%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRA010+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 01:22:53 PM UTC 2026
% Result : Theorem 17.81s 12.62s
% Output : Proof 17.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 11
% Syntax : Number of formulae : 94 ( 57 unt; 0 def)
% Number of atoms : 275 ( 116 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 287 ( 106 ~; 81 |; 82 &)
% ( 2 <=>; 14 =>; 0 <=; 2 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 2 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 8 con; 0-5 aty)
% Number of variables : 183 ( 12 sgn 93 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,conjecture,
( complete
=> ! [P,V1,V2] :
( ( ! [E1,E2] :
( ( sequential(E1,E2)
& on_path(E2,P)
& on_path(E1,P) )
=> ? [E3] : triangle(E1,E2,E3) )
& path(V1,V2,P) )
=> number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complete_means_sequential_pairs_and_triangles) ).
fof(f18_neg,negated_conjecture,
~ ( complete
=> ! [P,V1,V2] :
( ( ! [E1,E2] :
( ( sequential(E1,E2)
& on_path(E2,P)
& on_path(E1,P) )
=> ? [E3] : triangle(E1,E2,E3) )
& path(V1,V2,P) )
=> number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
( ? [P,V1,V2] :
( number_of_in(sequential_pairs,P) != number_of_in(triangles,P)
& ! [E1,E2] :
( ? [E3] : triangle(E1,E2,E3)
| ~ sequential(E1,E2)
| ~ on_path(E2,P)
| ~ on_path(E1,P) )
& path(V1,V2,P) )
& complete ),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
! [E1,E2] :
( number_of_in(sequential_pairs,sk9) != number_of_in(triangles,sk9)
& ( triangle(E1,E2,sk12(E1,E2))
| ~ sequential(E1,E2)
| ~ on_path(E2,sk9)
| ~ on_path(E1,sk9) )
& path(sk10,sk11,sk9)
& complete ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9,sk10,sk11,sk12])],[f18_nnf]) ).
cnf(c74,plain,
number_of_in(sequential_pairs,sk9) != number_of_in(triangles,sk9),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t19,plain,
eq(number_of_in(sequential_pairs,sk9),number_of_in(triangles,sk9)) = false,
inference(equality_encoding,[status(esa)],[c74]) ).
cnf(t484,plain,
eq(number_of_in(sequential_pairs,sk9),number_of_in(triangles,sk9)) = false,
inference(orient,[status(thm)],[t19]) ).
fof(f15,axiom,
! [P,V1,V2] :
( ( ! [E1,E2] :
( ( sequential(E1,E2)
& on_path(E2,P)
& on_path(E1,P) )
=> ? [E3] : triangle(E1,E2,E3) )
& path(V1,V2,P) )
=> number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
fof(f15_nnf,plain,
! [P,V1,V2] :
( number_of_in(sequential_pairs,P) = number_of_in(triangles,P)
| ? [E1,E2] :
( ! [E3] : ~ triangle(E1,E2,E3)
& sequential(E1,E2)
& on_path(E2,P)
& on_path(E1,P) )
| ~ path(V1,V2,P) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [V1,V2,P,E3] :
( number_of_in(sequential_pairs,P) = number_of_in(triangles,P)
| ( ~ triangle(sk6(P,V1,V2),sk7(P,V1,V2),E3)
& sequential(sk6(P,V1,V2),sk7(P,V1,V2))
& on_path(sk7(P,V1,V2),P)
& on_path(sk6(P,V1,V2),P) )
| ~ path(V1,V2,P) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk6,sk7])],[f15_nnf]) ).
cnf(c68,plain,
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ triangle(sk6(X0,X1,X2),sk7(X0,X1,X2),X5)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t115,plain,
ifeq(path(X1,X2,X3),true,ifeq(triangle(sk6(X3,X1,X2),sk7(X3,X1,X2),X4),true,number_of_in(sequential_pairs,X3),number_of_in(triangles,X3)),number_of_in(triangles,X3)) = number_of_in(triangles,X3),
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t500,plain,
ifeq(path(X1,X2,X3),true,ifeq(triangle(sk6(X3,X1,X2),sk7(X3,X1,X2),X4),true,number_of_in(sequential_pairs,X3),number_of_in(triangles,X3)),number_of_in(triangles,X3)) = number_of_in(triangles,X3),
inference(orient,[status(thm)],[t115]) ).
cnf(c73,plain,
( triangle(X3,X4,sk12(X3,X4))
| ~ sequential(X3,X4)
| ~ on_path(X4,sk9)
| ~ on_path(X3,sk9) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t98,plain,
ifeq(on_path(X1,sk9),true,ifeq(on_path(X2,sk9),true,ifeq(sequential(X1,X2),true,triangle(X1,X2,sk12(X1,X2)),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(t308,plain,
ifeq(on_path(X1,sk9),true,ifeq(on_path(X2,sk9),true,ifeq(sequential(X1,X2),true,triangle(X1,X2,sk12(X1,X2)),true),true),true) = true,
inference(orient,[status(thm)],[t98]) ).
cnf(c67,plain,
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| sequential(sk6(X0,X1,X2),sk7(X0,X1,X2))
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi53,axiom,
ifeq(path(X0,X1,X2),true,or(sequential(sk6(X2,X0,X1),sk7(X2,X0,X1)),eq(number_of_in(sequential_pairs,X2),number_of_in(triangles,X2))),true) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(c72,plain,
path(sk10,sk11,sk9),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi58,negated_conjecture,
path(sk10,sk11,sk9) = true,
inference(equality_encoding,[status(esa)],[c72]) ).
cnf(t85,plain,
or(sequential(sk6(sk9,sk10,sk11),sk7(sk9,sk10,sk11)),eq(number_of_in(sequential_pairs,sk9),number_of_in(triangles,sk9))) = true,
inference(hyper_resolution,[status(thm)],[hi53,hi58]) ).
cnf(t225,plain,
or(sequential(sk6(sk9,sk10,sk11),sk7(sk9,sk10,sk11)),eq(number_of_in(sequential_pairs,sk9),number_of_in(triangles,sk9))) = true,
inference(orient,[status(thm)],[t85]) ).
cnf(t1889,plain,
or(sequential(sk6(sk9,sk10,sk11),sk7(sk9,sk10,sk11)),false) = true,
inference(step,[status(thm)],[t225,t484]) ).
cnf(t6,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t182,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t1890,plain,
sequential(sk6(sk9,sk10,sk11),sk7(sk9,sk10,sk11)) = true,
inference(step,[status(thm)],[t1889,t182]) ).
cnf(t494,plain,
sequential(sk6(sk9,sk10,sk11),sk7(sk9,sk10,sk11)) = true,
inference(rw,[status(thm)],[t1890]) ).
cnf(t718,plain,
sequential(sk6(sk9,sk10,sk11),sk7(sk9,sk10,sk11)) = true,
inference(orient,[status(thm)],[t494]) ).
cnf(t725,plain,
true = ifeq(on_path(sk6(sk9,sk10,sk11),sk9),true,ifeq(on_path(sk7(sk9,sk10,sk11),sk9),true,ifeq(true,true,triangle(sk6(sk9,sk10,sk11),sk7(sk9,sk10,sk11),sk12(sk6(sk9,sk10,sk11),sk7(sk9,sk10,sk11))),true),true),true),
inference(cp,[status(thm)],[t308,t718]) ).
cnf(c65,plain,
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| on_path(sk6(X0,X1,X2),X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi51,axiom,
ifeq(path(X0,X1,X2),true,or(on_path(sk6(X2,X0,X1),X2),eq(number_of_in(sequential_pairs,X2),number_of_in(triangles,X2))),true) = true,
inference(equality_encoding,[status(esa)],[c65]) ).
cnf(t49,plain,
or(on_path(sk6(sk9,sk10,sk11),sk9),eq(number_of_in(sequential_pairs,sk9),number_of_in(triangles,sk9))) = true,
inference(hyper_resolution,[status(thm)],[hi51,hi58]) ).
cnf(t240,plain,
or(on_path(sk6(sk9,sk10,sk11),sk9),eq(number_of_in(sequential_pairs,sk9),number_of_in(triangles,sk9))) = true,
inference(orient,[status(thm)],[t49]) ).
cnf(t1887,plain,
or(on_path(sk6(sk9,sk10,sk11),sk9),false) = true,
inference(step,[status(thm)],[t240,t484]) ).
cnf(t1888,plain,
on_path(sk6(sk9,sk10,sk11),sk9) = true,
inference(step,[status(thm)],[t1887,t182]) ).
cnf(t493,plain,
on_path(sk6(sk9,sk10,sk11),sk9) = true,
inference(rw,[status(thm)],[t1888]) ).
cnf(t527,plain,
on_path(sk6(sk9,sk10,sk11),sk9) = true,
inference(orient,[status(thm)],[t493]) ).
cnf(t2064,plain,
true = ifeq(true,true,ifeq(on_path(sk7(sk9,sk10,sk11),sk9),true,ifeq(true,true,triangle(sk6(sk9,sk10,sk11),sk7(sk9,sk10,sk11),sk12(sk6(sk9,sk10,sk11),sk7(sk9,sk10,sk11))),true),true),true),
inference(step,[status(thm)],[t725,t527]) ).
cnf(t13,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t184,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t13]) ).
cnf(t2065,plain,
true = ifeq(on_path(sk7(sk9,sk10,sk11),sk9),true,ifeq(true,true,triangle(sk6(sk9,sk10,sk11),sk7(sk9,sk10,sk11),sk12(sk6(sk9,sk10,sk11),sk7(sk9,sk10,sk11))),true),true),
inference(step,[status(thm)],[t2064,t184]) ).
cnf(c66,plain,
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| on_path(sk7(X0,X1,X2),X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi52,axiom,
ifeq(path(X0,X1,X2),true,or(on_path(sk7(X2,X0,X1),X2),eq(number_of_in(sequential_pairs,X2),number_of_in(triangles,X2))),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t50,plain,
or(on_path(sk7(sk9,sk10,sk11),sk9),eq(number_of_in(sequential_pairs,sk9),number_of_in(triangles,sk9))) = true,
inference(hyper_resolution,[status(thm)],[hi52,hi58]) ).
cnf(t241,plain,
or(on_path(sk7(sk9,sk10,sk11),sk9),eq(number_of_in(sequential_pairs,sk9),number_of_in(triangles,sk9))) = true,
inference(orient,[status(thm)],[t50]) ).
cnf(t1885,plain,
or(on_path(sk7(sk9,sk10,sk11),sk9),false) = true,
inference(step,[status(thm)],[t241,t484]) ).
cnf(t1886,plain,
on_path(sk7(sk9,sk10,sk11),sk9) = true,
inference(step,[status(thm)],[t1885,t182]) ).
cnf(t492,plain,
on_path(sk7(sk9,sk10,sk11),sk9) = true,
inference(rw,[status(thm)],[t1886]) ).
cnf(t515,plain,
on_path(sk7(sk9,sk10,sk11),sk9) = true,
inference(orient,[status(thm)],[t492]) ).
cnf(t2066,plain,
true = ifeq(true,true,ifeq(true,true,triangle(sk6(sk9,sk10,sk11),sk7(sk9,sk10,sk11),sk12(sk6(sk9,sk10,sk11),sk7(sk9,sk10,sk11))),true),true),
inference(step,[status(thm)],[t2065,t515]) ).
cnf(t2067,plain,
true = ifeq(true,true,triangle(sk6(sk9,sk10,sk11),sk7(sk9,sk10,sk11),sk12(sk6(sk9,sk10,sk11),sk7(sk9,sk10,sk11))),true),
inference(step,[status(thm)],[t2066,t184]) ).
cnf(t2068,plain,
true = triangle(sk6(sk9,sk10,sk11),sk7(sk9,sk10,sk11),sk12(sk6(sk9,sk10,sk11),sk7(sk9,sk10,sk11))),
inference(step,[status(thm)],[t2067,t184]) ).
cnf(t1817,plain,
triangle(sk6(sk9,sk10,sk11),sk7(sk9,sk10,sk11),sk12(sk6(sk9,sk10,sk11),sk7(sk9,sk10,sk11))) = true,
inference(orient,[status(thm)],[t2068]) ).
cnf(t1821,plain,
number_of_in(triangles,sk9) = ifeq(path(sk10,sk11,sk9),true,ifeq(true,true,number_of_in(sequential_pairs,sk9),number_of_in(triangles,sk9)),number_of_in(triangles,sk9)),
inference(cp,[status(thm)],[t500,t1817]) ).
cnf(t11,plain,
path(sk10,sk11,sk9) = true,
inference(equality_encoding,[status(esa)],[c72]) ).
cnf(t368,plain,
path(sk10,sk11,sk9) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t2069,plain,
number_of_in(triangles,sk9) = ifeq(true,true,ifeq(true,true,number_of_in(sequential_pairs,sk9),number_of_in(triangles,sk9)),number_of_in(triangles,sk9)),
inference(step,[status(thm)],[t1821,t368]) ).
cnf(t2070,plain,
number_of_in(triangles,sk9) = ifeq(true,true,number_of_in(sequential_pairs,sk9),number_of_in(triangles,sk9)),
inference(step,[status(thm)],[t2069,t184]) ).
cnf(t2071,plain,
number_of_in(triangles,sk9) = number_of_in(sequential_pairs,sk9),
inference(step,[status(thm)],[t2070,t184]) ).
cnf(t1823,plain,
number_of_in(sequential_pairs,sk9) = number_of_in(triangles,sk9),
inference(orient,[status(thm)],[t2071]) ).
cnf(t2078,plain,
eq(number_of_in(triangles,sk9),number_of_in(triangles,sk9)) = false,
inference(step,[status(thm)],[t484,t1823]) ).
cnf(t5,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t188,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t2079,plain,
true = false,
inference(step,[status(thm)],[t2078,t188]) ).
cnf(t1831,plain,
true = false,
inference(rw,[status(thm)],[t2079]) ).
cnf(t1833,plain,
false = true,
inference(orient,[status(thm)],[t1831]) ).
fof(f0,axiom,
! [E] :
( edge(E)
=> head_of(E) != tail_of(E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_loops) ).
fof(f0_nnf,plain,
! [E] :
( head_of(E) != tail_of(E)
| ~ edge(E) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [E] :
( head_of(E) != tail_of(E)
| ~ edge(E) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f4,axiom,
! [V1,V2,P] :
( path(V1,V2,P)
=> ( ? [E] :
( ( ( P = path_cons(E,empty)
& V2 = head_of(E) )
<~> ? [TP] :
( P = path_cons(E,TP)
& path(head_of(E),V2,TP) ) )
& V1 = tail_of(E)
& edge(E) )
& vertex(V2)
& vertex(V1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_properties) ).
fof(f4_nnf,plain,
! [V1,V2,P] :
( ( ? [E] :
( ( ( ? [TP] :
( P = path_cons(E,TP)
& path(head_of(E),V2,TP) )
& ( P != path_cons(E,empty)
| V2 != head_of(E) ) )
| ( ! [TP] :
( P != path_cons(E,TP)
| ~ path(head_of(E),V2,TP) )
& P = path_cons(E,empty)
& V2 = head_of(E) ) )
& V1 = tail_of(E)
& edge(E) )
& vertex(V2)
& vertex(V1) )
| ~ path(V1,V2,P) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [V1,V2,P,TP] :
( ( ( ( P = path_cons(sk1(V1,V2,P),sk2(V1,V2,P))
& path(head_of(sk1(V1,V2,P)),V2,sk2(V1,V2,P))
& ( P != path_cons(sk1(V1,V2,P),empty)
| V2 != head_of(sk1(V1,V2,P)) ) )
| ( ( P != path_cons(sk1(V1,V2,P),TP)
| ~ path(head_of(sk1(V1,V2,P)),V2,TP) )
& P = path_cons(sk1(V1,V2,P),empty)
& V2 = head_of(sk1(V1,V2,P)) ) )
& V1 = tail_of(sk1(V1,V2,P))
& edge(sk1(V1,V2,P))
& vertex(V2)
& vertex(V1) )
| ~ path(V1,V2,P) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2])],[f4_nnf]) ).
cnf(c25,plain,
( X2 != path_cons(sk1(X0,X1,X2),empty)
| X1 != head_of(sk1(X0,X1,X2))
| X2 != path_cons(sk1(X0,X1,X2),X4)
| ~ path(head_of(sk1(X0,X1,X2)),X1,X4)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f7,axiom,
! [E1,E2] :
( sequential(E1,E2)
<=> ( head_of(E1) = tail_of(E2)
& E1 != E2
& edge(E2)
& edge(E1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_defn) ).
fof(f7_nnf,plain,
! [E1,E2] :
( ( head_of(E1) != tail_of(E2)
| E1 = E2
| ~ edge(E2)
| ~ edge(E1)
| sequential(E1,E2) )
& ( ( head_of(E1) = tail_of(E2)
& E1 != E2
& edge(E2)
& edge(E1) )
| ~ sequential(E1,E2) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [E1,E2] :
( ( head_of(E1) != tail_of(E2)
| E1 = E2
| ~ edge(E2)
| ~ edge(E1)
| sequential(E1,E2) )
& ( ( head_of(E1) = tail_of(E2)
& E1 != E2
& edge(E2)
& edge(E1) )
| ~ sequential(E1,E2) ) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c36,plain,
( X0 != X1
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f9,axiom,
! [P,V1,V2] :
( path(V1,V2,P)
=> ! [E1,E2] :
( precedes(E1,E2,P)
=> ( ( sequential(E1,E2)
<~> ? [E3] :
( precedes(E3,E2,P)
& sequential(E1,E3) ) )
& on_path(E2,P)
& on_path(E1,P) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_properties) ).
fof(f9_nnf,plain,
! [P,V1,V2] :
( ! [E1,E2] :
( ( ( ( ? [E3] :
( precedes(E3,E2,P)
& sequential(E1,E3) )
& ~ sequential(E1,E2) )
| ( ! [E3] :
( ~ precedes(E3,E2,P)
| ~ sequential(E1,E3) )
& sequential(E1,E2) ) )
& on_path(E2,P)
& on_path(E1,P) )
| ~ precedes(E1,E2,P) )
| ~ path(V1,V2,P) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [V1,V2,P,E1,E2,E3] :
( ( ( ( precedes(sk4(P,V1,V2,E1,E2),E2,P)
& sequential(E1,sk4(P,V1,V2,E1,E2))
& ~ sequential(E1,E2) )
| ( ( ~ precedes(E3,E2,P)
| ~ sequential(E1,E3) )
& sequential(E1,E2) ) )
& on_path(E2,P)
& on_path(E1,P) )
| ~ precedes(E1,E2,P)
| ~ path(V1,V2,P) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f9_nnf]) ).
cnf(c46,plain,
( ~ sequential(X3,X4)
| ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5)
| ~ precedes(X3,X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
fof(f10,axiom,
! [V1,V2,SP] :
( shortest_path(V1,V2,SP)
<=> ( ! [P] :
( path(V1,V2,P)
=> less_or_equal(length_of(SP),length_of(P)) )
& V1 != V2
& path(V1,V2,SP) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_defn) ).
fof(f10_nnf,plain,
! [V1,V2,SP] :
( ( ? [P] :
( ~ less_or_equal(length_of(SP),length_of(P))
& path(V1,V2,P) )
| V1 = V2
| ~ path(V1,V2,SP)
| shortest_path(V1,V2,SP) )
& ( ( ! [P] :
( less_or_equal(length_of(SP),length_of(P))
| ~ path(V1,V2,P) )
& V1 != V2
& path(V1,V2,SP) )
| ~ shortest_path(V1,V2,SP) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [V1,V2,SP,P] :
( ( ( ~ less_or_equal(length_of(SP),length_of(sk5(V1,V2,SP)))
& path(V1,V2,sk5(V1,V2,SP)) )
| V1 = V2
| ~ path(V1,V2,SP)
| shortest_path(V1,V2,SP) )
& ( ( ( less_or_equal(length_of(SP),length_of(P))
| ~ path(V1,V2,P) )
& V1 != V2
& path(V1,V2,SP) )
| ~ shortest_path(V1,V2,SP) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5])],[f10_nnf]) ).
cnf(c50,plain,
( X0 != X1
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
fof(f11,axiom,
! [V1,V2,E1,E2,P] :
( ( precedes(E1,E2,P)
& shortest_path(V1,V2,P) )
=> ( ~ precedes(E2,E1,P)
& ~ ? [E3] :
( head_of(E3) = head_of(E2)
& tail_of(E3) = tail_of(E1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_properties) ).
fof(f11_nnf,plain,
! [V1,V2,E1,E2,P] :
( ( ~ precedes(E2,E1,P)
& ! [E3] :
( head_of(E3) != head_of(E2)
| tail_of(E3) != tail_of(E1) ) )
| ~ precedes(E1,E2,P)
| ~ shortest_path(V1,V2,P) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [V1,V2,P,E1,E2,E3] :
( ( ~ precedes(E2,E1,P)
& ( head_of(E3) != head_of(E2)
| tail_of(E3) != tail_of(E1) ) )
| ~ precedes(E1,E2,P)
| ~ shortest_path(V1,V2,P) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c54,plain,
( head_of(X5) != head_of(X3)
| tail_of(X5) != tail_of(X2)
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(c55,plain,
( ~ precedes(X3,X2,X4)
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c25,c36,c46,c50,c54,c55,c74]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1833]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRA010+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/10.36 % Computer : n012.cluster.edu
% 0.08/10.36 % Model : x86_64 x86_64
% 0.08/10.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.36 % Memory : 8046.5625MB
% 0.08/10.36 % OS : Linux 6.8.0-71-generic
% 0.08/10.36 % CPULimit : 300
% 0.08/10.36 % WCLimit : 300
% 0.08/10.36 % DateTime : Wed Sep 23 12:44:38 UTC 2026
% 0.08/10.36 % CPUTime :
% 0.08/10.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 17.81/12.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.81/12.62 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------