%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU388+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 : Sun Sep 27 08:46:10 AM UTC 2026
% Result : Theorem 5.25s 1.12s
% Output : CNFRefutation 5.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 46 ( 11 unt; 0 def)
% Number of atoms : 186 ( 26 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 237 ( 97 ~; 104 |; 26 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 75 ( 0 sgn 29 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_yellow19,axiom,
! [A] :
( ( top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> neighborhood_system(A,B) = a_2_0_yellow19(A,B) ) ),
file('theBenchmark.p',d1_yellow19) ).
fof(fraenkel_a_2_0_yellow19,axiom,
! [A,B,C] :
( ( element(C,the_carrier(B))
& top_str(B)
& topological_space(B)
& ~ empty_carrier(B) )
=> ( in(A,a_2_0_yellow19(B,C))
<=> ? [D] :
( A = D
& point_neighbourhood(D,B,C) ) ) ),
file('theBenchmark.p',fraenkel_a_2_0_yellow19) ).
fof(t3_yellow19,conjecture,
! [A] :
( ( top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( in(C,neighborhood_system(A,B))
<=> point_neighbourhood(C,A,B) ) ) ),
file('theBenchmark.p',t3_yellow19) ).
fof(t3_yellow19_neg,negated_conjecture,
~ ! [A] :
( ( top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( in(C,neighborhood_system(A,B))
<=> point_neighbourhood(C,A,B) ) ) ),
inference(assume_negation,[status(cth)],[t3_yellow19]) ).
fof(nnf_119,plain,
? [A] :
( ? [B] :
( ? [C] :
( ( ~ point_neighbourhood(C,A,B)
| ~ in(C,neighborhood_system(A,B)) )
& ( point_neighbourhood(C,A,B)
| in(C,neighborhood_system(A,B)) ) )
& element(B,the_carrier(A)) )
& top_str(A)
& topological_space(A)
& ~ empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[t3_yellow19_neg]) ).
fof(sk_t3_yellow19_neg,plain,
( ( ~ point_neighbourhood(sK2,sK0,sK3)
| ~ in(sK2,neighborhood_system(sK0,sK3)) )
& ( point_neighbourhood(sK2,sK0,sK3)
| in(sK2,neighborhood_system(sK0,sK3)) )
& element(sK3,the_carrier(sK0))
& top_str(sK0)
& topological_space(sK0)
& ~ empty_carrier(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK3,sK2]),skolemize(A,sK0),skolemize(B,sK3),skolemize(C,sK2)],[nnf_119]) ).
cnf(c_198,negated_conjecture,
topological_space(sK0),
inference(split_conjunct,[status(thm)],[sk_t3_yellow19_neg]) ).
fof(nnf_72,plain,
! [A,B,C] :
( ( ( ! [D] :
( D != A
| ~ point_neighbourhood(D,B,C) )
| in(A,a_2_0_yellow19(B,C)) )
& ( ? [X0] :
( X0 = A
& point_neighbourhood(X0,B,C) )
| ~ in(A,a_2_0_yellow19(B,C)) ) )
| ~ element(C,the_carrier(B))
| ~ top_str(B)
| ~ topological_space(B)
| empty_carrier(B) ),
inference(fof_nnf,[status(thm)],[fraenkel_a_2_0_yellow19]) ).
fof(sk_fraenkel_a_2_0_yellow19_sk,plain,
! [A,B,C] :
( ( ( ! [D] :
( D != A
| ~ point_neighbourhood(D,B,C) )
| in(A,a_2_0_yellow19(B,C)) )
& ( ( sK1(A,B,C) = A
& point_neighbourhood(sK1(A,B,C),B,C) )
| ~ in(A,a_2_0_yellow19(B,C)) ) )
| ~ element(C,the_carrier(B))
| ~ top_str(B)
| ~ topological_space(B)
| empty_carrier(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1(A,B,C))],[nnf_72]) ).
fof(sk_fraenkel_a_2_0_yellow19,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 != VAR_2
| ~ point_neighbourhood(VAR_3,VAR_0,VAR_1)
| in(VAR_2,a_2_0_yellow19(VAR_0,VAR_1))
| ~ element(VAR_1,the_carrier(VAR_0))
| ~ top_str(VAR_0)
| ~ topological_space(VAR_0)
| empty_carrier(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( sK1(VAR_2,VAR_0,VAR_1) = VAR_2
| ~ in(VAR_2,a_2_0_yellow19(VAR_0,VAR_1))
| ~ element(VAR_1,the_carrier(VAR_0))
| ~ top_str(VAR_0)
| ~ topological_space(VAR_0)
| empty_carrier(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( point_neighbourhood(sK1(VAR_2,VAR_0,VAR_1),VAR_0,VAR_1)
| ~ in(VAR_2,a_2_0_yellow19(VAR_0,VAR_1))
| ~ element(VAR_1,the_carrier(VAR_0))
| ~ top_str(VAR_0)
| ~ topological_space(VAR_0)
| empty_carrier(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_fraenkel_a_2_0_yellow19_sk]) ).
cnf(c_224,plain,
( D != C
| ~ point_neighbourhood(D,A,B)
| in(C,a_2_0_yellow19(A,B))
| ~ element(B,the_carrier(A))
| ~ top_str(A)
| ~ topological_space(A)
| empty_carrier(A) ),
inference(split_conjunct,[status(thm)],[sk_fraenkel_a_2_0_yellow19]) ).
cnf(c_225,plain,
( sK1(C,A,B) = C
| ~ in(C,a_2_0_yellow19(A,B))
| ~ element(B,the_carrier(A))
| ~ top_str(A)
| ~ topological_space(A)
| empty_carrier(A) ),
inference(split_conjunct,[status(thm)],[sk_fraenkel_a_2_0_yellow19]) ).
cnf(c_226,plain,
( point_neighbourhood(sK1(C,A,B),A,B)
| ~ in(C,a_2_0_yellow19(A,B))
| ~ element(B,the_carrier(A))
| ~ top_str(A)
| ~ topological_space(A)
| empty_carrier(A) ),
inference(split_conjunct,[status(thm)],[sk_fraenkel_a_2_0_yellow19]) ).
cnf(c_233,plain,
( a_2_0_yellow19(A,B) = neighborhood_system(A,B)
| ~ element(B,the_carrier(A))
| ~ top_str(A)
| ~ topological_space(A)
| empty_carrier(A) ),
inference(clausify,[status(thm)],[d1_yellow19]) ).
cnf(c_320,negated_conjecture,
( a_2_0_yellow19(sK0,A) = neighborhood_system(sK0,A)
| ~ element(A,the_carrier(sK0))
| ~ top_str(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_198,c_233]) ).
cnf(c_321,negated_conjecture,
( neighborhood_system(sK0,A) = a_2_0_yellow19(sK0,A)
| ~ element(A,the_carrier(sK0))
| ~ top_str(sK0)
| empty_carrier(sK0) ),
inference(copy,[status(thm)],[c_320]) ).
cnf(c_327,negated_conjecture,
( point_neighbourhood(sK1(B,sK0,A),sK0,A)
| ~ in(B,a_2_0_yellow19(sK0,A))
| ~ element(A,the_carrier(sK0))
| ~ top_str(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_198,c_226]) ).
cnf(c_328,negated_conjecture,
( sK1(B,sK0,A) = B
| ~ in(B,a_2_0_yellow19(sK0,A))
| ~ element(A,the_carrier(sK0))
| ~ top_str(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_198,c_225]) ).
cnf(c_329,negated_conjecture,
( C != B
| ~ point_neighbourhood(C,sK0,A)
| in(B,a_2_0_yellow19(sK0,A))
| ~ element(A,the_carrier(sK0))
| ~ top_str(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_198,c_224]) ).
cnf(c_647,negated_conjecture,
( ~ point_neighbourhood(sK2,sK0,sK3)
| ~ in(sK2,neighborhood_system(sK0,sK3)) ),
inference(split_conjunct,[status(thm)],[sk_t3_yellow19_neg]) ).
cnf(c_648,negated_conjecture,
( point_neighbourhood(sK2,sK0,sK3)
| in(sK2,neighborhood_system(sK0,sK3)) ),
inference(split_conjunct,[status(thm)],[sk_t3_yellow19_neg]) ).
cnf(c_649,negated_conjecture,
element(sK3,the_carrier(sK0)),
inference(split_conjunct,[status(thm)],[sk_t3_yellow19_neg]) ).
cnf(c_650,negated_conjecture,
top_str(sK0),
inference(split_conjunct,[status(thm)],[sk_t3_yellow19_neg]) ).
cnf(c_651,negated_conjecture,
~ empty_carrier(sK0),
inference(split_conjunct,[status(thm)],[sk_t3_yellow19_neg]) ).
cnf(c_3644,negated_conjecture,
( C != B
| ~ point_neighbourhood(C,sK0,A)
| in(B,a_2_0_yellow19(sK0,A))
| ~ element(A,the_carrier(sK0))
| ~ top_str(sK0) ),
inference(resolve,[status(thm)],[c_651,c_329]) ).
cnf(c_946,negated_conjecture,
( C != B
| ~ point_neighbourhood(C,sK0,A)
| in(B,a_2_0_yellow19(sK0,A))
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_650,c_3644]) ).
cnf(c_3645,negated_conjecture,
( sK1(B,sK0,A) = B
| ~ in(B,a_2_0_yellow19(sK0,A))
| ~ element(A,the_carrier(sK0))
| ~ top_str(sK0) ),
inference(resolve,[status(thm)],[c_651,c_328]) ).
cnf(c_947,negated_conjecture,
( sK1(B,sK0,A) = B
| ~ in(B,a_2_0_yellow19(sK0,A))
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_650,c_3645]) ).
cnf(c_3646,negated_conjecture,
( point_neighbourhood(sK1(B,sK0,A),sK0,A)
| ~ in(B,a_2_0_yellow19(sK0,A))
| ~ element(A,the_carrier(sK0))
| ~ top_str(sK0) ),
inference(resolve,[status(thm)],[c_651,c_327]) ).
cnf(c_948,negated_conjecture,
( point_neighbourhood(sK1(B,sK0,A),sK0,A)
| ~ in(B,a_2_0_yellow19(sK0,A))
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_650,c_3646]) ).
cnf(c_3647,negated_conjecture,
( neighborhood_system(sK0,A) = a_2_0_yellow19(sK0,A)
| ~ element(A,the_carrier(sK0))
| ~ top_str(sK0) ),
inference(resolve,[status(thm)],[c_651,c_321]) ).
cnf(c_954,negated_conjecture,
( neighborhood_system(sK0,A) = a_2_0_yellow19(sK0,A)
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_650,c_3647]) ).
cnf(c_3648,negated_conjecture,
( B != A
| ~ point_neighbourhood(B,sK0,sK3)
| in(A,a_2_0_yellow19(sK0,sK3)) ),
inference(resolve,[status(thm)],[c_946,c_649]) ).
cnf(c_3649,negated_conjecture,
( in(sK2,neighborhood_system(sK0,sK3))
| sK2 != A
| in(A,a_2_0_yellow19(sK0,sK3)) ),
inference(resolve,[status(thm)],[c_3648,c_648]) ).
cnf(c_2110,plain,
( in(sK2,neighborhood_system(sK0,sK3))
| in(sK2,a_2_0_yellow19(sK0,sK3)) ),
inference(xxres,[status(thm)],[c_3649]) ).
cnf(c_2129,plain,
neighborhood_system(sK0,sK3) = a_2_0_yellow19(sK0,sK3),
inference(resolve,[status(thm)],[c_954,c_649]) ).
cnf(c_3650,plain,
( in(sK2,a_2_0_yellow19(sK0,sK3))
| in(sK2,a_2_0_yellow19(sK0,sK3)) ),
inference(paramod,[status(thm)],[c_2129,c_2110]) ).
cnf(c_2133,plain,
in(sK2,a_2_0_yellow19(sK0,sK3)),
inference(copy,[status(thm)],[c_3650]) ).
cnf(c_3651,negated_conjecture,
( ~ point_neighbourhood(sK2,sK0,sK3)
| ~ in(sK2,a_2_0_yellow19(sK0,sK3)) ),
inference(paramod,[status(thm)],[c_2129,c_647]) ).
cnf(c_2134,negated_conjecture,
~ point_neighbourhood(sK2,sK0,sK3),
inference(resolve,[status(thm)],[c_2133,c_3651]) ).
cnf(c_3652,negated_conjecture,
( sK1(sK2,sK0,sK3) = sK2
| ~ element(sK3,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_2133,c_947]) ).
cnf(c_3637,negated_conjecture,
sK1(sK2,sK0,sK3) = sK2,
inference(resolve,[status(thm)],[c_649,c_3652]) ).
cnf(c_3653,negated_conjecture,
( point_neighbourhood(sK1(A,sK0,sK3),sK0,sK3)
| ~ in(A,a_2_0_yellow19(sK0,sK3)) ),
inference(resolve,[status(thm)],[c_948,c_649]) ).
cnf(c_3654,negated_conjecture,
point_neighbourhood(sK1(sK2,sK0,sK3),sK0,sK3),
inference(resolve,[status(thm)],[c_3653,c_2133]) ).
cnf(c_3655,negated_conjecture,
point_neighbourhood(sK2,sK0,sK3),
inference(paramod,[status(thm)],[c_3637,c_3654]) ).
cnf(c_3643,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2134,c_3655]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU388+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 09:27:30 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3696542 was started by sandbox on n015,
% 0.09/0.36 % Sat Sep 26 09:27:30 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.39
% 0.12/0.39 % From the command line: assign(max_seconds, 300).
% 5.25/1.12
% 5.25/1.12 % given #500 (I,wt=7): 1061 lower_bounded_relstr(c7). [back_unit_del(532),unit_del(a,727),unit_del(b,725),unit_del(c,1052)].
% 5.25/1.12
% 5.25/1.12 % SZS status Theorem for theBenchmark
% 5.25/1.12
% 5.25/1.12 % Proof 1 at 0.66 (+ 0.05) seconds.
% 5.25/1.12 % Length of proof is 28.
% 5.25/1.12 % Level of proof is 8.
% 5.25/1.12 % Maximum clause weight is 30.000.
% 5.25/1.12 % Given clauses 622.
% 5.25/1.12
% 5.25/1.12 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------