%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRA002+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n008.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 01:23:33 PM UTC 2026
% Result : Theorem 10.43s 2.26s
% Output : CNFRefutation 10.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 11
% Syntax : Number of formulae : 139 ( 16 unt; 0 def)
% Number of atoms : 516 ( 153 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 640 ( 263 ~; 282 |; 76 &)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 2 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-3 aty)
% Number of variables : 343 ( 0 sgn 327 !; 16 ?; 139 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( edge(X0)
=> head_of(X0) != tail_of(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',no_loops) ).
fof(f8,axiom,
! [X0,X1] :
( sequential(X0,X1)
<=> ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',sequential_defn) ).
fof(f9,axiom,
! [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) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',precedes_defn) ).
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/sandbox2/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/sandbox2/benchmark/Axioms/GRA001+0.ax',shortest_path_properties) ).
fof(f13,axiom,
! [X0,X1,X2] :
( triangle(X0,X1,X2)
<=> ( sequential(X2,X0)
& sequential(X1,X2)
& sequential(X0,X1)
& edge(X2)
& edge(X1)
& edge(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',triangle_defn) ).
fof(f15,axiom,
! [X0,X1,X2] :
( path(X0,X1,X2)
=> number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_length_sequential_pairs) ).
fof(f16,axiom,
! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
=> ? [X5] : triangle(X3,X4,X5) )
& path(X1,X2,X0) )
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
fof(f17,axiom,
! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',graph_has_them_all) ).
fof(f18,axiom,
( complete
=> ! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ? [X5] :
( head_of(X5) = tail_of(X2)
& tail_of(X5) = head_of(X3)
& edge(X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',back_edge) ).
fof(f19,conjecture,
( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maximal_path_length) ).
fof(f20,negated_conjecture,
~ ( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,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,[],[f13]) ).
fof(f22,plain,
( ~ complete
| ! [X0,X1,X2,X3,X4] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ? [X5] :
( head_of(X5) = tail_of(X2)
& tail_of(X5) = head_of(X3)
& edge(X5) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f23,plain,
( ~ complete
| ! [X0,X1,X2,X3,X4] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ? [X5] :
( head_of(X5) = tail_of(X2)
& tail_of(X5) = head_of(X3)
& edge(X5) ) ) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
( complete
& ? [X0,X1,X2] :
( shortest_path(X1,X2,X0)
& ~ less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f25,plain,
! [X0] :
( ~ edge(X0)
| head_of(X0) != tail_of(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f28,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(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(flattening,[],[f28]) ).
fof(f31,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(ennf_transformation,[],[f9]) ).
fof(f32,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(flattening,[],[f31]) ).
fof(f33,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(f34,plain,
! [X0,X1,X2] :
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0)
& ! [X5] : ~ triangle(X3,X4,X5) )
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0)
& ! [X5] : ~ triangle(X3,X4,X5) )
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(flattening,[],[f35]) ).
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(ennf_transformation,[],[f21]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1)
| ~ edge(X2)
| ~ edge(X1)
| ~ edge(X0)
| triangle(X0,X1,X2) ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
( ~ complete
| ! [X0,X1,X2,X3,X4] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ( tail_of(X2) = head_of(sK0(X2,X3))
& head_of(X3) = tail_of(sK0(X2,X3))
& edge(sK0(X2,X3)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X5,sK0(X2,X3))],[f23]) ).
fof(f41,plain,
( complete
& shortest_path(sK2,sK3,sK1)
& ~ less_or_equal(minus(length_of(sK1),n1),number_of_in(triangles,graph)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f24]) ).
fof(f49,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,[],[f33]) ).
fof(f50,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,[],[f49]) ).
fof(f51,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,[],[f50]) ).
fof(f52,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,sK6(X0,X1,X2))
& ~ less_or_equal(length_of(X2),length_of(sK6(X0,X1,X2))) )
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X3,sK6(X0,X1,X2))],[f51]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ( sequential(sK7(X0),sK8(X0))
& on_path(sK8(X0),X0)
& on_path(sK7(X0),X0)
& ! [X5] : ~ triangle(sK7(X0),sK8(X0),X5) )
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X3,sK7(X0)),skolemize(X4,sK8(X0))],[f36]) ).
fof(f54,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,[],[f8]) ).
fof(f55,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,[],[f54]) ).
fof(f56,plain,
! [X2,X3,X0,X1,X4] :
( ~ complete
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| tail_of(X2) = head_of(sK0(X2,X3)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f57,plain,
! [X2,X3,X0,X1,X4] :
( ~ complete
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| head_of(X3) = tail_of(sK0(X2,X3)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f58,plain,
! [X2,X3,X0,X1,X4] :
( ~ complete
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| edge(sK0(X2,X3)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f59,plain,
complete,
inference(cnf_transformation,[],[f41]) ).
fof(f60,plain,
shortest_path(sK2,sK3,sK1),
inference(cnf_transformation,[],[f41]) ).
fof(f61,plain,
~ less_or_equal(minus(length_of(sK1),n1),number_of_in(triangles,graph)),
inference(cnf_transformation,[],[f41]) ).
fof(f62,plain,
! [X0] :
( ~ edge(X0)
| head_of(X0) != tail_of(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f70,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5) ),
inference(cnf_transformation,[],[f29]) ).
fof(f77,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ sequential(X3,X4)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| precedes(X3,X4,X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f80,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f83,plain,
! [X2,X0,X1] :
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f84,plain,
! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
inference(cnf_transformation,[],[f17]) ).
fof(f85,plain,
! [X2,X0,X1] :
( sequential(sK7(X0),sK8(X0))
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f86,plain,
! [X2,X0,X1] :
( on_path(sK8(X0),X0)
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f87,plain,
! [X2,X0,X1] :
( on_path(sK7(X0),X0)
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f88,plain,
! [X2,X0,X1,X5] :
( ~ triangle(sK7(X0),sK8(X0),X5)
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f91,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| head_of(X0) = tail_of(X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f93,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f94,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f95,plain,
! [X0,X1] :
( head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0)
| sequential(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f96,plain,
! [X2,X0,X1] :
( ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1)
| ~ edge(X2)
| ~ edge(X1)
| ~ edge(X0)
| triangle(X0,X1,X2) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( edge(sK0(X3,X4))
| ~ complete
| ~ precedes(X3,X4,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( tail_of(sK0(X3,X4)) = head_of(X4) )
| ~ complete
| ~ precedes(X3,X4,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK0(X3,X4)) = tail_of(X3) )
| ~ complete
| ~ precedes(X3,X4,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_52,negated_conjecture,
~ less_or_equal(minus(length_of(sK1),n1),number_of_in(triangles,graph)),
inference(cnf_transformation,[],[f61]) ).
tcf(c_53,negated_conjecture,
shortest_path(sK2,sK3,sK1),
inference(cnf_transformation,[],[f60]) ).
tcf(c_54,negated_conjecture,
complete,
inference(cnf_transformation,[],[f59]) ).
tcf(c_55,plain,
! [X0: $i] :
( ~ edge(X0)
| ( head_of(X0) != tail_of(X0) ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ precedes(X2,X0,X5)
| ~ shortest_path(X3,X4,X5)
| ( tail_of(X1) != tail_of(X2) )
| ( head_of(X0) != head_of(X1) ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( precedes(X3,X4,X2)
| ~ sequential(X3,X4)
| ~ on_path(X4,X2)
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( minus(length_of(X2),n1) = number_of_in(sequential_pairs,X2) )
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
inference(cnf_transformation,[],[f84]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0) )
| ~ path(X2,X3,X0)
| ~ triangle(sK7(X0),sK8(X0),X1) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( on_path(sK7(X2),X2)
| ( number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2) )
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( on_path(sK8(X2),X2)
| ( number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2) )
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(sK7(X2),sK8(X2))
| ( number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2) )
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( X0 = X1 )
| ~ edge(X1)
| ~ edge(X0)
| ( head_of(X0) != tail_of(X1) ) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( edge(X0)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = tail_of(X1) )
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( triangle(X1,X2,X0)
| ~ edge(X2)
| ~ edge(X1)
| ~ edge(X0)
| ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( edge(sK0(X3,X4))
| ~ shortest_path(X0,X1,X2)
| ~ precedes(X3,X4,X2) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_54,c_49]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( edge(sK0(X3,X4))
| ~ precedes(X3,X4,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_113]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK0(X3,X4)) = tail_of(X3) )
| ~ shortest_path(X0,X1,X2)
| ~ precedes(X3,X4,X2) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_54,c_51]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK0(X3,X4)) = tail_of(X3) )
| ~ precedes(X3,X4,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_115]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( tail_of(sK0(X3,X4)) = head_of(X4) )
| ~ shortest_path(X0,X1,X2)
| ~ precedes(X3,X4,X2) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_54,c_50]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( tail_of(sK0(X3,X4)) = head_of(X4) )
| ~ precedes(X3,X4,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_117]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i,X2: $i] :
( triangle(X1,X2,X0)
| ~ edge(X2)
| ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_89,c_86,c_85,c_89]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i,X2: $i] :
( triangle(X1,X2,X0)
| ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_119,c_85]) ).
tcf(c_660,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0) )
| ~ sequential(X4,X1)
| ~ sequential(X2,X4)
| ~ sequential(X1,X2)
| ~ path(X5,X6,X0)
| ( X3 != X4 )
| ( sK8(X0) != X2 )
| ( sK7(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_78,c_160]) ).
tcf(c_661,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0) )
| ~ sequential(X3,sK7(X0))
| ~ sequential(sK8(X0),X3)
| ~ path(X1,X2,X0)
| ~ sequential(sK7(X0),sK8(X0)) ),
inference(unflattening,[status(thm)],[c_660]) ).
tcf(c_673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2) )
| ~ sequential(X3,sK7(X2))
| ~ sequential(sK8(X2),X3)
| ~ path(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_661,c_81]) ).
tcf(c_2799,plain,
path(sK2,sK3,sK1),
inference(superposition,[status(thm)],[c_53,c_73]) ).
tcf(c_2820,plain,
minus(length_of(sK1),n1) = number_of_in(sequential_pairs,sK1),
inference(superposition,[status(thm)],[c_2799,c_76]) ).
tcf(c_2821,plain,
~ less_or_equal(number_of_in(sequential_pairs,sK1),number_of_in(triangles,graph)),
inference(demodulation,[status(thm)],[c_52,c_2820]) ).
tcf(c_2836,plain,
! [X0: $i,X1: $i] :
( edge(sK0(X0,X1))
| ~ precedes(X0,X1,sK1) ),
inference(superposition,[status(thm)],[c_53,c_114]) ).
tcf(c_2877,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ precedes(X1,X0,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(X0) != tail_of(X1) ) ),
inference(equality_resolution,[status(thm)],[c_62]) ).
tcf(c_2887,plain,
( on_path(sK7(sK1),sK1)
| ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) ) ),
inference(superposition,[status(thm)],[c_2799,c_79]) ).
tcf(c_2896,plain,
( on_path(sK8(sK1),sK1)
| ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) ) ),
inference(superposition,[status(thm)],[c_2799,c_80]) ).
tcf(c_2905,plain,
( sequential(sK7(sK1),sK8(sK1))
| ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) ) ),
inference(superposition,[status(thm)],[c_2799,c_81]) ).
tcf(c_2932,plain,
( ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ( head_of(sK7(sK1)) = tail_of(sK8(sK1)) ) ),
inference(superposition,[status(thm)],[c_2905,c_88]) ).
tcf(c_2933,plain,
( edge(sK8(sK1))
| ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) ) ),
inference(superposition,[status(thm)],[c_2905,c_86]) ).
tcf(c_2934,plain,
( edge(sK7(sK1))
| ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) ) ),
inference(superposition,[status(thm)],[c_2905,c_85]) ).
tcf(c_2984,plain,
( ( head_of(sK7(sK1)) = tail_of(sK8(sK1)) )
| ~ less_or_equal(number_of_in(triangles,sK1),number_of_in(triangles,graph)) ),
inference(superposition,[status(thm)],[c_2932,c_2821]) ).
tcf(c_2987,plain,
head_of(sK7(sK1)) = tail_of(sK8(sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_2984,c_77]) ).
tcf(c_2988,plain,
( ~ edge(sK8(sK1))
| ( head_of(sK7(sK1)) != head_of(sK8(sK1)) ) ),
inference(superposition,[status(thm)],[c_2987,c_55]) ).
tcf(c_3093,plain,
! [X0: $i,X1: $i] :
( precedes(X0,X1,sK1)
| ~ on_path(X1,sK1)
| ~ on_path(X0,sK1)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2799,c_69]) ).
tcf(c_3154,plain,
! [X0: $i,X1: $i] :
( edge(sK0(X0,X1))
| ~ on_path(X1,sK1)
| ~ on_path(X0,sK1)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_3093,c_2836]) ).
tcf(c_3255,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK0(X0,X1)) = tail_of(X0) )
| ~ precedes(X0,X1,sK1) ),
inference(superposition,[status(thm)],[c_53,c_116]) ).
tcf(c_3299,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK0(X0,X1)) = tail_of(X0) )
| ~ on_path(X1,sK1)
| ~ on_path(X0,sK1)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_3093,c_3255]) ).
tcf(c_3315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ shortest_path(X2,X3,X1)
| ~ precedes(sK8(sK1),X0,X1)
| ( head_of(sK7(sK1)) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_2987,c_2877]) ).
tcf(c_3337,plain,
! [X0: $i,X1: $i] :
( ( tail_of(sK0(X0,X1)) = head_of(X1) )
| ~ precedes(X0,X1,sK1) ),
inference(superposition,[status(thm)],[c_53,c_118]) ).
tcf(c_3344,plain,
! [X0: $i,X1: $i] :
( ( tail_of(sK0(X0,X1)) = head_of(X1) )
| ~ on_path(X1,sK1)
| ~ on_path(X0,sK1)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_3093,c_3337]) ).
tcf(c_3376,plain,
( ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ( head_of(sK0(sK7(sK1),sK8(sK1))) = tail_of(sK7(sK1)) )
| ~ on_path(sK8(sK1),sK1)
| ~ on_path(sK7(sK1),sK1) ),
inference(superposition,[status(thm)],[c_2905,c_3299]) ).
tcf(c_3397,plain,
( ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ( tail_of(sK0(sK7(sK1),sK8(sK1))) = head_of(sK8(sK1)) )
| ~ on_path(sK8(sK1),sK1)
| ~ on_path(sK7(sK1),sK1) ),
inference(superposition,[status(thm)],[c_2905,c_3344]) ).
tcf(c_3586,plain,
! [X0: $i] :
( ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ~ sequential(X0,sK7(sK1))
| ~ sequential(sK8(sK1),X0) ),
inference(superposition,[status(thm)],[c_2799,c_673]) ).
tcf(c_3836,plain,
( ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ( head_of(sK0(sK7(sK1),sK8(sK1))) = tail_of(sK7(sK1)) ) ),
inference(global_subsumption_just,[status(thm)],[c_3376,c_2887,c_2896,c_3376]) ).
tcf(c_3843,plain,
! [X0: $i] :
( sequential(sK0(sK7(sK1),sK8(sK1)),X0)
| ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ( sK0(sK7(sK1),sK8(sK1)) = X0 )
| ~ edge(X0)
| ~ edge(sK0(sK7(sK1),sK8(sK1)))
| ( tail_of(sK7(sK1)) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_3836,c_84]) ).
tcf(c_3894,plain,
( ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ( tail_of(sK0(sK7(sK1),sK8(sK1))) = head_of(sK8(sK1)) ) ),
inference(global_subsumption_just,[status(thm)],[c_3397,c_2887,c_2896,c_3397]) ).
tcf(c_3900,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK8(sK1),sK0(sK7(sK1),sK8(sK1)),X0)
| ( head_of(sK7(sK1)) != head_of(sK8(sK1)) ) ),
inference(superposition,[status(thm)],[c_3894,c_3315]) ).
tcf(c_3903,plain,
( ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ~ edge(sK0(sK7(sK1),sK8(sK1)))
| ( head_of(sK0(sK7(sK1),sK8(sK1))) != head_of(sK8(sK1)) ) ),
inference(superposition,[status(thm)],[c_3894,c_55]) ).
tcf(c_3906,plain,
! [X0: $i] :
( sequential(X0,sK0(sK7(sK1),sK8(sK1)))
| ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ( sK0(sK7(sK1),sK8(sK1)) = X0 )
| ~ edge(X0)
| ~ edge(sK0(sK7(sK1),sK8(sK1)))
| ( head_of(sK8(sK1)) != head_of(X0) ) ),
inference(superposition,[status(thm)],[c_3894,c_84]) ).
tcf(c_7104,plain,
( ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ( head_of(sK7(sK1)) != head_of(sK8(sK1)) ) ),
inference(global_subsumption_just,[status(thm)],[c_3900,c_2933,c_2988]) ).
tcf(c_10534,plain,
( sequential(sK0(sK7(sK1),sK8(sK1)),sK7(sK1))
| ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ( sK0(sK7(sK1),sK8(sK1)) = sK7(sK1) )
| ~ edge(sK7(sK1))
| ~ edge(sK0(sK7(sK1),sK8(sK1))) ),
inference(equality_resolution,[status(thm)],[c_3843]) ).
tcf(c_12270,plain,
( ~ edge(sK7(sK1))
| ( head_of(sK7(sK1)) != tail_of(sK7(sK1)) ) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_13874,plain,
( sequential(sK0(sK7(sK1),sK8(sK1)),sK7(sK1))
| ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ( sK0(sK7(sK1),sK8(sK1)) = sK7(sK1) )
| ~ edge(sK0(sK7(sK1),sK8(sK1))) ),
inference(global_subsumption_just,[status(thm)],[c_10534,c_2934,c_10534]) ).
tcf(c_16155,plain,
( sequential(sK8(sK1),sK0(sK7(sK1),sK8(sK1)))
| ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ( sK0(sK7(sK1),sK8(sK1)) = sK8(sK1) )
| ~ edge(sK8(sK1))
| ~ edge(sK0(sK7(sK1),sK8(sK1))) ),
inference(equality_resolution,[status(thm)],[c_3906]) ).
tcf(c_16414,plain,
( sequential(sK8(sK1),sK0(sK7(sK1),sK8(sK1)))
| ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ( sK0(sK7(sK1),sK8(sK1)) = sK8(sK1) )
| ~ edge(sK0(sK7(sK1),sK8(sK1))) ),
inference(global_subsumption_just,[status(thm)],[c_16155,c_2933,c_16155]) ).
tcf(c_16438,plain,
( ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ( sK0(sK7(sK1),sK8(sK1)) = sK8(sK1) )
| ~ edge(sK0(sK7(sK1),sK8(sK1)))
| ~ sequential(sK0(sK7(sK1),sK8(sK1)),sK7(sK1)) ),
inference(superposition,[status(thm)],[c_16414,c_3586]) ).
tcf(c_16682,plain,
( ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ( sK0(sK7(sK1),sK8(sK1)) = sK8(sK1) )
| ~ sequential(sK0(sK7(sK1),sK8(sK1)),sK7(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16438,c_85]) ).
tcf(c_16692,plain,
( ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ( sK0(sK7(sK1),sK8(sK1)) = sK8(sK1) )
| ( sK0(sK7(sK1),sK8(sK1)) = sK7(sK1) )
| ~ edge(sK0(sK7(sK1),sK8(sK1))) ),
inference(superposition,[status(thm)],[c_13874,c_16682]) ).
tcf(c_16705,plain,
( ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ( sK0(sK7(sK1),sK8(sK1)) = sK8(sK1) )
| ( sK0(sK7(sK1),sK8(sK1)) = sK7(sK1) )
| ~ on_path(sK8(sK1),sK1)
| ~ on_path(sK7(sK1),sK1)
| ~ sequential(sK7(sK1),sK8(sK1)) ),
inference(superposition,[status(thm)],[c_3154,c_16692]) ).
tcf(c_16716,plain,
( ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ( sK0(sK7(sK1),sK8(sK1)) = sK8(sK1) )
| ( sK0(sK7(sK1),sK8(sK1)) = sK7(sK1) ) ),
inference(global_subsumption_just,[status(thm)],[c_16705,c_2887,c_2896,c_2905,c_16705]) ).
tcf(c_16730,plain,
( ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ( sK0(sK7(sK1),sK8(sK1)) = sK7(sK1) )
| ~ edge(sK0(sK7(sK1),sK8(sK1))) ),
inference(superposition,[status(thm)],[c_16716,c_3903]) ).
tcf(c_16731,plain,
( ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ( head_of(sK8(sK1)) = tail_of(sK8(sK1)) )
| ( sK0(sK7(sK1),sK8(sK1)) = sK7(sK1) ) ),
inference(superposition,[status(thm)],[c_16716,c_3894]) ).
tcf(c_16741,plain,
( ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ( head_of(sK7(sK1)) = head_of(sK8(sK1)) )
| ( sK0(sK7(sK1),sK8(sK1)) = sK7(sK1) ) ),
inference(light_normalisation,[status(thm)],[c_16731,c_2987]) ).
tcf(c_18246,plain,
( ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ( sK0(sK7(sK1),sK8(sK1)) = sK7(sK1) ) ),
inference(global_subsumption_just,[status(thm)],[c_16730,c_7104,c_16741]) ).
tcf(c_18257,plain,
( ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ( head_of(sK8(sK1)) = tail_of(sK7(sK1)) ) ),
inference(superposition,[status(thm)],[c_18246,c_3894]) ).
tcf(c_18258,plain,
( ( number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1) )
| ( head_of(sK7(sK1)) = tail_of(sK7(sK1)) ) ),
inference(superposition,[status(thm)],[c_18246,c_3836]) ).
tcf(c_18277,plain,
number_of_in(triangles,sK1) = number_of_in(sequential_pairs,sK1),
inference(global_subsumption_just,[status(thm)],[c_18257,c_2934,c_12270,c_18258]) ).
tcf(c_18340,plain,
~ less_or_equal(number_of_in(triangles,sK1),number_of_in(triangles,graph)),
inference(demodulation,[status(thm)],[c_2821,c_18277]) ).
tcf(c_18341,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_18340,c_77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRA002+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 12:43:09 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 10.43/2.26 % SZS status Started for theBenchmark.p
% 10.43/2.26 % SZS status Theorem for theBenchmark.p
% 10.43/2.26
% 10.43/2.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.43/2.26
% 10.43/2.26 % ------ iProver source info
% 10.43/2.26
% 10.43/2.26 % git: date: 2026-07-19 20:42:38 +0200
% 10.43/2.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.43/2.26 % git: non_committed_changes: false
% 10.43/2.26
% 10.43/2.26 % ------ Parsing...
% 10.43/2.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.43/2.26
% 10.43/2.26 % ------ 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 %
% 10.43/2.26
% 10.43/2.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.43/2.26
% 10.43/2.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.43/2.26 % ------ Proving...
% 10.43/2.26 % ------ Problem Properties
% 10.43/2.26
% 10.43/2.26 %
% 10.43/2.26 % clauses 39
% 10.43/2.26 % conjectures 2
% 10.43/2.26 % EPR 12
% 10.43/2.26 % Horn 26
% 10.43/2.26 % unary 5
% 10.43/2.26 % binary 8
% 10.43/2.26 % lits 126
% 10.43/2.26 % lits eq 33
% 10.43/2.26 % fd_pure 0
% 10.43/2.26 % fd_pseudo 0
% 10.43/2.26 % fd_cond 0
% 10.43/2.26 % fd_pseudo_cond 5
% 10.43/2.26 % AC symbols 0
% 10.43/2.26
% 10.43/2.26 % ------ Schedule dynamic 5 is on
% 10.43/2.26
% 10.43/2.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.43/2.26
% 10.43/2.26
% 10.43/2.26 % ------
% 10.43/2.26 % Current options:
% 10.43/2.26 % ------
% 10.43/2.26
% 10.43/2.26
% 10.43/2.26 %
% 10.43/2.26
% 10.43/2.26 % ------ Proving...
% 10.43/2.26 %
% 10.43/2.26
% 10.43/2.26 % SZS status Theorem for theBenchmark.p
% 10.43/2.26
% 10.43/2.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.43/2.26
% 10.43/2.26
%------------------------------------------------------------------------------