%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU144+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 : n016.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 08:45:09 AM UTC 2026
% Result : Theorem 0.33s 15.43s
% Output : CNFRefutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 11 unt; 0 def)
% Number of atoms : 80 ( 12 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 82 ( 36 ~; 32 |; 8 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 23 !; 3 ?)
% 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(l2_zfmisc_1,conjecture,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',l2_zfmisc_1) ).
fof(l2_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
inference(assume_negation,[status(cth)],[l2_zfmisc_1]) ).
cnf(c_8,plain,
( C = A
| ~ in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_9,plain,
( C != A
| in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
fof(nnf_3,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_3]) ).
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_12,plain,
( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_13,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_14,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
fof(nnf_6,plain,
? [A,B] :
( ( ~ in(A,B)
| ~ subset(singleton(A),B) )
& ( in(A,B)
| subset(singleton(A),B) ) ),
inference(fof_nnf,[status(thm)],[l2_zfmisc_1_neg]) ).
fof(sk_l2_zfmisc_1_neg,plain,
( ( ~ in(sK1,sK2)
| ~ subset(singleton(sK1),sK2) )
& ( in(sK1,sK2)
| subset(singleton(sK1),sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2)],[nnf_6]) ).
cnf(c_16,negated_conjecture,
( in(sK1,sK2)
| subset(singleton(sK1),sK2) ),
inference(split_conjunct,[status(thm)],[sk_l2_zfmisc_1_neg]) ).
cnf(c_17,negated_conjecture,
( ~ in(sK1,sK2)
| ~ subset(singleton(sK1),sK2) ),
inference(split_conjunct,[status(thm)],[sk_l2_zfmisc_1_neg]) ).
cnf(c_20,plain,
( A != B
| in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_9]) ).
cnf(c_25,plain,
( in(A,sK2)
| ~ in(A,singleton(sK1))
| in(sK1,sK2) ),
inference(resolve,[status(thm)],[c_16,c_12]) ).
cnf(c_26,plain,
( ~ in(sK1,singleton(sK1))
| in(sK1,sK2) ),
inference(factor,[status(thm)],[c_25]) ).
cnf(c_27,plain,
( in(sK0(singleton(sK1),sK2),singleton(sK1))
| ~ in(sK1,sK2) ),
inference(resolve,[status(thm)],[c_17,c_13]) ).
cnf(c_29,plain,
in(A,singleton(A)),
inference(xxres,[status(thm)],[c_20]) ).
cnf(c_30,plain,
in(sK1,sK2),
inference(resolve,[status(thm)],[c_29,c_26]) ).
cnf(c_31,plain,
in(sK0(singleton(sK1),sK2),singleton(sK1)),
inference(resolve,[status(thm)],[c_30,c_27]) ).
cnf(c_32,negated_conjecture,
~ subset(singleton(sK1),sK2),
inference(resolve,[status(thm)],[c_30,c_17]) ).
cnf(c_34,negated_conjecture,
~ in(sK0(singleton(sK1),sK2),sK2),
inference(resolve,[status(thm)],[c_14,c_32]) ).
cnf(c_193,plain,
( in(A,B)
| ~ subset(singleton(A),B) ),
inference(resolve,[status(thm)],[c_12,c_29]) ).
cnf(c_43,plain,
~ subset(singleton(sK0(singleton(sK1),sK2)),sK2),
inference(resolve,[status(thm)],[c_193,c_34]) ).
cnf(c_194,plain,
( sK0(singleton(sK1),sK2) = A
| singleton(A) != singleton(sK1) ),
inference(resolve,[status(thm)],[c_31,c_8]) ).
cnf(c_46,plain,
( sK0(singleton(sK1),sK2) = A
| singleton(sK1) != singleton(A) ),
inference(copy,[status(thm)],[c_194]) ).
cnf(c_134,plain,
~ in(sK0(singleton(sK0(singleton(sK1),sK2)),sK2),sK2),
inference(resolve,[status(thm)],[c_14,c_43]) ).
cnf(c_191,plain,
sK0(singleton(sK1),sK2) = sK1,
inference(xxres,[status(thm)],[c_46]) ).
cnf(c_195,plain,
~ in(sK0(singleton(sK1),sK2),sK2),
inference(paramod,[status(thm)],[c_191,c_134]) ).
cnf(c_196,plain,
~ in(sK1,sK2),
inference(paramod,[status(thm)],[c_191,c_195]) ).
cnf(c_192,plain,
$false,
inference(resolve,[status(thm)],[c_30,c_196]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU144+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.07/15.40 % CPULimit : 300
% 0.07/15.40 % WCLimit : 300
% 0.07/15.40 % DateTime : Sat Sep 26 08:39:23 UTC 2026
% 0.33/15.40 % CPUTime :
% 0.33/15.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.33/15.40 % Process 2353479 was started by sandbox on n013,
% 0.33/15.40 % Sat Sep 26 08:39:23 2026
% 0.33/15.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.33/15.41
% 0.33/15.41 % From the command line: assign(max_seconds, 300).
% 0.33/15.43
% 0.33/15.43 % SZS status Theorem for theBenchmark
% 0.33/15.43
% 0.33/15.43 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.33/15.43 % Length of proof is 24.
% 0.33/15.43 % Level of proof is 9.
% 0.33/15.43 % Maximum clause weight is 11.000.
% 0.33/15.43 % Given clauses 67.
% 0.33/15.43
% 0.33/15.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------