TSTP Solution File: GRA008+2 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : GRA008+2 : TPTP v8.2.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n005.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 Jun 24 06:35:27 EDT 2024
% Result : Theorem 7.08s 1.61s
% Output : CNFRefutation 7.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 134 ( 27 unt; 0 def)
% Number of atoms : 532 ( 89 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 651 ( 253 ~; 224 |; 136 &)
% ( 7 <=>; 28 =>; 0 <=; 3 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 2 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 390 ( 46 sgn 238 !; 38 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( edge(X0)
=> head_of(X0) != tail_of(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_loops) ).
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(f13,axiom,
! [X6,X7,X8] :
( triangle(X6,X7,X8)
<=> ( sequential(X8,X6)
& sequential(X7,X8)
& sequential(X6,X7)
& edge(X8)
& edge(X7)
& edge(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangle_defn) ).
fof(f18,axiom,
( complete
=> ! [X1,X2,X6,X7,X3] :
( ( precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ? [X8] :
( tail_of(X6) = head_of(X8)
& tail_of(X8) = head_of(X7)
& edge(X8) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',back_edge) ).
fof(f19,conjecture,
( complete
=> ! [X1,X2,X6,X7,X3] :
( ( sequential(X6,X7)
& precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ? [X8] : triangle(X6,X7,X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_is_triangle) ).
fof(f20,negated_conjecture,
~ ( complete
=> ! [X1,X2,X6,X7,X3] :
( ( sequential(X6,X7)
& precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ? [X8] : triangle(X6,X7,X8) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f26,plain,
! [X0,X1] :
( sequential(X0,X1)
<=> ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) ) ),
inference(rectify,[],[f8]) ).
fof(f27,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(f28,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(f29,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(f30,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(f31,plain,
! [X0,X1,X2] :
( triangle(X0,X1,X2)
<=> ( sequential(X2,X0)
& sequential(X1,X2)
& sequential(X0,X1)
& edge(X2)
& edge(X1)
& edge(X0) ) ),
inference(rectify,[],[f13]) ).
fof(f36,plain,
( complete
=> ! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ? [X5] :
( tail_of(X2) = head_of(X5)
& head_of(X3) = tail_of(X5)
& edge(X5) ) ) ),
inference(rectify,[],[f18]) ).
fof(f37,plain,
~ ( complete
=> ! [X0,X1,X2,X3,X4] :
( ( sequential(X2,X3)
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ? [X5] : triangle(X2,X3,X5) ) ),
inference(rectify,[],[f20]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( sequential(X2,X0)
& sequential(X1,X2)
& sequential(X0,X1)
& edge(X2)
& edge(X1)
& edge(X0) )
=> triangle(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f39,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f50,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,[],[f27]) ).
fof(f51,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,[],[f50]) ).
fof(f52,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,[],[f28]) ).
fof(f53,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,[],[f29]) ).
fof(f54,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,[],[f30]) ).
fof(f55,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,[],[f54]) ).
fof(f56,plain,
! [X0,X1,X2] :
( triangle(X0,X1,X2)
| ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1)
| ~ edge(X2)
| ~ edge(X1)
| ~ edge(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f57,plain,
! [X0,X1,X2] :
( triangle(X0,X1,X2)
| ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1)
| ~ edge(X2)
| ~ edge(X1)
| ~ edge(X0) ),
inference(flattening,[],[f56]) ).
fof(f62,plain,
( ! [X0,X1,X2,X3,X4] :
( ? [X5] :
( tail_of(X2) = head_of(X5)
& head_of(X3) = tail_of(X5)
& edge(X5) )
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) )
| ~ complete ),
inference(ennf_transformation,[],[f36]) ).
fof(f63,plain,
( ! [X0,X1,X2,X3,X4] :
( ? [X5] :
( tail_of(X2) = head_of(X5)
& head_of(X3) = tail_of(X5)
& edge(X5) )
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) )
| ~ complete ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
( ? [X0,X1,X2,X3,X4] :
( ! [X5] : ~ triangle(X2,X3,X5)
& sequential(X2,X3)
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
& complete ),
inference(ennf_transformation,[],[f37]) ).
fof(f65,plain,
( ? [X0,X1,X2,X3,X4] :
( ! [X5] : ~ triangle(X2,X3,X5)
& sequential(X2,X3)
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
& complete ),
inference(flattening,[],[f64]) ).
fof(f78,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,[],[f26]) ).
fof(f79,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,[],[f78]) ).
fof(f80,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,[],[f52]) ).
fof(f81,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,[],[f80]) ).
fof(f82,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,[],[f81]) ).
fof(f83,plain,
! [X0,X3,X4] :
( ? [X6] :
( precedes(X6,X4,X0)
& sequential(X3,X6) )
=> ( precedes(sK4(X0,X3,X4),X4,X0)
& sequential(X3,sK4(X0,X3,X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
| ~ sequential(X3,X4) )
& ( ( precedes(sK4(X0,X3,X4),X4,X0)
& sequential(X3,sK4(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,[sK4])],[f82,f83]) ).
fof(f85,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,[],[f53]) ).
fof(f86,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,[],[f85]) ).
fof(f87,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,[],[f86]) ).
fof(f88,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(sK5(X0,X1,X2)))
& path(X0,X1,sK5(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ( ~ less_or_equal(length_of(X2),length_of(sK5(X0,X1,X2)))
& path(X0,X1,sK5(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,[sK5])],[f87,f88]) ).
fof(f92,plain,
! [X2,X3] :
( ? [X5] :
( tail_of(X2) = head_of(X5)
& head_of(X3) = tail_of(X5)
& edge(X5) )
=> ( tail_of(X2) = head_of(sK8(X2,X3))
& head_of(X3) = tail_of(sK8(X2,X3))
& edge(sK8(X2,X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f93,plain,
( ! [X0,X1,X2,X3,X4] :
( ( tail_of(X2) = head_of(sK8(X2,X3))
& head_of(X3) = tail_of(sK8(X2,X3))
& edge(sK8(X2,X3)) )
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) )
| ~ complete ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f63,f92]) ).
fof(f94,plain,
( ? [X0,X1,X2,X3,X4] :
( ! [X5] : ~ triangle(X2,X3,X5)
& sequential(X2,X3)
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( ! [X5] : ~ triangle(sK11,sK12,X5)
& sequential(sK11,sK12)
& precedes(sK11,sK12,sK13)
& shortest_path(sK9,sK10,sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f95,plain,
( ! [X5] : ~ triangle(sK11,sK12,X5)
& sequential(sK11,sK12)
& precedes(sK11,sK12,sK13)
& shortest_path(sK9,sK10,sK13)
& complete ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13])],[f65,f94]) ).
fof(f96,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f122,plain,
! [X0,X1] :
( edge(X0)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f123,plain,
! [X0,X1] :
( edge(X1)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f126,plain,
! [X0,X1] :
( sequential(X0,X1)
| head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f127,plain,
! [X2,X3,X0,X1,X4] :
( precedes(X3,X4,X0)
| ~ sequential(X3,X4)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f129,plain,
! [X2,X3,X0,X1,X4] :
( on_path(X3,X0)
| ~ precedes(X3,X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f130,plain,
! [X2,X3,X0,X1,X4] :
( on_path(X4,X0)
| ~ precedes(X3,X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f134,plain,
! [X2,X0,X1] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f89]) ).
fof(f140,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X2,X4)
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) ),
inference(cnf_transformation,[],[f55]) ).
fof(f141,plain,
! [X2,X0,X1] :
( triangle(X0,X1,X2)
| ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1)
| ~ edge(X2)
| ~ edge(X1)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f149,plain,
! [X2,X3,X0,X1,X4] :
( edge(sK8(X2,X3))
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ~ complete ),
inference(cnf_transformation,[],[f93]) ).
fof(f150,plain,
! [X2,X3,X0,X1,X4] :
( head_of(X3) = tail_of(sK8(X2,X3))
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ~ complete ),
inference(cnf_transformation,[],[f93]) ).
fof(f151,plain,
! [X2,X3,X0,X1,X4] :
( tail_of(X2) = head_of(sK8(X2,X3))
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ~ complete ),
inference(cnf_transformation,[],[f93]) ).
fof(f152,plain,
complete,
inference(cnf_transformation,[],[f95]) ).
fof(f153,plain,
shortest_path(sK9,sK10,sK13),
inference(cnf_transformation,[],[f95]) ).
fof(f154,plain,
precedes(sK11,sK12,sK13),
inference(cnf_transformation,[],[f95]) ).
fof(f155,plain,
sequential(sK11,sK12),
inference(cnf_transformation,[],[f95]) ).
fof(f156,plain,
! [X5] : ~ triangle(sK11,sK12,X5),
inference(cnf_transformation,[],[f95]) ).
cnf(c_49,plain,
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f96]) ).
cnf(c_75,plain,
( head_of(X0) != tail_of(X1)
| ~ edge(X0)
| ~ edge(X1)
| X0 = X1
| sequential(X0,X1) ),
inference(cnf_transformation,[],[f126]) ).
cnf(c_78,plain,
( ~ sequential(X0,X1)
| edge(X1) ),
inference(cnf_transformation,[],[f123]) ).
cnf(c_79,plain,
( ~ sequential(X0,X1)
| edge(X0) ),
inference(cnf_transformation,[],[f122]) ).
cnf(c_81,plain,
( ~ path(X0,X1,X2)
| ~ on_path(X3,X2)
| ~ on_path(X4,X2)
| ~ sequential(X3,X4)
| precedes(X3,X4,X2) ),
inference(cnf_transformation,[],[f127]) ).
cnf(c_85,plain,
( ~ path(X0,X1,X2)
| ~ precedes(X3,X4,X2)
| on_path(X4,X2) ),
inference(cnf_transformation,[],[f130]) ).
cnf(c_86,plain,
( ~ path(X0,X1,X2)
| ~ precedes(X3,X4,X2)
| on_path(X3,X2) ),
inference(cnf_transformation,[],[f129]) ).
cnf(c_91,plain,
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f134]) ).
cnf(c_92,plain,
( ~ precedes(X0,X1,X2)
| ~ precedes(X1,X0,X2)
| ~ shortest_path(X3,X4,X2) ),
inference(cnf_transformation,[],[f140]) ).
cnf(c_94,plain,
( ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0)
| ~ edge(X0)
| ~ edge(X1)
| ~ edge(X2)
| triangle(X0,X1,X2) ),
inference(cnf_transformation,[],[f141]) ).
cnf(c_102,plain,
( ~ precedes(X0,X1,X2)
| ~ shortest_path(X3,X4,X2)
| ~ complete
| head_of(sK8(X0,X1)) = tail_of(X0) ),
inference(cnf_transformation,[],[f151]) ).
cnf(c_103,plain,
( ~ precedes(X0,X1,X2)
| ~ shortest_path(X3,X4,X2)
| ~ complete
| tail_of(sK8(X0,X1)) = head_of(X1) ),
inference(cnf_transformation,[],[f150]) ).
cnf(c_104,plain,
( ~ precedes(X0,X1,X2)
| ~ shortest_path(X3,X4,X2)
| ~ complete
| edge(sK8(X0,X1)) ),
inference(cnf_transformation,[],[f149]) ).
cnf(c_105,negated_conjecture,
~ triangle(sK11,sK12,X0),
inference(cnf_transformation,[],[f156]) ).
cnf(c_106,negated_conjecture,
sequential(sK11,sK12),
inference(cnf_transformation,[],[f155]) ).
cnf(c_107,negated_conjecture,
precedes(sK11,sK12,sK13),
inference(cnf_transformation,[],[f154]) ).
cnf(c_108,negated_conjecture,
shortest_path(sK9,sK10,sK13),
inference(cnf_transformation,[],[f153]) ).
cnf(c_109,negated_conjecture,
complete,
inference(cnf_transformation,[],[f152]) ).
cnf(c_147,plain,
( ~ shortest_path(X3,X4,X2)
| ~ precedes(X0,X1,X2)
| edge(sK8(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_104,c_109,c_104]) ).
cnf(c_148,plain,
( ~ precedes(X0,X1,X2)
| ~ shortest_path(X3,X4,X2)
| edge(sK8(X0,X1)) ),
inference(renaming,[status(thm)],[c_147]) ).
cnf(c_155,plain,
( ~ shortest_path(X3,X4,X2)
| ~ precedes(X0,X1,X2)
| tail_of(sK8(X0,X1)) = head_of(X1) ),
inference(global_subsumption_just,[status(thm)],[c_103,c_109,c_103]) ).
cnf(c_156,plain,
( ~ precedes(X0,X1,X2)
| ~ shortest_path(X3,X4,X2)
| tail_of(sK8(X0,X1)) = head_of(X1) ),
inference(renaming,[status(thm)],[c_155]) ).
cnf(c_157,plain,
( ~ shortest_path(X3,X4,X2)
| ~ precedes(X0,X1,X2)
| head_of(sK8(X0,X1)) = tail_of(X0) ),
inference(global_subsumption_just,[status(thm)],[c_102,c_109,c_102]) ).
cnf(c_158,plain,
( ~ precedes(X0,X1,X2)
| ~ shortest_path(X3,X4,X2)
| head_of(sK8(X0,X1)) = tail_of(X0) ),
inference(renaming,[status(thm)],[c_157]) ).
cnf(c_162,plain,
( ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0)
| ~ edge(X2)
| triangle(X0,X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_94,c_79,c_78,c_94]) ).
cnf(c_207,plain,
( ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0)
| triangle(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_162,c_78]) ).
cnf(c_985,plain,
( X0 != sK11
| X1 != sK12
| X2 != X3
| ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0) ),
inference(resolution_lifted,[status(thm)],[c_207,c_105]) ).
cnf(c_986,plain,
( ~ sequential(X0,sK11)
| ~ sequential(sK12,X0)
| ~ sequential(sK11,sK12) ),
inference(unflattening,[status(thm)],[c_985]) ).
cnf(c_988,plain,
( ~ sequential(sK12,X0)
| ~ sequential(X0,sK11) ),
inference(global_subsumption_just,[status(thm)],[c_986,c_106,c_986]) ).
cnf(c_989,plain,
( ~ sequential(X0,sK11)
| ~ sequential(sK12,X0) ),
inference(renaming,[status(thm)],[c_988]) ).
cnf(c_2742,negated_conjecture,
shortest_path(sK9,sK10,sK13),
inference(demodulation,[status(thm)],[c_108]) ).
cnf(c_2743,negated_conjecture,
precedes(sK11,sK12,sK13),
inference(demodulation,[status(thm)],[c_107]) ).
cnf(c_2744,negated_conjecture,
sequential(sK11,sK12),
inference(demodulation,[status(thm)],[c_106]) ).
cnf(c_3733,plain,
edge(sK12),
inference(superposition,[status(thm)],[c_2744,c_78]) ).
cnf(c_3738,plain,
edge(sK11),
inference(superposition,[status(thm)],[c_2744,c_79]) ).
cnf(c_3751,plain,
path(sK9,sK10,sK13),
inference(superposition,[status(thm)],[c_2742,c_91]) ).
cnf(c_3929,plain,
( ~ precedes(X0,X1,sK13)
| on_path(X1,sK13) ),
inference(superposition,[status(thm)],[c_3751,c_85]) ).
cnf(c_3984,plain,
on_path(sK12,sK13),
inference(superposition,[status(thm)],[c_2743,c_3929]) ).
cnf(c_4057,plain,
( ~ precedes(X0,X1,sK13)
| on_path(X0,sK13) ),
inference(superposition,[status(thm)],[c_3751,c_86]) ).
cnf(c_4118,plain,
on_path(sK11,sK13),
inference(superposition,[status(thm)],[c_2743,c_4057]) ).
cnf(c_4172,plain,
( ~ shortest_path(X0,X1,sK13)
| ~ precedes(sK12,sK11,sK13) ),
inference(superposition,[status(thm)],[c_2743,c_92]) ).
cnf(c_4735,plain,
( ~ shortest_path(X0,X1,sK13)
| edge(sK8(sK11,sK12)) ),
inference(superposition,[status(thm)],[c_2743,c_148]) ).
cnf(c_4743,plain,
edge(sK8(sK11,sK12)),
inference(superposition,[status(thm)],[c_2742,c_4735]) ).
cnf(c_4867,plain,
( ~ sequential(X0,X1)
| ~ on_path(X0,sK13)
| ~ on_path(X1,sK13)
| precedes(X0,X1,sK13) ),
inference(superposition,[status(thm)],[c_3751,c_81]) ).
cnf(c_5131,plain,
( ~ shortest_path(X0,X1,sK13)
| ~ on_path(sK11,sK13)
| ~ on_path(sK12,sK13)
| ~ sequential(sK12,sK11) ),
inference(superposition,[status(thm)],[c_4867,c_4172]) ).
cnf(c_5136,plain,
( ~ shortest_path(X0,X1,sK13)
| ~ sequential(sK12,sK11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5131,c_3984,c_4118]) ).
cnf(c_5188,plain,
~ sequential(sK12,sK11),
inference(superposition,[status(thm)],[c_2742,c_5136]) ).
cnf(c_7628,plain,
( ~ shortest_path(X0,X1,sK13)
| tail_of(sK8(sK11,sK12)) = head_of(sK12) ),
inference(superposition,[status(thm)],[c_2743,c_156]) ).
cnf(c_7695,plain,
tail_of(sK8(sK11,sK12)) = head_of(sK12),
inference(superposition,[status(thm)],[c_2742,c_7628]) ).
cnf(c_7707,plain,
( head_of(sK8(sK11,sK12)) != head_of(sK12)
| ~ edge(sK8(sK11,sK12)) ),
inference(superposition,[status(thm)],[c_7695,c_49]) ).
cnf(c_7710,plain,
( head_of(X0) != head_of(sK12)
| ~ edge(sK8(sK11,sK12))
| ~ edge(X0)
| sK8(sK11,sK12) = X0
| sequential(X0,sK8(sK11,sK12)) ),
inference(superposition,[status(thm)],[c_7695,c_75]) ).
cnf(c_7713,plain,
head_of(sK8(sK11,sK12)) != head_of(sK12),
inference(forward_subsumption_resolution,[status(thm)],[c_7707,c_4743]) ).
cnf(c_7735,plain,
( head_of(X0) != head_of(sK12)
| ~ edge(X0)
| sK8(sK11,sK12) = X0
| sequential(X0,sK8(sK11,sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7710,c_4743]) ).
cnf(c_8450,plain,
( ~ edge(sK12)
| sK8(sK11,sK12) = sK12
| sequential(sK12,sK8(sK11,sK12)) ),
inference(equality_resolution,[status(thm)],[c_7735]) ).
cnf(c_8451,plain,
( sK8(sK11,sK12) = sK12
| sequential(sK12,sK8(sK11,sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8450,c_3733]) ).
cnf(c_8578,plain,
( ~ shortest_path(X0,X1,sK13)
| head_of(sK8(sK11,sK12)) = tail_of(sK11) ),
inference(superposition,[status(thm)],[c_2743,c_158]) ).
cnf(c_8622,plain,
head_of(sK8(sK11,sK12)) = tail_of(sK11),
inference(superposition,[status(thm)],[c_2742,c_8578]) ).
cnf(c_8628,plain,
head_of(sK12) != tail_of(sK11),
inference(demodulation,[status(thm)],[c_7713,c_8622]) ).
cnf(c_8646,plain,
( tail_of(X0) != tail_of(sK11)
| ~ edge(sK8(sK11,sK12))
| ~ edge(X0)
| sK8(sK11,sK12) = X0
| sequential(sK8(sK11,sK12),X0) ),
inference(superposition,[status(thm)],[c_8622,c_75]) ).
cnf(c_8679,plain,
( tail_of(X0) != tail_of(sK11)
| ~ edge(X0)
| sK8(sK11,sK12) = X0
| sequential(sK8(sK11,sK12),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8646,c_4743]) ).
cnf(c_9418,plain,
( ~ edge(sK11)
| sK8(sK11,sK12) = sK11
| sequential(sK8(sK11,sK12),sK11) ),
inference(equality_resolution,[status(thm)],[c_8679]) ).
cnf(c_9419,plain,
( sK8(sK11,sK12) = sK11
| sequential(sK8(sK11,sK12),sK11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9418,c_3738]) ).
cnf(c_9444,plain,
( ~ sequential(sK12,sK8(sK11,sK12))
| sK8(sK11,sK12) = sK11 ),
inference(superposition,[status(thm)],[c_9419,c_989]) ).
cnf(c_9482,plain,
( sK8(sK11,sK12) = sK11
| sK8(sK11,sK12) = sK12 ),
inference(superposition,[status(thm)],[c_8451,c_9444]) ).
cnf(c_9576,plain,
( sK8(sK11,sK12) = sK11
| sequential(sK12,sK11) ),
inference(superposition,[status(thm)],[c_9482,c_9419]) ).
cnf(c_9615,plain,
sK8(sK11,sK12) = sK11,
inference(forward_subsumption_resolution,[status(thm)],[c_9576,c_5188]) ).
cnf(c_9654,plain,
head_of(sK12) = tail_of(sK11),
inference(demodulation,[status(thm)],[c_7695,c_9615]) ).
cnf(c_9659,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9654,c_8628]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : GRA008+2 : TPTP v8.2.0. Bugfixed v3.2.0.
% 0.10/0.13 % Command : run_iprover %s %d THM
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Jun 18 15:17:54 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 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
% 7.08/1.61 % SZS status Started for theBenchmark.p
% 7.08/1.61 % SZS status Theorem for theBenchmark.p
% 7.08/1.61
% 7.08/1.61 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.08/1.61
% 7.08/1.61 ------ iProver source info
% 7.08/1.61
% 7.08/1.61 git: date: 2024-06-12 09:56:46 +0000
% 7.08/1.61 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 7.08/1.61 git: non_committed_changes: false
% 7.08/1.61
% 7.08/1.61 ------ Parsing...
% 7.08/1.61 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.08/1.61
% 7.08/1.61 ------ Preprocessing... sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 7.08/1.61
% 7.08/1.61 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.08/1.61
% 7.08/1.61 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.08/1.61 ------ Proving...
% 7.08/1.61 ------ Problem Properties
% 7.08/1.61
% 7.08/1.61
% 7.08/1.61 clauses 59
% 7.08/1.61 conjectures 3
% 7.08/1.61 EPR 19
% 7.08/1.61 Horn 41
% 7.08/1.61 unary 6
% 7.08/1.61 binary 15
% 7.08/1.61 lits 180
% 7.08/1.61 lits eq 46
% 7.08/1.61 fd_pure 0
% 7.08/1.61 fd_pseudo 0
% 7.08/1.61 fd_cond 0
% 7.08/1.61 fd_pseudo_cond 5
% 7.08/1.61 AC symbols 0
% 7.08/1.61
% 7.08/1.61 ------ Schedule dynamic 5 is on
% 7.08/1.61
% 7.08/1.61 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.08/1.61
% 7.08/1.61
% 7.08/1.61 ------
% 7.08/1.61 Current options:
% 7.08/1.61 ------
% 7.08/1.61
% 7.08/1.61
% 7.08/1.61
% 7.08/1.61
% 7.08/1.61 ------ Proving...
% 7.08/1.61
% 7.08/1.61
% 7.08/1.61 % SZS status Theorem for theBenchmark.p
% 7.08/1.61
% 7.08/1.61 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.08/1.61
% 7.08/1.62
%------------------------------------------------------------------------------