%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET890+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 08:37:14 AM UTC 2026
% Result : Theorem 0.03s 0.42s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 14 unt; 0 def)
% Number of atoms : 111 ( 32 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_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
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(t31_zfmisc_1,conjecture,
! [A] : union(singleton(A)) = A,
file('theBenchmark.p',t31_zfmisc_1) ).
fof(t31_zfmisc_1_neg,negated_conjecture,
~ ! [A] : union(singleton(A)) = A,
inference(assume_negation,[status(cth)],[t31_zfmisc_1]) ).
cnf(c_15,plain,
( C = A
| ~ in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_16,plain,
( C != A
| in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_19,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_25,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_26,plain,
( in(sK1(A,B),A)
| in(sK0(A,B),B)
| union(A) = B ),
inference(split_conjunct,[status(thm)],[sk_d4_tarski]) ).
cnf(c_27,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_31,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
fof(nnf_10,plain,
? [A] : union(singleton(A)) != A,
inference(fof_nnf,[status(thm)],[t31_zfmisc_1_neg]) ).
fof(sk_t31_zfmisc_1_neg,plain,
union(singleton(sK2)) != sK2,
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(A,sK2)],[nnf_10]) ).
cnf(c_32,negated_conjecture,
union(singleton(sK2)) != sK2,
inference(split_conjunct,[status(thm)],[sk_t31_zfmisc_1_neg]) ).
cnf(c_35,plain,
( ~ in(B,A)
| ~ in(sK0(A,B),B)
| union(A) = B ),
inference(factor,[status(thm)],[c_27]) ).
cnf(c_36,plain,
( A = B
| ~ in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_15]) ).
cnf(c_37,plain,
( A != B
| in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_16]) ).
cnf(c_56,plain,
( in(sK0(A,B),C)
| ~ subset(sK1(A,B),C)
| in(sK0(A,B),B)
| union(A) = B ),
inference(resolve,[status(thm)],[c_25,c_19]) ).
cnf(c_60,plain,
( ~ subset(sK1(A,B),B)
| in(sK0(A,B),B)
| union(A) = B ),
inference(factor,[status(thm)],[c_56]) ).
cnf(c_99,plain,
in(A,singleton(A)),
inference(xxres,[status(thm)],[c_37]) ).
cnf(c_265,negated_conjecture,
( ~ in(sK2,singleton(sK2))
| ~ in(sK0(singleton(sK2),sK2),sK2) ),
inference(resolve,[status(thm)],[c_35,c_32]) ).
cnf(c_111,negated_conjecture,
~ in(sK0(singleton(sK2),sK2),sK2),
inference(resolve,[status(thm)],[c_265,c_99]) ).
cnf(c_266,plain,
( in(sK1(singleton(sK2),sK2),singleton(sK2))
| union(singleton(sK2)) = sK2 ),
inference(resolve,[status(thm)],[c_111,c_26]) ).
cnf(c_140,negated_conjecture,
in(sK1(singleton(sK2),sK2),singleton(sK2)),
inference(resolve,[status(thm)],[c_32,c_266]) ).
cnf(c_210,plain,
sK1(singleton(sK2),sK2) = sK2,
inference(resolve,[status(thm)],[c_140,c_36]) ).
cnf(c_267,negated_conjecture,
( ~ subset(sK1(singleton(sK2),sK2),sK2)
| in(sK0(singleton(sK2),sK2),sK2) ),
inference(resolve,[status(thm)],[c_60,c_32]) ).
cnf(c_268,negated_conjecture,
~ subset(sK1(singleton(sK2),sK2),sK2),
inference(resolve,[status(thm)],[c_267,c_111]) ).
cnf(c_269,negated_conjecture,
~ subset(sK2,sK2),
inference(paramod,[status(thm)],[c_210,c_268]) ).
cnf(c_264,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_31,c_269]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET890+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n004.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
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 08:24:24 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.36 % Process 1234580 was started by sandbox2 on n004,
% 0.03/0.36 % Sat Sep 26 08:24:24 2026
% 0.03/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.37
% 0.03/0.37 % From the command line: assign(max_seconds, 300).
% 0.03/0.42
% 0.03/0.42 % SZS status Theorem for theBenchmark
% 0.03/0.42
% 0.03/0.42 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.03/0.42 % Length of proof is 23.
% 0.03/0.42 % Level of proof is 7.
% 0.03/0.42 % Maximum clause weight is 29.000.
% 0.03/0.42 % Given clauses 75.
% 0.03/0.42
% 0.03/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------