%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU155+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 : n013.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 08:45:13 AM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 6 unt; 0 def)
% Number of atoms : 53 ( 2 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 56 ( 23 ~; 18 |; 9 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 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 : 39 ( 0 sgn 23 !; 4 ?)
% 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(l50_zfmisc_1,conjecture,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('theBenchmark.p',l50_zfmisc_1) ).
fof(l50_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
inference(assume_negation,[status(cth)],[l50_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(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_10,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_13,plain,
( ~ in(D,A)
| ~ in(C,D)
| in(C,B)
| union(A) != B ),
inference(clausify,[status(thm)],[d4_tarski]) ).
fof(nnf_6,plain,
? [A,B] :
( ~ subset(A,union(B))
& in(A,B) ),
inference(fof_nnf,[status(thm)],[l50_zfmisc_1_neg]) ).
fof(sk_l50_zfmisc_1_neg,plain,
( ~ subset(sK1,union(sK2))
& in(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2)],[nnf_6]) ).
cnf(c_18,negated_conjecture,
in(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_l50_zfmisc_1_neg]) ).
cnf(c_19,negated_conjecture,
~ subset(sK1,union(sK2)),
inference(split_conjunct,[status(thm)],[sk_l50_zfmisc_1_neg]) ).
cnf(c_62,plain,
in(sK0(sK1,union(sK2)),sK1),
inference(resolve,[status(thm)],[c_19,c_9]) ).
cnf(c_63,negated_conjecture,
~ in(sK0(sK1,union(sK2)),union(sK2)),
inference(resolve,[status(thm)],[c_10,c_19]) ).
cnf(c_101,plain,
( ~ in(C,B)
| ~ in(A,C)
| in(A,union(B)) ),
inference(xxres,[status(thm)],[c_13]) ).
cnf(c_102,plain,
( ~ in(A,sK2)
| ~ in(sK0(sK1,union(sK2)),A) ),
inference(resolve,[status(thm)],[c_101,c_63]) ).
cnf(c_103,negated_conjecture,
~ in(sK0(sK1,union(sK2)),sK1),
inference(resolve,[status(thm)],[c_102,c_18]) ).
cnf(c_100,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_62,c_103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU155+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 08:41:07 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2357034 was started by sandbox on n013,
% 0.09/0.37 % Sat Sep 26 08:41:07 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.38
% 0.14/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.39
% 0.14/0.39 % Assigning unary symbol union kb_weight 0 and highest precedence (10).
% 0.14/0.39
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39
% 0.14/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.39 % Length of proof is 11.
% 0.14/0.39 % Level of proof is 3.
% 0.14/0.39 % Maximum clause weight is 23.000.
% 0.14/0.39 % Given clauses 29.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------