%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRA003+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n004.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 : Fri Sep 25 01:23:34 PM UTC 2026
% Result : Theorem 3.16s 16.54s
% Output : CNFRefutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 77 ( 19 unt; 0 def)
% Number of atoms : 358 ( 84 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 448 ( 167 ~; 153 |; 114 &)
% ( 2 <=>; 8 =>; 0 <=; 4 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 225 ( 0 sgn 196 !; 29 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1,X2] :
( path(X0,X1,X2)
=> ( ? [X3] :
( ( ( X2 = path_cons(X3,empty)
& X1 = head_of(X3) )
<~> ? [X4] :
( X2 = path_cons(X3,X4)
& path(head_of(X3),X1,X4) ) )
& X0 = tail_of(X3)
& edge(X3) )
& vertex(X1)
& vertex(X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',path_properties) ).
fof(f6,axiom,
! [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) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',on_path_properties) ).
fof(f10,axiom,
! [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) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',precedes_properties) ).
fof(f11,axiom,
! [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) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',shortest_path_defn) ).
fof(f12,axiom,
! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( ~ precedes(X3,X2,X4)
& ~ ? [X5] :
( head_of(X5) = head_of(X3)
& tail_of(X5) = tail_of(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',shortest_path_properties) ).
fof(f18,conjecture,
! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( path(X0,X1,X4)
& X2 != X3
& edge(X3)
& edge(X2)
& X0 != X1
& vertex(X1)
& vertex(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vertices_and_edges) ).
fof(f19,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( path(X0,X1,X4)
& X2 != X3
& edge(X3)
& edge(X2)
& X0 != X1
& vertex(X1)
& vertex(X0) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ~ path(X0,X1,X2)
| ( ? [X3] :
( ( ( X2 = path_cons(X3,empty)
& X1 = head_of(X3) )
<~> ? [X4] :
( X2 = path_cons(X3,X4)
& path(head_of(X3),X1,X4) ) )
& X0 = tail_of(X3)
& edge(X3) )
& vertex(X1)
& vertex(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f27,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(ennf_transformation,[],[f6]) ).
fof(f28,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(flattening,[],[f27]) ).
fof(f33,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(ennf_transformation,[],[f10]) ).
fof(f34,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(ennf_transformation,[],[f11]) ).
fof(f35,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(ennf_transformation,[],[f12]) ).
fof(f36,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(flattening,[],[f35]) ).
fof(f43,plain,
? [X0,X1,X2,X3,X4] :
( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4)
& ( ~ path(X0,X1,X4)
| X2 = X3
| ~ edge(X3)
| ~ edge(X2)
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f44,plain,
? [X0,X1,X2,X3,X4] :
( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4)
& ( ~ path(X0,X1,X4)
| X2 = X3
| ~ edge(X3)
| ~ edge(X2)
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) ) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ~ path(X0,X1,X2)
| ( ? [X3] :
( ( ( X2 = path_cons(X3,empty)
& X1 = head_of(X3) )
| ? [X4] :
( X2 = path_cons(X3,X4)
& path(head_of(X3),X1,X4) ) )
& ( path_cons(X3,empty) != X2
| head_of(X3) != X1
| ! [X4] :
( path_cons(X3,X4) != X2
| ~ path(head_of(X3),X1,X4) ) )
& X0 = tail_of(X3)
& edge(X3) )
& vertex(X1)
& vertex(X0) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ~ path(X0,X1,X2)
| ( ? [X3] :
( ( ( X2 = path_cons(X3,empty)
& X1 = head_of(X3) )
| ? [X4] :
( X2 = path_cons(X3,X4)
& path(head_of(X3),X1,X4) ) )
& ( path_cons(X3,empty) != X2
| head_of(X3) != X1
| ! [X4] :
( path_cons(X3,X4) != X2
| ~ path(head_of(X3),X1,X4) ) )
& X0 = tail_of(X3)
& edge(X3) )
& vertex(X1)
& vertex(X0) ) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ~ path(X0,X1,X2)
| ( ? [X3] :
( ( ( X2 = path_cons(X3,empty)
& X1 = head_of(X3) )
| ? [X5] :
( path_cons(X3,X5) = X2
& path(head_of(X3),X1,X5) ) )
& ( path_cons(X3,empty) != X2
| head_of(X3) != X1
| ! [X4] :
( path_cons(X3,X4) != X2
| ~ path(head_of(X3),X1,X4) ) )
& X0 = tail_of(X3)
& edge(X3) )
& vertex(X1)
& vertex(X0) ) ),
inference(rectify,[],[f46]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ~ path(X0,X1,X2)
| ( ( ( path_cons(sK0(X0,X1,X2),empty) = X2
& head_of(sK0(X0,X1,X2)) = X1 )
| ( path_cons(sK0(X0,X1,X2),sK1(X0,X1,X2)) = X2
& path(head_of(sK0(X0,X1,X2)),X1,sK1(X0,X1,X2)) ) )
& ( path_cons(sK0(X0,X1,X2),empty) != X2
| head_of(sK0(X0,X1,X2)) != X1
| ! [X4] :
( path_cons(sK0(X0,X1,X2),X4) != X2
| ~ path(head_of(sK0(X0,X1,X2)),X1,X4) ) )
& tail_of(sK0(X0,X1,X2)) = X0
& edge(sK0(X0,X1,X2))
& vertex(X1)
& vertex(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X5,sK1(X0,X1,X2))],[f47]) ).
fof(f52,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) ) )
& ( ~ sequential(X3,X4)
| ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f53,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) ) )
& ( ~ sequential(X3,X4)
| ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ~ precedes(X3,X4,X0)
| ( ( sequential(X3,X4)
| ? [X6] :
( precedes(X6,X4,X0)
& sequential(X3,X6) ) )
& ( ~ sequential(X3,X4)
| ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
inference(rectify,[],[f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ~ precedes(X3,X4,X0)
| ( ( sequential(X3,X4)
| ( precedes(sK3(X0,X3,X4),X4,X0)
& sequential(X3,sK3(X0,X3,X4)) ) )
& ( ~ sequential(X3,X4)
| ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X6,sK3(X0,X3,X4))],[f54]) ).
fof(f56,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) ) )
& ( ? [X3] :
( path(X0,X1,X3)
& ~ less_or_equal(length_of(X2),length_of(X3)) )
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f57,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) ) )
& ( ? [X3] :
( path(X0,X1,X3)
& ~ less_or_equal(length_of(X2),length_of(X3)) )
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ( ~ shortest_path(X0,X1,X2)
| ( ! [X4] :
( ~ path(X0,X1,X4)
| less_or_equal(length_of(X2),length_of(X4)) )
& X0 != X1
& path(X0,X1,X2) ) )
& ( ? [X3] :
( path(X0,X1,X3)
& ~ less_or_equal(length_of(X2),length_of(X3)) )
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ) ),
inference(rectify,[],[f57]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ( ~ shortest_path(X0,X1,X2)
| ( ! [X4] :
( ~ path(X0,X1,X4)
| less_or_equal(length_of(X2),length_of(X4)) )
& X0 != X1
& path(X0,X1,X2) ) )
& ( ( path(X0,X1,sK4(X0,X1,X2))
& ~ less_or_equal(length_of(X2),length_of(sK4(X0,X1,X2))) )
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f58]) ).
fof(f61,plain,
( precedes(sK9,sK10,sK11)
& shortest_path(sK7,sK8,sK11)
& ( ~ path(sK7,sK8,sK11)
| sK9 = sK10
| ~ edge(sK10)
| ~ edge(sK9)
| sK7 = sK8
| ~ vertex(sK8)
| ~ vertex(sK7) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9),skolemize(X3,sK10),skolemize(X4,sK11)],[f44]) ).
fof(f74,plain,
! [X2,X0,X1] :
( ~ path(X0,X1,X2)
| vertex(X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f75,plain,
! [X2,X0,X1] :
( ~ path(X0,X1,X2)
| vertex(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f78,plain,
! [X2,X3,X0,X1] :
( ~ on_path(X3,X2)
| ~ path(X0,X1,X2)
| edge(X3) ),
inference(cnf_transformation,[],[f28]) ).
fof(f92,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ precedes(X3,X4,X0)
| on_path(X4,X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f93,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ precedes(X3,X4,X0)
| on_path(X3,X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f95,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| X0 != X1 ),
inference(cnf_transformation,[],[f59]) ).
fof(f96,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f59]) ).
fof(f99,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X3,X2,X4) ),
inference(cnf_transformation,[],[f36]) ).
fof(f109,plain,
precedes(sK9,sK10,sK11),
inference(cnf_transformation,[],[f61]) ).
fof(f110,plain,
shortest_path(sK7,sK8,sK11),
inference(cnf_transformation,[],[f61]) ).
fof(f111,plain,
( ~ path(sK7,sK8,sK11)
| sK9 = sK10
| ~ edge(sK10)
| ~ edge(sK9)
| sK7 = sK8
| ~ vertex(sK8)
| ~ vertex(sK7) ),
inference(cnf_transformation,[],[f61]) ).
fof(f118,plain,
! [X2,X1] : ~ shortest_path(X1,X1,X2),
inference(equality_resolution,[],[f95]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( vertex(X0)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( vertex(X1)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( edge(X3)
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( on_path(X3,X2)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( on_path(X4,X2)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] : ~ shortest_path(X0,X0,X1),
inference(cnf_transformation,[],[f118]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ shortest_path(X3,X4,X2)
| ~ precedes(X1,X0,X2)
| ~ precedes(X0,X1,X2) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_96,negated_conjecture,
( ( sK9 = sK10 )
| ( sK7 = sK8 )
| ~ vertex(sK8)
| ~ vertex(sK7)
| ~ edge(sK10)
| ~ edge(sK9)
| ~ path(sK7,sK8,sK11) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_97,negated_conjecture,
shortest_path(sK7,sK8,sK11),
inference(cnf_transformation,[],[f110]) ).
tcf(c_98,negated_conjecture,
precedes(sK9,sK10,sK11),
inference(cnf_transformation,[],[f109]) ).
tcf(c_172,plain,
( ( sK9 = sK10 )
| ( sK7 = sK8 )
| ~ vertex(sK8)
| ~ edge(sK10)
| ~ edge(sK9)
| ~ path(sK7,sK8,sK11) ),
inference(backward_subsumption_resolution,[status(thm)],[c_96,c_54]) ).
tcf(c_177,plain,
( ( sK9 = sK10 )
| ( sK7 = sK8 )
| ~ edge(sK10)
| ~ edge(sK9)
| ~ path(sK7,sK8,sK11) ),
inference(backward_subsumption_resolution,[status(thm)],[c_172,c_55]) ).
tcf(c_1013,plain,
! [X0: $i,X1: $i,X2: $i] :
( path(X0,X1,X2)
| ( X2 != sK11 )
| ( X1 != sK8 )
| ( X0 != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_83,c_97]) ).
tcf(c_1014,plain,
path(sK7,sK8,sK11),
inference(unflattening,[status(thm)],[c_1013]) ).
tcf(c_1018,plain,
! [X0: $i,X1: $i] :
( ( X1 != sK11 )
| ( X0 != sK8 )
| ( X0 != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_84,c_97]) ).
tcf(c_1019,plain,
sK7 != sK8,
inference(unflattening,[status(thm)],[c_1018]) ).
tcf(c_1086,plain,
( ( sK9 = sK10 )
| ( sK7 = sK8 )
| ~ edge(sK10)
| ~ edge(sK9) ),
inference(backward_subsumption_resolution,[status(thm)],[c_177,c_1014]) ).
tcf(c_1088,plain,
( ( sK9 = sK10 )
| ~ edge(sK10)
| ~ edge(sK9) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1086,c_1019]) ).
tcf(c_1941,plain,
( ( sK9 = sK10 )
| ~ edge(sK10)
| ~ edge(sK9) ),
inference(demodulation,[status(thm)],[c_1088]) ).
tcf(c_1942,negated_conjecture,
precedes(sK9,sK10,sK11),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_1943,negated_conjecture,
shortest_path(sK7,sK8,sK11),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_2710,plain,
path(sK7,sK8,sK11),
inference(superposition,[status(thm)],[c_1943,c_83]) ).
tcf(c_2730,plain,
! [X0: $i] :
( edge(X0)
| ~ on_path(X0,sK11) ),
inference(superposition,[status(thm)],[c_2710,c_63]) ).
tcf(c_2846,plain,
! [X0: $i,X1: $i] :
( on_path(X0,sK11)
| ~ precedes(X0,X1,sK11) ),
inference(superposition,[status(thm)],[c_2710,c_76]) ).
tcf(c_2865,plain,
! [X0: $i,X1: $i] :
( on_path(X1,sK11)
| ~ precedes(X0,X1,sK11) ),
inference(superposition,[status(thm)],[c_2710,c_77]) ).
tcf(c_2890,plain,
on_path(sK9,sK11),
inference(superposition,[status(thm)],[c_1942,c_2846]) ).
tcf(c_2891,plain,
edge(sK9),
inference(superposition,[status(thm)],[c_2890,c_2730]) ).
tcf(c_2892,plain,
( ( sK9 = sK10 )
| ~ edge(sK10) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1941,c_2891]) ).
tcf(c_2900,plain,
on_path(sK10,sK11),
inference(superposition,[status(thm)],[c_1942,c_2865]) ).
tcf(c_2901,plain,
edge(sK10),
inference(superposition,[status(thm)],[c_2900,c_2730]) ).
tcf(c_2903,plain,
sK9 = sK10,
inference(global_subsumption_just,[status(thm)],[c_2892,c_1019,c_1086,c_2891,c_2901]) ).
tcf(c_2907,plain,
precedes(sK9,sK9,sK11),
inference(demodulation,[status(thm)],[c_1942,c_2903]) ).
tcf(c_2974,plain,
! [X0: $i,X1: $i] :
( ~ precedes(sK9,sK9,sK11)
| ~ shortest_path(X0,X1,sK11) ),
inference(superposition,[status(thm)],[c_2907,c_87]) ).
tcf(c_2975,plain,
! [X0: $i,X1: $i] : ~ shortest_path(X0,X1,sK11),
inference(forward_subsumption_resolution,[status(thm)],[c_2974,c_2907]) ).
tcf(c_2976,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_1943,c_2975]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA003+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/15.61 % Computer : n004.cluster.edu
% 0.11/15.61 % Model : x86_64 x86_64
% 0.11/15.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.61 % Memory : 8046.5625MB
% 0.11/15.61 % OS : Linux 6.8.0-71-generic
% 0.11/15.61 % CPULimit : 300
% 0.11/15.61 % WCLimit : 300
% 0.11/15.61 % DateTime : Wed Sep 23 12:42:52 UTC 2026
% 0.11/15.61 % CPUTime :
% 0.11/15.61 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/15.65 Running first-order theorem proving
% 0.11/15.65 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/15.67
% 0.11/15.67 % ======== iProver multi-core TPTP/SMT =========
% 0.11/15.67
% 0.11/15.67 % Detected problem language: tptp
% 0.11/15.68 % Proving...
% 3.16/16.54 % SZS status Started for theBenchmark.p
% 3.16/16.54 % SZS status Theorem for theBenchmark.p
% 3.16/16.54
% 3.16/16.54 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.16/16.54
% 3.16/16.54 % ------ iProver source info
% 3.16/16.54
% 3.16/16.54 % git: date: 2026-07-19 20:42:38 +0200
% 3.16/16.54 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.16/16.54 % git: non_committed_changes: false
% 3.16/16.54
% 3.16/16.54 % ------ Parsing...
% 3.16/16.54 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.16/16.54
% 3.16/16.54 % ------ 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 %
% 3.16/16.54
% 3.16/16.54 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.16/16.54
% 3.16/16.54 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.16/16.54 % ------ Proving...
% 3.16/16.54 % ------ Problem Properties
% 3.16/16.54
% 3.16/16.54 %
% 3.16/16.54 % clauses 44
% 3.16/16.54 % conjectures 2
% 3.16/16.54 % EPR 15
% 3.16/16.54 % Horn 31
% 3.16/16.54 % unary 5
% 3.16/16.54 % binary 10
% 3.16/16.54 % lits 129
% 3.16/16.54 % lits eq 27
% 3.16/16.54 % fd_pure 0
% 3.16/16.54 % fd_pseudo 0
% 3.16/16.54 % fd_cond 0
% 3.16/16.54 % fd_pseudo_cond 3
% 3.16/16.54 % AC symbols 0
% 3.16/16.54
% 3.16/16.54 % ------ Schedule dynamic 5 is on
% 3.16/16.54
% 3.16/16.54 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.16/16.54
% 3.16/16.54
% 3.16/16.54 % ------
% 3.16/16.54 % Current options:
% 3.16/16.54 % ------
% 3.16/16.54
% 3.16/16.54
% 3.16/16.54 %
% 3.16/16.54
% 3.16/16.54 % ------ Proving...
% 3.16/16.54 %
% 3.16/16.54
% 3.16/16.54 % SZS status Theorem for theBenchmark.p
% 3.16/16.54
% 3.16/16.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.16/16.54
% 3.16/16.54
%------------------------------------------------------------------------------