%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU317+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 08:45:47 AM UTC 2026
% Result : Theorem 247.74s 33.80s
% Output : CNFRefutation 247.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 38 ( 11 unt; 0 def)
% Number of atoms : 150 ( 0 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 186 ( 74 ~; 76 |; 23 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 77 ( 0 sgn 50 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t45_pre_topc,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ! [C] :
( in(C,the_carrier(A))
=> ( in(C,topstr_closure(A,B))
<=> ! [D] :
( element(D,powerset(the_carrier(A)))
=> ( ( subset(B,D)
& closed_subset(D,A) )
=> in(C,D) ) ) ) ) ) ),
file('theBenchmark.p',t45_pre_topc) ).
fof(t48_pre_topc,conjecture,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset(B,topstr_closure(A,B)) ) ),
file('theBenchmark.p',t48_pre_topc) ).
fof(t48_pre_topc_neg,negated_conjecture,
~ ! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset(B,topstr_closure(A,B)) ) ),
inference(assume_negation,[status(cth)],[t48_pre_topc]) ).
fof(nnf_37,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ? [D] :
( ~ in(C,D)
& subset(B,D)
& closed_subset(D,A)
& element(D,powerset(the_carrier(A))) )
| in(C,topstr_closure(A,B)) )
& ( ! [X0] :
( in(C,X0)
| ~ subset(B,X0)
| ~ closed_subset(X0,A)
| ~ element(X0,powerset(the_carrier(A))) )
| ~ in(C,topstr_closure(A,B)) ) )
| ~ in(C,the_carrier(A)) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[t45_pre_topc]) ).
fof(sk_t45_pre_topc_sk,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ( ~ in(C,sK0(A,B,C))
& subset(B,sK0(A,B,C))
& closed_subset(sK0(A,B,C),A)
& element(sK0(A,B,C),powerset(the_carrier(A))) )
| in(C,topstr_closure(A,B)) )
& ( ! [X0] :
( in(C,X0)
| ~ subset(B,X0)
| ~ closed_subset(X0,A)
| ~ element(X0,powerset(the_carrier(A))) )
| ~ in(C,topstr_closure(A,B)) ) )
| ~ in(C,the_carrier(A)) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(D,sK0(A,B,C))],[nnf_37]) ).
fof(sk_t45_pre_topc,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ in(VAR_2,sK0(VAR_0,VAR_1,VAR_2))
| in(VAR_2,topstr_closure(VAR_0,VAR_1))
| ~ in(VAR_2,the_carrier(VAR_0))
| ~ element(VAR_1,powerset(the_carrier(VAR_0)))
| ~ top_str(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( subset(VAR_1,sK0(VAR_0,VAR_1,VAR_2))
| in(VAR_2,topstr_closure(VAR_0,VAR_1))
| ~ in(VAR_2,the_carrier(VAR_0))
| ~ element(VAR_1,powerset(the_carrier(VAR_0)))
| ~ top_str(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( closed_subset(sK0(VAR_0,VAR_1,VAR_2),VAR_0)
| in(VAR_2,topstr_closure(VAR_0,VAR_1))
| ~ in(VAR_2,the_carrier(VAR_0))
| ~ element(VAR_1,powerset(the_carrier(VAR_0)))
| ~ top_str(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( element(sK0(VAR_0,VAR_1,VAR_2),powerset(the_carrier(VAR_0)))
| in(VAR_2,topstr_closure(VAR_0,VAR_1))
| ~ in(VAR_2,the_carrier(VAR_0))
| ~ element(VAR_1,powerset(the_carrier(VAR_0)))
| ~ top_str(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in(VAR_2,VAR_3)
| ~ subset(VAR_1,VAR_3)
| ~ closed_subset(VAR_3,VAR_0)
| ~ element(VAR_3,powerset(the_carrier(VAR_0)))
| ~ in(VAR_2,topstr_closure(VAR_0,VAR_1))
| ~ in(VAR_2,the_carrier(VAR_0))
| ~ element(VAR_1,powerset(the_carrier(VAR_0)))
| ~ top_str(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_t45_pre_topc_sk]) ).
cnf(c_44,plain,
( ~ in(C,sK0(A,B,C))
| in(C,topstr_closure(A,B))
| ~ in(C,the_carrier(A))
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ),
inference(split_conjunct,[status(thm)],[sk_t45_pre_topc]) ).
fof(nnf_43,plain,
? [A] :
( ? [B] :
( ~ subset(B,topstr_closure(A,B))
& element(B,powerset(the_carrier(A))) )
& top_str(A) ),
inference(fof_nnf,[status(thm)],[t48_pre_topc_neg]) ).
fof(sk_t48_pre_topc_neg,plain,
( ~ subset(sK2,topstr_closure(sK1,sK2))
& element(sK2,powerset(the_carrier(sK1)))
& top_str(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2)],[nnf_43]) ).
cnf(c_45,negated_conjecture,
top_str(sK1),
inference(split_conjunct,[status(thm)],[sk_t48_pre_topc_neg]) ).
cnf(c_46,plain,
( subset(B,sK0(A,B,C))
| in(C,topstr_closure(A,B))
| ~ in(C,the_carrier(A))
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ),
inference(split_conjunct,[status(thm)],[sk_t45_pre_topc]) ).
cnf(c_53,negated_conjecture,
~ subset(sK2,topstr_closure(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_t48_pre_topc_neg]) ).
cnf(c_54,negated_conjecture,
element(sK2,powerset(the_carrier(sK1))),
inference(split_conjunct,[status(thm)],[sk_t48_pre_topc_neg]) ).
cnf(c_61,plain,
( subset(A,B)
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
fof(nnf_17,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(sk_d3_tarski_sk,plain,
! [A,B] :
( ( ( ~ in(sK3(A,B),B)
& in(sK3(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(C,sK3(A,B))],[nnf_17]) ).
fof(sk_d3_tarski,plain,
( ! [VAR_0,VAR_1] :
( ~ in(sK3(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK3(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(VAR_2,VAR_1)
| ~ in(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_d3_tarski_sk]) ).
cnf(c_83,plain,
( ~ in(sK3(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_84,plain,
( in(sK3(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_85,plain,
( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_111,negated_conjecture,
( ~ in(B,sK0(sK1,A,B))
| in(B,topstr_closure(sK1,A))
| ~ in(B,the_carrier(sK1))
| ~ element(A,powerset(the_carrier(sK1))) ),
inference(resolve,[status(thm)],[c_44,c_45]) ).
cnf(c_112,negated_conjecture,
( subset(A,sK0(sK1,A,B))
| in(B,topstr_closure(sK1,A))
| ~ in(B,the_carrier(sK1))
| ~ element(A,powerset(the_carrier(sK1))) ),
inference(resolve,[status(thm)],[c_46,c_45]) ).
cnf(c_126,plain,
subset(sK2,the_carrier(sK1)),
inference(resolve,[status(thm)],[c_61,c_54]) ).
cnf(c_140,negated_conjecture,
~ in(sK3(sK2,topstr_closure(sK1,sK2)),topstr_closure(sK1,sK2)),
inference(resolve,[status(thm)],[c_83,c_53]) ).
cnf(c_142,plain,
in(sK3(sK2,topstr_closure(sK1,sK2)),sK2),
inference(resolve,[status(thm)],[c_84,c_53]) ).
cnf(c_196,plain,
( in(A,the_carrier(sK1))
| ~ in(A,sK2) ),
inference(resolve,[status(thm)],[c_126,c_85]) ).
cnf(c_677,plain,
in(sK3(sK2,topstr_closure(sK1,sK2)),the_carrier(sK1)),
inference(resolve,[status(thm)],[c_196,c_142]) ).
cnf(c_2468,plain,
( subset(A,sK0(sK1,A,sK3(sK2,topstr_closure(sK1,sK2))))
| in(sK3(sK2,topstr_closure(sK1,sK2)),topstr_closure(sK1,A))
| ~ element(A,powerset(the_carrier(sK1))) ),
inference(resolve,[status(thm)],[c_677,c_112]) ).
cnf(c_28702,negated_conjecture,
( ~ in(A,sK0(sK1,sK2,A))
| in(A,topstr_closure(sK1,sK2))
| ~ in(A,the_carrier(sK1)) ),
inference(resolve,[status(thm)],[c_111,c_54]) ).
cnf(c_28703,negated_conjecture,
( ~ in(sK3(sK2,topstr_closure(sK1,sK2)),sK0(sK1,sK2,sK3(sK2,topstr_closure(sK1,sK2))))
| in(sK3(sK2,topstr_closure(sK1,sK2)),topstr_closure(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_28702,c_677]) ).
cnf(c_2472,negated_conjecture,
~ in(sK3(sK2,topstr_closure(sK1,sK2)),sK0(sK1,sK2,sK3(sK2,topstr_closure(sK1,sK2)))),
inference(resolve,[status(thm)],[c_28703,c_140]) ).
cnf(c_28704,negated_conjecture,
( subset(sK2,sK0(sK1,sK2,sK3(sK2,topstr_closure(sK1,sK2))))
| in(sK3(sK2,topstr_closure(sK1,sK2)),topstr_closure(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_2468,c_54]) ).
cnf(c_28680,negated_conjecture,
subset(sK2,sK0(sK1,sK2,sK3(sK2,topstr_closure(sK1,sK2)))),
inference(resolve,[status(thm)],[c_140,c_28704]) ).
cnf(c_28705,plain,
( in(sK3(sK2,topstr_closure(sK1,sK2)),A)
| ~ subset(sK2,A) ),
inference(resolve,[status(thm)],[c_85,c_142]) ).
cnf(c_28706,plain,
~ subset(sK2,sK0(sK1,sK2,sK3(sK2,topstr_closure(sK1,sK2)))),
inference(resolve,[status(thm)],[c_28705,c_2472]) ).
cnf(c_28701,plain,
$false,
inference(resolve,[status(thm)],[c_28680,c_28706]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU317+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n007.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 09:09:25 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 3385656 was started by sandbox2 on n007,
% 0.12/0.37 % Sat Sep 26 09:09:25 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 247.74/33.80
% 247.74/33.80 % given #500 (F,wt=6): 1198 -in(c3,f2(powerset(f3(c3)))). [ur(258,b,1192,a)].
% 247.74/33.80
% 247.74/33.80 % given #1000 (A,wt=8): 398 -element(powerset(f3(f3(c5))),f3(f3(c5))). [ur(62,b,368,a,c,235,a)].
% 247.74/33.80
% 247.74/33.80 % given #1500 (T,wt=9): 2607 element(f1(powerset(A),A),powerset(B)) | -empty(A). [resolve(326,b,803,a)].
% 247.74/33.80
% 247.74/33.80 % given #2000 (F,wt=8): 4851 -in(powerset(the_carrier(c4)),powerset(f2(the_carrier(c4)))). [ur(63,b,1001,a)].
% 247.74/33.80
% 247.74/33.80 % given #2500 (T,wt=7): 12669 v5_membered(f2(f3(powerset(f3(f3(c3)))))). [resolve(11349,a,408,a)].
% 247.74/33.80
% 247.74/33.80 % given #3000 (F,wt=9): 2867 -in(f3(f3(f3(c5))),f2(powerset(powerset(empty_set)))). [ur(59,b,82,a,c,1661,a)].
% 247.74/33.80
% 247.74/33.80 % given #3500 (T,wt=10): 11025 element(f1(the_carrier(c4),f2(powerset(f2(c5)))),the_carrier(c4)). [resolve(1062,a,63,a)].
% 247.74/33.80
% 247.74/33.80 % given #4000 (F,wt=9): 8603 -subset(powerset(c3),f1(c3,f1(f3(c3),empty_set))). [ur(85,b,211,a,c,3155,a)].
% 247.74/33.80
% 247.74/33.80 % given #4500 (T,wt=8): 23055 v3_membered(f1(powerset(c3),f1(powerset(c3),c3))). [resolve(19808,a,71,a)].
% 247.74/33.80
% 247.74/33.80 % given #5000 (F,wt=9): 18525 -in(powerset(powerset(A)),powerset(f3(f3(powerset(empty_set))))). [ur(63,b,3689,a)].
% 247.74/33.80
% 247.74/33.80 % given #5500 (A,wt=15): 1702 v4_membered(f1(powerset(f2(powerset(f2(powerset(f3(c3)))))),f2(powerset(f2(powerset(f3(c3))))))). [resolve(1216,a,454,a)].
% 247.74/33.80
% 247.74/33.80 % given #6000 (T,wt=10): 25453 v5_membered(f2(powerset(f1(powerset(c3),f2(f3(f3(c3))))))). [resolve(25424,a,144,a)].
% 247.74/33.80
% 247.74/33.80 % given #6500 (F,wt=10): 5160 -subset(c5,f1(powerset(f1(f3(f3(c5)),empty_set)),empty_set)). [ur(85,b,5118,a,c,1443,a)].
% 247.74/33.80
% 247.74/33.80 % given #7000 (T,wt=11): 7192 v5_membered(f2(powerset(f3(f3(f3(f3(f3(f3(f3(c3)))))))))). [resolve(2807,a,144,a)].
% 247.74/33.80
% 247.74/33.80 % given #7500 (F,wt=10): 10685 -element(powerset(f3(powerset(A))),powerset(f3(f3(powerset(empty_set))))). [ur(236,b,8690,a)].
% 247.74/33.80
% 247.74/33.80 % SZS status Theorem for theBenchmark
% 247.74/33.80
% 247.74/33.80 % Proof 1 at 27.11 (+ 4.12) seconds.
% 247.74/33.80 % Length of proof is 24.
% 247.74/33.80 % Level of proof is 7.
% 247.74/33.80 % Maximum clause weight is 24.000.
% 247.74/33.80 % Given clauses 7993.
% 247.74/33.80
% 247.74/33.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------