%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET941+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 08:37:20 AM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 8 unt; 0 def)
% Number of atoms : 117 ( 17 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 141 ( 54 ~; 55 |; 24 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 79 ( 0 sgn 54 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
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(t94_zfmisc_1,conjecture,
! [A,B] :
( ! [C] :
( in(C,A)
=> subset(C,B) )
=> subset(union(A),B) ),
file('theBenchmark.p',t94_zfmisc_1) ).
fof(t94_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( ! [C] :
( in(C,A)
=> subset(C,B) )
=> subset(union(A),B) ),
inference(assume_negation,[status(cth)],[t94_zfmisc_1]) ).
fof(nnf_2,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(sK0(A,B),B)
& in(sK0(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0(A,B))],[nnf_2]) ).
fof(sk_d3_tarski,plain,
( ! [VAR_0,VAR_1] :
( ~ in(sK0(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK0(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_9,plain,
( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_10,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_11,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
fof(nnf_3,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(sK4(A,B),D) )
| ~ in(sK4(A,B),B) )
& ( ( in(sK5(A,B),A)
& in(sK4(A,B),sK5(A,B)) )
| in(sK4(A,B),B) ) )
| union(A) = B )
& ( ! [X1] :
( ( ! [X3] :
( ~ in(X3,A)
| ~ in(X1,X3) )
| in(X1,B) )
& ( ( in(sK1(A,B,X1),A)
& in(X1,sK1(A,B,X1)) )
| ~ in(X1,B) ) )
| union(A) != B ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK4,sK5]),skolemize(X2,sK1(A,B,X1)),skolemize(C,sK4(A,B)),skolemize(X0,sK5(A,B))],[nnf_3]) ).
fof(sk_d4_tarski,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ in(VAR_2,VAR_0)
| ~ in(sK4(VAR_0,VAR_1),VAR_2)
| ~ in(sK4(VAR_0,VAR_1),VAR_1)
| union(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1] :
( in(sK5(VAR_0,VAR_1),VAR_0)
| in(sK4(VAR_0,VAR_1),VAR_1)
| union(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1] :
( in(sK4(VAR_0,VAR_1),sK5(VAR_0,VAR_1))
| in(sK4(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(sK1(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,sK1(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_12,plain,
( in(C,sK1(A,B,C))
| ~ in(C,B)
| union(A) != B ),
inference(split_conjunct,[status(thm)],[sk_d4_tarski]) ).
cnf(c_13,plain,
( in(sK1(A,B,C),A)
| ~ in(C,B)
| union(A) != B ),
inference(split_conjunct,[status(thm)],[sk_d4_tarski]) ).
fof(nnf_7,plain,
? [A,B] :
( ~ subset(union(A),B)
& ! [C] :
( subset(C,B)
| ~ in(C,A) ) ),
inference(fof_nnf,[status(thm)],[t94_zfmisc_1_neg]) ).
fof(sk_t94_zfmisc_1_neg,plain,
( ~ subset(union(sK2),sK3)
& ! [C] :
( subset(C,sK3)
| ~ in(C,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(A,sK2),skolemize(B,sK3)],[nnf_7]) ).
cnf(c_21,negated_conjecture,
( subset(A,sK3)
| ~ in(A,sK2) ),
inference(split_conjunct,[status(thm)],[sk_t94_zfmisc_1_neg]) ).
cnf(c_22,negated_conjecture,
~ subset(union(sK2),sK3),
inference(split_conjunct,[status(thm)],[sk_t94_zfmisc_1_neg]) ).
cnf(c_42,plain,
in(sK0(union(sK2),sK3),union(sK2)),
inference(resolve,[status(thm)],[c_22,c_10]) ).
cnf(c_44,negated_conjecture,
~ in(sK0(union(sK2),sK3),sK3),
inference(resolve,[status(thm)],[c_11,c_22]) ).
cnf(c_183,plain,
( in(sK1(A,union(sK2),sK0(union(sK2),sK3)),A)
| union(A) != union(sK2) ),
inference(resolve,[status(thm)],[c_42,c_13]) ).
cnf(c_52,plain,
( in(sK1(A,union(sK2),sK0(union(sK2),sK3)),A)
| union(sK2) != union(A) ),
inference(copy,[status(thm)],[c_183]) ).
cnf(c_110,plain,
in(sK1(sK2,union(sK2),sK0(union(sK2),sK3)),sK2),
inference(xxres,[status(thm)],[c_52]) ).
cnf(c_114,plain,
subset(sK1(sK2,union(sK2),sK0(union(sK2),sK3)),sK3),
inference(resolve,[status(thm)],[c_110,c_21]) ).
cnf(c_184,plain,
( in(A,sK3)
| ~ in(A,sK1(sK2,union(sK2),sK0(union(sK2),sK3))) ),
inference(resolve,[status(thm)],[c_9,c_114]) ).
cnf(c_125,plain,
~ in(sK0(union(sK2),sK3),sK1(sK2,union(sK2),sK0(union(sK2),sK3))),
inference(resolve,[status(thm)],[c_184,c_44]) ).
cnf(c_185,plain,
( in(sK0(union(sK2),sK3),sK1(A,union(sK2),sK0(union(sK2),sK3)))
| union(A) != union(sK2) ),
inference(resolve,[status(thm)],[c_12,c_42]) ).
cnf(c_186,plain,
union(sK2) != union(sK2),
inference(resolve,[status(thm)],[c_185,c_125]) ).
cnf(c_182,plain,
$false,
inference(copy,[status(thm)],[c_186]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET941+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n005.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 26 08:27:16 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 1690865 was started by sandbox on n005,
% 0.07/0.35 % Sat Sep 26 08:27:16 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.36
% 0.07/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.39
% 0.13/0.39 % SZS status Theorem for theBenchmark
% 0.13/0.39
% 0.13/0.39 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.13/0.39 % Length of proof is 17.
% 0.13/0.39 % Level of proof is 7.
% 0.13/0.39 % Maximum clause weight is 15.000.
% 0.13/0.39 % Given clauses 65.
% 0.13/0.39
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------