(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_47,negated_conjecture,
edge(esk12_0),
inference(spm,[status(thm)],[c_0_33,c_0_43]) ).
cnf(c_0_48,negated_conjecture,
( precedes(X1,esk11_0,esk13_0)
| ~ sequential(X1,esk11_0)
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_34]) ).
cnf(c_0_49,negated_conjecture,
~ precedes(esk12_0,esk11_0,esk13_0),
inference(spm,[status(thm)],[c_0_45,c_0_18]) ).
fof(c_0_50,plain,
! [X84] :
( ~ edge(X84)
| head_of(X84) != tail_of(X84) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[no_loops])]) ).
cnf(c_0_51,negated_conjecture,
( esk11_0 = esk12_0
| sequential(esk12_0,esk11_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_46]),c_0_47])]) ).
cnf(c_0_52,negated_conjecture,
~ sequential(esk12_0,esk11_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_43]),c_0_49]) ).
cnf(c_0_53,plain,
( ~ edge(X1)
| head_of(X1) != tail_of(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_54,negated_conjecture,
esk11_0 = esk12_0,
inference(sr,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_55,negated_conjecture,
tail_of(esk12_0) != head_of(esk12_0),
inference(spm,[status(thm)],[c_0_53,c_0_47]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_54]),c_0_55]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA004+1 : TPTP v9.2.1. Bugfixed v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n006.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:05:46 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.29/1.73 % Version : CSE_E---1.7
% 1.29/1.73 % Problem : theBenchmark.p
% 1.29/1.73 % SZS status Theorem for theBenchmark.p
% 1.29/1.73 % SZS output start CNFRefutation
% See solution above
% 1.29/1.73 % Total time : 1.374s
%------------------------------------------------------------------------------