TSTP Solution File: GRA004+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : GRA004+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n028.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 : Fri May 3 02:19:22 EDT 2024
% Result : Theorem 3.70s 1.19s
% Output : CNFRefutation 3.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 121 ( 17 unt; 0 def)
% Number of atoms : 512 ( 156 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 645 ( 254 ~; 242 |; 120 &)
% ( 5 <=>; 21 =>; 0 <=; 3 <~>)
% Maximal formula depth : 13 ( 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 : 361 ( 41 sgn 192 !; 38 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X1,X2,X3,X0] :
( ( on_path(X0,X3)
& path(X1,X2,X3) )
=> ( in_path(tail_of(X0),X3)
& in_path(head_of(X0),X3)
& edge(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',on_path_properties) ).
fof(f8,axiom,
! [X6,X7] :
( sequential(X6,X7)
<=> ( head_of(X6) = tail_of(X7)
& X6 != X7
& edge(X7)
& edge(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_defn) ).
fof(f9,axiom,
! [X3,X1,X2] :
( path(X1,X2,X3)
=> ! [X6,X7] :
( ( ( ? [X8] :
( precedes(X8,X7,X3)
& sequential(X6,X8) )
| sequential(X6,X7) )
& on_path(X7,X3)
& on_path(X6,X3) )
=> precedes(X6,X7,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_defn) ).
fof(f10,axiom,
! [X3,X1,X2] :
( path(X1,X2,X3)
=> ! [X6,X7] :
( precedes(X6,X7,X3)
=> ( ( sequential(X6,X7)
<~> ? [X8] :
( precedes(X8,X7,X3)
& sequential(X6,X8) ) )
& on_path(X7,X3)
& on_path(X6,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_properties) ).
fof(f11,axiom,
! [X1,X2,X9] :
( shortest_path(X1,X2,X9)
<=> ( ! [X3] :
( path(X1,X2,X3)
=> less_or_equal(length_of(X9),length_of(X3)) )
& X1 != X2
& path(X1,X2,X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_defn) ).
fof(f12,axiom,
! [X1,X2,X6,X7,X3] :
( ( precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ( ~ precedes(X7,X6,X3)
& ~ ? [X8] :
( head_of(X8) = head_of(X7)
& tail_of(X8) = tail_of(X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_properties) ).
fof(f18,conjecture,
! [X1,X2,X6,X7,X3] :
( ( precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ( head_of(X6) != head_of(X7)
& tail_of(X6) != head_of(X7)
& ~ ? [X8] :
( head_of(X8) = head_of(X7)
& tail_of(X8) = tail_of(X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_properties_lemma) ).
fof(f19,negated_conjecture,
~ ! [X1,X2,X6,X7,X3] :
( ( precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ( head_of(X6) != head_of(X7)
& tail_of(X6) != head_of(X7)
& ~ ? [X8] :
( head_of(X8) = head_of(X7)
& tail_of(X8) = tail_of(X6) ) ) ),
inference(negated_conjecture,[],[f18]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( ( on_path(X3,X2)
& path(X0,X1,X2) )
=> ( in_path(tail_of(X3),X2)
& in_path(head_of(X3),X2)
& edge(X3) ) ),
inference(rectify,[],[f6]) ).
fof(f25,plain,
! [X0,X1] :
( sequential(X0,X1)
<=> ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) ) ),
inference(rectify,[],[f8]) ).
fof(f26,plain,
! [X0,X1,X2] :
( path(X1,X2,X0)
=> ! [X3,X4] :
( ( ( ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) )
| sequential(X3,X4) )
& on_path(X4,X0)
& on_path(X3,X0) )
=> precedes(X3,X4,X0) ) ),
inference(rectify,[],[f9]) ).
fof(f27,plain,
! [X0,X1,X2] :
( path(X1,X2,X0)
=> ! [X3,X4] :
( precedes(X3,X4,X0)
=> ( ( sequential(X3,X4)
<~> ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
inference(rectify,[],[f10]) ).
fof(f28,plain,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( ! [X3] :
( path(X0,X1,X3)
=> less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1
& path(X0,X1,X2) ) ),
inference(rectify,[],[f11]) ).
fof(f29,plain,
! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( ~ precedes(X3,X2,X4)
& ~ ? [X5] :
( head_of(X3) = head_of(X5)
& tail_of(X2) = tail_of(X5) ) ) ),
inference(rectify,[],[f12]) ).
fof(f35,plain,
~ ! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( head_of(X2) != head_of(X3)
& tail_of(X2) != head_of(X3)
& ~ ? [X5] :
( head_of(X3) = head_of(X5)
& tail_of(X2) = tail_of(X5) ) ) ),
inference(rectify,[],[f19]) ).
fof(f43,plain,
! [X0,X1,X2,X3] :
( ( in_path(tail_of(X3),X2)
& in_path(head_of(X3),X2)
& edge(X3) )
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(ennf_transformation,[],[f23]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( ( in_path(tail_of(X3),X2)
& in_path(head_of(X3),X2)
& edge(X3) )
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(flattening,[],[f43]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( precedes(X3,X4,X0)
| ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
& ~ sequential(X3,X4) )
| ~ on_path(X4,X0)
| ~ on_path(X3,X0) )
| ~ path(X1,X2,X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( precedes(X3,X4,X0)
| ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
& ~ sequential(X3,X4) )
| ~ on_path(X4,X0)
| ~ on_path(X3,X0) )
| ~ path(X1,X2,X0) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( ( sequential(X3,X4)
<~> ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f50,plain,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) )
& X0 != X1
& path(X0,X1,X2) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f51,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ precedes(X3,X2,X4)
& ! [X5] :
( head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5) ) )
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) ),
inference(ennf_transformation,[],[f29]) ).
fof(f52,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ precedes(X3,X2,X4)
& ! [X5] :
( head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5) ) )
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) ),
inference(flattening,[],[f51]) ).
fof(f59,plain,
? [X0,X1,X2,X3,X4] :
( ( head_of(X2) = head_of(X3)
| tail_of(X2) = head_of(X3)
| ? [X5] :
( head_of(X3) = head_of(X5)
& tail_of(X2) = tail_of(X5) ) )
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) ),
inference(ennf_transformation,[],[f35]) ).
fof(f60,plain,
? [X0,X1,X2,X3,X4] :
( ( head_of(X2) = head_of(X3)
| tail_of(X2) = head_of(X3)
| ? [X5] :
( head_of(X3) = head_of(X5)
& tail_of(X2) = tail_of(X5) ) )
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) ),
inference(flattening,[],[f59]) ).
fof(f69,plain,
! [X0,X1] :
( ( sequential(X0,X1)
| head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0) )
& ( ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) )
| ~ sequential(X0,X1) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f70,plain,
! [X0,X1] :
( ( sequential(X0,X1)
| head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0) )
& ( ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) )
| ~ sequential(X0,X1) ) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
| ~ sequential(X3,X4) )
& ( ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) )
| sequential(X3,X4) )
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(nnf_transformation,[],[f49]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
| ~ sequential(X3,X4) )
& ( ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) )
| sequential(X3,X4) )
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
| ~ sequential(X3,X4) )
& ( ? [X6] :
( precedes(X6,X4,X0)
& sequential(X3,X6) )
| sequential(X3,X4) )
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(rectify,[],[f72]) ).
fof(f74,plain,
! [X0,X3,X4] :
( ? [X6] :
( precedes(X6,X4,X0)
& sequential(X3,X6) )
=> ( precedes(sK3(X0,X3,X4),X4,X0)
& sequential(X3,sK3(X0,X3,X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
| ~ sequential(X3,X4) )
& ( ( precedes(sK3(X0,X3,X4),X4,X0)
& sequential(X3,sK3(X0,X3,X4)) )
| sequential(X3,X4) )
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f73,f74]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) )
| X0 = X1
| ~ path(X0,X1,X2) )
& ( ( ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) )
& X0 != X1
& path(X0,X1,X2) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) )
| X0 = X1
| ~ path(X0,X1,X2) )
& ( ( ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) )
& X0 != X1
& path(X0,X1,X2) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) )
| X0 = X1
| ~ path(X0,X1,X2) )
& ( ( ! [X4] :
( less_or_equal(length_of(X2),length_of(X4))
| ~ path(X0,X1,X4) )
& X0 != X1
& path(X0,X1,X2) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) )
=> ( ~ less_or_equal(length_of(X2),length_of(sK4(X0,X1,X2)))
& path(X0,X1,sK4(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ( ~ less_or_equal(length_of(X2),length_of(sK4(X0,X1,X2)))
& path(X0,X1,sK4(X0,X1,X2)) )
| X0 = X1
| ~ path(X0,X1,X2) )
& ( ( ! [X4] :
( less_or_equal(length_of(X2),length_of(X4))
| ~ path(X0,X1,X4) )
& X0 != X1
& path(X0,X1,X2) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f78,f79]) ).
fof(f83,plain,
( ? [X0,X1,X2,X3,X4] :
( ( head_of(X2) = head_of(X3)
| tail_of(X2) = head_of(X3)
| ? [X5] :
( head_of(X3) = head_of(X5)
& tail_of(X2) = tail_of(X5) ) )
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( ( head_of(sK9) = head_of(sK10)
| head_of(sK10) = tail_of(sK9)
| ? [X5] :
( head_of(X5) = head_of(sK10)
& tail_of(X5) = tail_of(sK9) ) )
& precedes(sK9,sK10,sK11)
& shortest_path(sK7,sK8,sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
( ? [X5] :
( head_of(X5) = head_of(sK10)
& tail_of(X5) = tail_of(sK9) )
=> ( head_of(sK10) = head_of(sK12)
& tail_of(sK9) = tail_of(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
( ( head_of(sK9) = head_of(sK10)
| head_of(sK10) = tail_of(sK9)
| ( head_of(sK10) = head_of(sK12)
& tail_of(sK9) = tail_of(sK12) ) )
& precedes(sK9,sK10,sK11)
& shortest_path(sK7,sK8,sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11,sK12])],[f60,f84,f83]) ).
fof(f100,plain,
! [X2,X3,X0,X1] :
( edge(X3)
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f110,plain,
! [X0,X1] :
( sequential(X0,X1)
| head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f112,plain,
! [X2,X3,X0,X1,X4,X5] :
( precedes(X3,X4,X0)
| ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f113,plain,
! [X2,X3,X0,X1,X4] :
( on_path(X3,X0)
| ~ precedes(X3,X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f114,plain,
! [X2,X3,X0,X1,X4] :
( on_path(X4,X0)
| ~ precedes(X3,X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f118,plain,
! [X2,X0,X1] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f123,plain,
! [X2,X3,X0,X1,X4,X5] :
( head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5)
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) ),
inference(cnf_transformation,[],[f52]) ).
fof(f124,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X2,X4)
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) ),
inference(cnf_transformation,[],[f52]) ).
fof(f133,plain,
shortest_path(sK7,sK8,sK11),
inference(cnf_transformation,[],[f85]) ).
fof(f134,plain,
precedes(sK9,sK10,sK11),
inference(cnf_transformation,[],[f85]) ).
fof(f135,plain,
( head_of(sK9) = head_of(sK10)
| head_of(sK10) = tail_of(sK9)
| tail_of(sK9) = tail_of(sK12) ),
inference(cnf_transformation,[],[f85]) ).
fof(f136,plain,
( head_of(sK9) = head_of(sK10)
| head_of(sK10) = tail_of(sK9)
| head_of(sK10) = head_of(sK12) ),
inference(cnf_transformation,[],[f85]) ).
cnf(c_65,plain,
( ~ path(X0,X1,X2)
| ~ on_path(X3,X2)
| edge(X3) ),
inference(cnf_transformation,[],[f100]) ).
cnf(c_69,plain,
( head_of(X0) != tail_of(X1)
| ~ edge(X0)
| ~ edge(X1)
| X0 = X1
| sequential(X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
cnf(c_74,plain,
( ~ path(X0,X1,X2)
| ~ precedes(X3,X4,X2)
| ~ on_path(X4,X2)
| ~ on_path(X5,X2)
| ~ sequential(X5,X3)
| precedes(X5,X4,X2) ),
inference(cnf_transformation,[],[f112]) ).
cnf(c_79,plain,
( ~ path(X0,X1,X2)
| ~ precedes(X3,X4,X2)
| on_path(X4,X2) ),
inference(cnf_transformation,[],[f114]) ).
cnf(c_80,plain,
( ~ path(X0,X1,X2)
| ~ precedes(X3,X4,X2)
| on_path(X3,X2) ),
inference(cnf_transformation,[],[f113]) ).
cnf(c_85,plain,
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f118]) ).
cnf(c_86,plain,
( ~ precedes(X0,X1,X2)
| ~ precedes(X1,X0,X2)
| ~ shortest_path(X3,X4,X2) ),
inference(cnf_transformation,[],[f124]) ).
cnf(c_87,plain,
( head_of(X0) != head_of(X1)
| tail_of(X1) != tail_of(X2)
| ~ precedes(X2,X0,X3)
| ~ shortest_path(X4,X5,X3) ),
inference(cnf_transformation,[],[f123]) ).
cnf(c_96,negated_conjecture,
( head_of(sK9) = head_of(sK10)
| head_of(sK10) = head_of(sK12)
| head_of(sK10) = tail_of(sK9) ),
inference(cnf_transformation,[],[f136]) ).
cnf(c_97,negated_conjecture,
( head_of(sK9) = head_of(sK10)
| head_of(sK10) = tail_of(sK9)
| tail_of(sK9) = tail_of(sK12) ),
inference(cnf_transformation,[],[f135]) ).
cnf(c_98,negated_conjecture,
precedes(sK9,sK10,sK11),
inference(cnf_transformation,[],[f134]) ).
cnf(c_99,negated_conjecture,
shortest_path(sK7,sK8,sK11),
inference(cnf_transformation,[],[f133]) ).
cnf(c_140,plain,
( ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2)
| ~ on_path(X5,X2)
| ~ sequential(X5,X3)
| precedes(X5,X4,X2) ),
inference(global_subsumption_just,[status(thm)],[c_74,c_79,c_74]) ).
cnf(c_141,plain,
( ~ path(X0,X1,X2)
| ~ precedes(X3,X4,X2)
| ~ on_path(X5,X2)
| ~ sequential(X5,X3)
| precedes(X5,X4,X2) ),
inference(renaming,[status(thm)],[c_140]) ).
cnf(c_734,plain,
( X0 != sK7
| X1 != sK8
| X2 != sK11
| path(X0,X1,X2) ),
inference(resolution_lifted,[status(thm)],[c_85,c_99]) ).
cnf(c_735,plain,
path(sK7,sK8,sK11),
inference(unflattening,[status(thm)],[c_734]) ).
cnf(c_753,plain,
( X0 != sK11
| X1 != sK7
| X2 != sK8
| ~ precedes(X3,X4,X0)
| ~ precedes(X4,X3,X0) ),
inference(resolution_lifted,[status(thm)],[c_86,c_99]) ).
cnf(c_754,plain,
( ~ precedes(X0,X1,sK11)
| ~ precedes(X1,X0,sK11) ),
inference(unflattening,[status(thm)],[c_753]) ).
cnf(c_755,plain,
~ precedes(sK10,sK10,sK11),
inference(instantiation,[status(thm)],[c_754]) ).
cnf(c_1421,plain,
( ~ path(X0_13,X1_13,X0_14)
| ~ precedes(X0_15,X1_15,X0_14)
| ~ on_path(X2_15,X0_14)
| ~ sequential(X2_15,X0_15)
| precedes(X2_15,X1_15,X0_14) ),
inference(subtyping,[status(esa)],[c_141]) ).
cnf(c_1423,negated_conjecture,
shortest_path(sK7,sK8,sK11),
inference(subtyping,[status(esa)],[c_99]) ).
cnf(c_1424,negated_conjecture,
precedes(sK9,sK10,sK11),
inference(subtyping,[status(esa)],[c_98]) ).
cnf(c_1425,negated_conjecture,
( head_of(sK9) = head_of(sK10)
| head_of(sK10) = tail_of(sK9)
| tail_of(sK9) = tail_of(sK12) ),
inference(subtyping,[status(esa)],[c_97]) ).
cnf(c_1426,negated_conjecture,
( head_of(sK9) = head_of(sK10)
| head_of(sK10) = head_of(sK12)
| head_of(sK10) = tail_of(sK9) ),
inference(subtyping,[status(esa)],[c_96]) ).
cnf(c_1433,plain,
( head_of(X0_15) != head_of(X1_15)
| tail_of(X1_15) != tail_of(X2_15)
| ~ precedes(X2_15,X0_15,X0_14)
| ~ shortest_path(X0_13,X1_13,X0_14) ),
inference(subtyping,[status(esa)],[c_87]) ).
cnf(c_1435,plain,
( ~ shortest_path(X0_13,X1_13,X0_14)
| path(X0_13,X1_13,X0_14) ),
inference(subtyping,[status(esa)],[c_85]) ).
cnf(c_1440,plain,
( ~ path(X0_13,X1_13,X0_14)
| ~ precedes(X0_15,X1_15,X0_14)
| on_path(X0_15,X0_14) ),
inference(subtyping,[status(esa)],[c_80]) ).
cnf(c_1441,plain,
( ~ path(X0_13,X1_13,X0_14)
| ~ precedes(X0_15,X1_15,X0_14)
| on_path(X1_15,X0_14) ),
inference(subtyping,[status(esa)],[c_79]) ).
cnf(c_1450,plain,
( head_of(X0_15) != tail_of(X1_15)
| ~ edge(X0_15)
| ~ edge(X1_15)
| X0_15 = X1_15
| sequential(X0_15,X1_15) ),
inference(subtyping,[status(esa)],[c_69]) ).
cnf(c_1453,plain,
( ~ path(X0_13,X1_13,X0_14)
| ~ on_path(X0_15,X0_14)
| edge(X0_15) ),
inference(subtyping,[status(esa)],[c_65]) ).
cnf(c_1465,plain,
X0_13 = X0_13,
theory(equality) ).
cnf(c_1467,plain,
X0_15 = X0_15,
theory(equality) ).
cnf(c_1469,plain,
( X0_13 != X1_13
| X2_13 != X1_13
| X2_13 = X0_13 ),
theory(equality) ).
cnf(c_1473,plain,
( X0_15 != X1_15
| head_of(X0_15) = head_of(X1_15) ),
theory(equality) ).
cnf(c_1474,plain,
( X0_15 != X1_15
| tail_of(X0_15) = tail_of(X1_15) ),
theory(equality) ).
cnf(c_1487,plain,
( sK10 != sK10
| head_of(sK10) = head_of(sK10) ),
inference(instantiation,[status(thm)],[c_1473]) ).
cnf(c_1496,plain,
sK10 = sK10,
inference(instantiation,[status(thm)],[c_1467]) ).
cnf(c_2300,plain,
( head_of(X0_15) != head_of(X1_15)
| tail_of(X1_15) != tail_of(X2_15)
| ~ precedes(X2_15,X0_15,sK11)
| ~ shortest_path(sK7,sK8,sK11) ),
inference(instantiation,[status(thm)],[c_1433]) ).
cnf(c_2319,plain,
( tail_of(X0_15) != X0_13
| tail_of(sK9) != X0_13
| tail_of(X0_15) = tail_of(sK9) ),
inference(instantiation,[status(thm)],[c_1469]) ).
cnf(c_2321,plain,
( X0_15 != sK9
| tail_of(X0_15) = tail_of(sK9) ),
inference(instantiation,[status(thm)],[c_1474]) ).
cnf(c_2322,plain,
( sK10 != sK9
| tail_of(sK10) = tail_of(sK9) ),
inference(instantiation,[status(thm)],[c_2321]) ).
cnf(c_2323,plain,
( tail_of(X0_15) != tail_of(sK9)
| head_of(sK10) != head_of(X0_15)
| ~ precedes(sK9,sK10,sK11)
| ~ shortest_path(sK7,sK8,sK11) ),
inference(instantiation,[status(thm)],[c_2300]) ).
cnf(c_2324,plain,
( head_of(sK10) != head_of(sK10)
| tail_of(sK10) != tail_of(sK9)
| ~ precedes(sK9,sK10,sK11)
| ~ shortest_path(sK7,sK8,sK11) ),
inference(instantiation,[status(thm)],[c_2323]) ).
cnf(c_2326,plain,
( ~ path(X0_13,X1_13,sK11)
| ~ precedes(X0_15,X1_15,sK11)
| ~ sequential(X2_15,X0_15)
| ~ on_path(X2_15,sK11)
| precedes(X2_15,X1_15,sK11) ),
inference(instantiation,[status(thm)],[c_1421]) ).
cnf(c_2348,plain,
tail_of(sK9) = tail_of(sK9),
inference(instantiation,[status(thm)],[c_1465]) ).
cnf(c_2357,plain,
( ~ path(X0_13,X1_13,sK11)
| ~ precedes(X0_15,X1_15,sK11)
| on_path(X1_15,sK11) ),
inference(instantiation,[status(thm)],[c_1441]) ).
cnf(c_2366,plain,
( tail_of(X0_15) != tail_of(X1_15)
| tail_of(sK9) != tail_of(X1_15)
| tail_of(X0_15) = tail_of(sK9) ),
inference(instantiation,[status(thm)],[c_2319]) ).
cnf(c_2368,plain,
( head_of(X0_15) != tail_of(sK9)
| ~ edge(X0_15)
| ~ edge(sK9)
| X0_15 = sK9
| sequential(X0_15,sK9) ),
inference(instantiation,[status(thm)],[c_1450]) ).
cnf(c_2369,plain,
( head_of(sK10) != tail_of(sK9)
| ~ edge(sK9)
| ~ edge(sK10)
| sK10 = sK9
| sequential(sK10,sK9) ),
inference(instantiation,[status(thm)],[c_2368]) ).
cnf(c_2383,plain,
( head_of(sK10) != head_of(sK9)
| tail_of(sK9) != tail_of(sK9)
| ~ precedes(sK9,sK10,sK11)
| ~ shortest_path(sK7,sK8,sK11) ),
inference(instantiation,[status(thm)],[c_2323]) ).
cnf(c_2442,plain,
( head_of(sK9) != X0_13
| head_of(sK10) != X0_13
| head_of(sK10) = head_of(sK9) ),
inference(instantiation,[status(thm)],[c_1469]) ).
cnf(c_2609,plain,
( head_of(sK9) != head_of(X0_15)
| head_of(sK10) != head_of(X0_15)
| head_of(sK10) = head_of(sK9) ),
inference(instantiation,[status(thm)],[c_2442]) ).
cnf(c_2610,plain,
( head_of(sK9) != head_of(sK10)
| head_of(sK10) != head_of(sK10)
| head_of(sK10) = head_of(sK9) ),
inference(instantiation,[status(thm)],[c_2609]) ).
cnf(c_2759,plain,
( ~ precedes(X0_15,X1_15,sK11)
| ~ path(sK7,sK8,sK11)
| on_path(X1_15,sK11) ),
inference(instantiation,[status(thm)],[c_2357]) ).
cnf(c_2807,plain,
path(sK7,sK8,sK11),
inference(superposition,[status(thm)],[c_1423,c_1435]) ).
cnf(c_2851,plain,
( ~ on_path(X0_15,sK11)
| edge(X0_15) ),
inference(superposition,[status(thm)],[c_2807,c_1453]) ).
cnf(c_2853,plain,
( ~ on_path(sK10,sK11)
| edge(sK10) ),
inference(instantiation,[status(thm)],[c_2851]) ).
cnf(c_2958,plain,
( ~ precedes(X0_15,X1_15,sK11)
| on_path(X0_15,sK11) ),
inference(superposition,[status(thm)],[c_2807,c_1440]) ).
cnf(c_2977,plain,
( tail_of(X0_15) != tail_of(sK12)
| tail_of(sK9) != tail_of(sK12)
| tail_of(X0_15) = tail_of(sK9) ),
inference(instantiation,[status(thm)],[c_2366]) ).
cnf(c_2992,plain,
( ~ path(sK7,sK8,sK11)
| ~ precedes(sK9,sK10,sK11)
| on_path(sK10,sK11) ),
inference(instantiation,[status(thm)],[c_2759]) ).
cnf(c_3092,plain,
on_path(sK9,sK11),
inference(superposition,[status(thm)],[c_1424,c_2958]) ).
cnf(c_3093,plain,
edge(sK9),
inference(superposition,[status(thm)],[c_3092,c_2851]) ).
cnf(c_3239,plain,
( tail_of(sK9) != tail_of(sK12)
| tail_of(sK12) != tail_of(sK12)
| tail_of(sK12) = tail_of(sK9) ),
inference(instantiation,[status(thm)],[c_2977]) ).
cnf(c_3615,plain,
( ~ path(X0_13,X1_13,sK11)
| ~ precedes(sK9,X0_15,sK11)
| ~ on_path(X1_15,sK11)
| ~ sequential(X1_15,sK9)
| precedes(X1_15,X0_15,sK11) ),
inference(instantiation,[status(thm)],[c_2326]) ).
cnf(c_3712,plain,
tail_of(sK12) = tail_of(sK12),
inference(instantiation,[status(thm)],[c_1465]) ).
cnf(c_5365,plain,
( ~ precedes(sK9,X0_15,sK11)
| ~ path(sK7,sK8,sK11)
| ~ on_path(X1_15,sK11)
| ~ sequential(X1_15,sK9)
| precedes(X1_15,X0_15,sK11) ),
inference(instantiation,[status(thm)],[c_3615]) ).
cnf(c_5366,plain,
( ~ path(sK7,sK8,sK11)
| ~ precedes(sK9,sK10,sK11)
| ~ on_path(sK10,sK11)
| ~ sequential(sK10,sK9)
| precedes(sK10,sK10,sK11) ),
inference(instantiation,[status(thm)],[c_5365]) ).
cnf(c_6464,plain,
( head_of(sK10) != head_of(sK12)
| tail_of(sK12) != tail_of(sK9)
| ~ precedes(sK9,sK10,sK11)
| ~ shortest_path(sK7,sK8,sK11) ),
inference(instantiation,[status(thm)],[c_2323]) ).
cnf(c_6467,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_6464,c_5366,c_3712,c_3239,c_3093,c_2992,c_2853,c_2610,c_2383,c_2369,c_2348,c_2324,c_2322,c_1426,c_1425,c_1496,c_1487,c_755,c_735,c_98,c_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRA004+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.07/0.14 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu May 2 21:45:18 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.49 Running first-order theorem proving
% 0.20/0.49 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.70/1.19 % SZS status Started for theBenchmark.p
% 3.70/1.19 % SZS status Theorem for theBenchmark.p
% 3.70/1.19
% 3.70/1.19 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.70/1.19
% 3.70/1.19 ------ iProver source info
% 3.70/1.19
% 3.70/1.19 git: date: 2024-05-02 19:28:25 +0000
% 3.70/1.19 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.70/1.19 git: non_committed_changes: false
% 3.70/1.19
% 3.70/1.19 ------ Parsing...
% 3.70/1.19 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.70/1.19
% 3.70/1.19 ------ Preprocessing... sup_sim: 0 sf_s rm: 7 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e
% 3.70/1.19
% 3.70/1.19 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.70/1.19
% 3.70/1.19 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.70/1.19 ------ Proving...
% 3.70/1.19 ------ Problem Properties
% 3.70/1.19
% 3.70/1.19
% 3.70/1.19 clauses 45
% 3.70/1.19 conjectures 4
% 3.70/1.19 EPR 14
% 3.70/1.19 Horn 30
% 3.70/1.19 unary 5
% 3.70/1.19 binary 10
% 3.70/1.19 lits 132
% 3.70/1.19 lits eq 32
% 3.70/1.19 fd_pure 0
% 3.70/1.19 fd_pseudo 0
% 3.70/1.19 fd_cond 0
% 3.70/1.19 fd_pseudo_cond 3
% 3.70/1.19 AC symbols 0
% 3.70/1.19
% 3.70/1.19 ------ Input Options Time Limit: Unbounded
% 3.70/1.19
% 3.70/1.19
% 3.70/1.19 ------
% 3.70/1.19 Current options:
% 3.70/1.19 ------
% 3.70/1.19
% 3.70/1.19
% 3.70/1.19
% 3.70/1.19
% 3.70/1.19 ------ Proving...
% 3.70/1.19
% 3.70/1.19
% 3.70/1.19 % SZS status Theorem for theBenchmark.p
% 3.70/1.19
% 3.70/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.70/1.19
% 3.70/1.19
%------------------------------------------------------------------------------