%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU164+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 : n005.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 08:45:16 AM UTC 2026
% Result : Theorem 0.23s 0.66s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 13 unt; 0 def)
% Number of atoms : 110 ( 25 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 126 ( 49 ~; 55 |; 16 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-3 aty)
% Number of variables : 74 ( 1 sgn 40 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('theBenchmark.p',d1_zfmisc_1) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d4_tarski,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('theBenchmark.p',d4_tarski) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t99_zfmisc_1,conjecture,
! [A] : union(powerset(A)) = A,
file('theBenchmark.p',t99_zfmisc_1) ).
fof(t99_zfmisc_1_neg,negated_conjecture,
~ ! [A] : union(powerset(A)) = A,
inference(assume_negation,[status(cth)],[t99_zfmisc_1]) ).
cnf(c_18,plain,
( subset(C,A)
| ~ in(C,B)
| powerset(A) != B ),
inference(clausify,[status(thm)],[d1_zfmisc_1]) ).
cnf(c_19,plain,
( ~ subset(C,A)
| in(C,B)
| powerset(A) != B ),
inference(clausify,[status(thm)],[d1_zfmisc_1]) ).
cnf(c_22,plain,
( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[d3_tarski]) ).
fof(nnf_5,plain,
! [A,B] :
( ( ? [C] :
( ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| ~ in(C,B) )
& ( ? [X0] :
( in(X0,A)
& in(C,X0) )
| in(C,B) ) )
| union(A) = B )
& ( ! [X1] :
( ( ! [X3] :
( ~ in(X3,A)
| ~ in(X1,X3) )
| in(X1,B) )
& ( ? [X2] :
( in(X2,A)
& in(X1,X2) )
| ~ in(X1,B) ) )
| union(A) != B ) ),
inference(fof_nnf,[status(thm)],[d4_tarski]) ).
fof(sk_d4_tarski_sk,plain,
! [A,B] :
( ( ( ( ! [D] :
( ~ in(D,A)
| ~ in(sK0(A,B),D) )
| ~ in(sK0(A,B),B) )
& ( ( in(sK1(A,B),A)
& in(sK0(A,B),sK1(A,B)) )
| in(sK0(A,B),B) ) )
| union(A) = B )
& ( ! [X1] :
( ( ! [X3] :
( ~ in(X3,A)
| ~ in(X1,X3) )
| in(X1,B) )
& ( ( in(sK5(A,B,X1),A)
& in(X1,sK5(A,B,X1)) )
| ~ in(X1,B) ) )
| union(A) != B ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK0,sK1]),skolemize(X2,sK5(A,B,X1)),skolemize(C,sK0(A,B)),skolemize(X0,sK1(A,B))],[nnf_5]) ).
fof(sk_d4_tarski,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ in(VAR_2,VAR_0)
| ~ in(sK0(VAR_0,VAR_1),VAR_2)
| ~ in(sK0(VAR_0,VAR_1),VAR_1)
| union(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1] :
( in(sK1(VAR_0,VAR_1),VAR_0)
| in(sK0(VAR_0,VAR_1),VAR_1)
| union(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1] :
( in(sK0(VAR_0,VAR_1),sK1(VAR_0,VAR_1))
| in(sK0(VAR_0,VAR_1),VAR_1)
| union(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ in(VAR_3,VAR_0)
| ~ in(VAR_2,VAR_3)
| in(VAR_2,VAR_1)
| union(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( in(sK5(VAR_0,VAR_1,VAR_2),VAR_0)
| ~ in(VAR_2,VAR_1)
| union(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( in(VAR_2,sK5(VAR_0,VAR_1,VAR_2))
| ~ in(VAR_2,VAR_1)
| union(VAR_0) != VAR_1 ) ),
inference(cnf_transformation,[status(thm)],[sk_d4_tarski_sk]) ).
cnf(c_28,plain,
( in(sK0(A,B),sK1(A,B))
| in(sK0(A,B),B)
| union(A) = B ),
inference(split_conjunct,[status(thm)],[sk_d4_tarski]) ).
cnf(c_29,plain,
( in(sK1(A,B),A)
| in(sK0(A,B),B)
| union(A) = B ),
inference(split_conjunct,[status(thm)],[sk_d4_tarski]) ).
cnf(c_30,plain,
( ~ in(C,A)
| ~ in(sK0(A,B),C)
| ~ in(sK0(A,B),B)
| union(A) = B ),
inference(split_conjunct,[status(thm)],[sk_d4_tarski]) ).
cnf(c_33,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
fof(nnf_12,plain,
? [A] : union(powerset(A)) != A,
inference(fof_nnf,[status(thm)],[t99_zfmisc_1_neg]) ).
fof(sk_t99_zfmisc_1_neg,plain,
union(powerset(sK2)) != sK2,
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(A,sK2)],[nnf_12]) ).
cnf(c_36,negated_conjecture,
union(powerset(sK2)) != sK2,
inference(split_conjunct,[status(thm)],[sk_t99_zfmisc_1_neg]) ).
cnf(c_39,plain,
( ~ in(B,A)
| ~ in(sK0(A,B),B)
| union(A) = B ),
inference(factor,[status(thm)],[c_30]) ).
cnf(c_45,plain,
( subset(A,B)
| ~ in(A,powerset(B)) ),
inference(xxres,[status(thm)],[c_18]) ).
cnf(c_47,plain,
( ~ subset(A,B)
| in(A,powerset(B)) ),
inference(xxres,[status(thm)],[c_19]) ).
cnf(c_65,plain,
( in(sK0(A,B),C)
| ~ subset(sK1(A,B),C)
| in(sK0(A,B),B)
| union(A) = B ),
inference(resolve,[status(thm)],[c_28,c_22]) ).
cnf(c_157,plain,
in(A,powerset(A)),
inference(resolve,[status(thm)],[c_47,c_33]) ).
cnf(c_790,negated_conjecture,
( ~ in(sK2,powerset(sK2))
| ~ in(sK0(powerset(sK2),sK2),sK2) ),
inference(resolve,[status(thm)],[c_39,c_36]) ).
cnf(c_172,negated_conjecture,
~ in(sK0(powerset(sK2),sK2),sK2),
inference(resolve,[status(thm)],[c_790,c_157]) ).
cnf(c_791,negated_conjecture,
( in(sK0(powerset(sK2),sK2),A)
| ~ subset(sK1(powerset(sK2),sK2),A)
| in(sK0(powerset(sK2),sK2),sK2) ),
inference(resolve,[status(thm)],[c_65,c_36]) ).
cnf(c_792,negated_conjecture,
( in(sK0(powerset(sK2),sK2),A)
| ~ subset(sK1(powerset(sK2),sK2),A) ),
inference(resolve,[status(thm)],[c_791,c_172]) ).
cnf(c_781,negated_conjecture,
~ subset(sK1(powerset(sK2),sK2),sK2),
inference(resolve,[status(thm)],[c_792,c_172]) ).
cnf(c_787,plain,
~ in(sK1(powerset(sK2),sK2),powerset(sK2)),
inference(resolve,[status(thm)],[c_45,c_781]) ).
cnf(c_793,plain,
( in(sK0(powerset(sK2),sK2),sK2)
| union(powerset(sK2)) = sK2 ),
inference(resolve,[status(thm)],[c_787,c_29]) ).
cnf(c_794,negated_conjecture,
in(sK0(powerset(sK2),sK2),sK2),
inference(resolve,[status(thm)],[c_36,c_793]) ).
cnf(c_789,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_172,c_794]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU164+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n005.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 08:42:46 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.46 % Process 1726740 was started by sandbox2 on n005,
% 0.19/0.46 % Sat Sep 26 08:42:46 2026
% 0.19/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.47
% 0.19/0.47 % From the command line: assign(max_seconds, 300).
% 0.23/0.66
% 0.23/0.66 % SZS status Theorem for theBenchmark
% 0.23/0.66
% 0.23/0.66 % Proof 1 at 0.12 (+ 0.05) seconds.
% 0.23/0.66 % Length of proof is 22.
% 0.23/0.66 % Level of proof is 7.
% 0.23/0.66 % Maximum clause weight is 29.000.
% 0.23/0.66 % Given clauses 122.
% 0.23/0.66
% 0.23/0.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------