%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET887+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 08:37:13 AM UTC 2026
% Result : Theorem 0.20s 0.49s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 12 unt; 0 def)
% Number of atoms : 72 ( 59 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 79 ( 39 ~; 22 |; 13 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 55 ( 13 sgn 24 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_tarski) ).
fof(l46_zfmisc_1,axiom,
! [A,B,C] :
( subset(A,unordered_pair(B,C))
<=> ~ ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set ) ),
file('theBenchmark.p',l46_zfmisc_1) ).
fof(t10_zfmisc_1,axiom,
! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
file('theBenchmark.p',t10_zfmisc_1) ).
fof(t8_zfmisc_1,axiom,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
file('theBenchmark.p',t8_zfmisc_1) ).
fof(t28_zfmisc_1,conjecture,
! [A,B,C,D] :
~ ( A != D
& A != C
& subset(unordered_pair(A,B),unordered_pair(C,D)) ),
file('theBenchmark.p',t28_zfmisc_1) ).
fof(t28_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C,D] :
~ ( A != D
& A != C
& subset(unordered_pair(A,B),unordered_pair(C,D)) ),
inference(assume_negation,[status(cth)],[t28_zfmisc_1]) ).
cnf(c_14,plain,
( ~ in(B,A)
| empty_set != A ),
inference(clausify,[status(thm)],[d1_xboole_0]) ).
cnf(c_18,plain,
( D != B
| in(D,C)
| unordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d2_tarski]) ).
cnf(c_23,plain,
( unordered_pair(B,C) = A
| singleton(C) = A
| singleton(B) = A
| empty_set = A
| ~ subset(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[l46_zfmisc_1]) ).
cnf(c_31,plain,
( B = C
| A = C
| unordered_pair(A,B) != unordered_pair(C,D) ),
inference(clausify,[status(thm)],[t10_zfmisc_1]) ).
cnf(c_32,plain,
( B = A
| singleton(A) != unordered_pair(B,C) ),
inference(clausify,[status(thm)],[t8_zfmisc_1]) ).
fof(nnf_11,plain,
? [A,B,C,D] :
( D != A
& C != A
& subset(unordered_pair(A,B),unordered_pair(C,D)) ),
inference(fof_nnf,[status(thm)],[t28_zfmisc_1_neg]) ).
fof(sk_t28_zfmisc_1_neg,plain,
( sK3 != sK0
& sK2 != sK0
& subset(unordered_pair(sK0,sK1),unordered_pair(sK2,sK3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK3)],[nnf_11]) ).
cnf(c_33,negated_conjecture,
subset(unordered_pair(sK0,sK1),unordered_pair(sK2,sK3)),
inference(split_conjunct,[status(thm)],[sk_t28_zfmisc_1_neg]) ).
cnf(c_34,negated_conjecture,
sK2 != sK0,
inference(split_conjunct,[status(thm)],[sk_t28_zfmisc_1_neg]) ).
cnf(c_35,negated_conjecture,
sK3 != sK0,
inference(split_conjunct,[status(thm)],[sk_t28_zfmisc_1_neg]) ).
cnf(c_43,plain,
~ in(A,empty_set),
inference(xxres,[status(thm)],[c_14]) ).
cnf(c_109,negated_conjecture,
( unordered_pair(sK2,sK3) = unordered_pair(sK0,sK1)
| singleton(sK3) = unordered_pair(sK0,sK1)
| singleton(sK2) = unordered_pair(sK0,sK1)
| empty_set = unordered_pair(sK0,sK1) ),
inference(resolve,[status(thm)],[c_33,c_23]) ).
cnf(c_79,negated_conjecture,
( unordered_pair(sK2,sK3) = unordered_pair(sK0,sK1)
| singleton(sK3) = unordered_pair(sK0,sK1)
| singleton(sK2) = unordered_pair(sK0,sK1)
| unordered_pair(sK0,sK1) = empty_set ),
inference(copy,[status(thm)],[c_109]) ).
cnf(c_110,negated_conjecture,
sK0 != sK2,
inference(copy,[status(thm)],[c_34]) ).
cnf(c_85,negated_conjecture,
singleton(sK2) != unordered_pair(sK0,A),
inference(resolve,[status(thm)],[c_32,c_110]) ).
cnf(c_88,negated_conjecture,
( unordered_pair(sK2,sK3) = unordered_pair(sK0,sK1)
| singleton(sK3) = unordered_pair(sK0,sK1)
| unordered_pair(sK0,sK1) = empty_set ),
inference(resolve,[status(thm)],[c_85,c_79]) ).
cnf(c_111,negated_conjecture,
( A = sK0
| unordered_pair(sK2,A) != unordered_pair(sK0,B) ),
inference(resolve,[status(thm)],[c_31,c_34]) ).
cnf(c_91,negated_conjecture,
unordered_pair(sK2,sK3) != unordered_pair(sK0,A),
inference(resolve,[status(thm)],[c_111,c_35]) ).
cnf(c_112,negated_conjecture,
sK0 != sK3,
inference(copy,[status(thm)],[c_35]) ).
cnf(c_94,negated_conjecture,
singleton(sK3) != unordered_pair(sK0,A),
inference(resolve,[status(thm)],[c_32,c_112]) ).
cnf(c_113,negated_conjecture,
( unordered_pair(sK2,sK3) = unordered_pair(sK0,sK1)
| unordered_pair(sK0,sK1) = empty_set ),
inference(resolve,[status(thm)],[c_94,c_88]) ).
cnf(c_99,negated_conjecture,
unordered_pair(sK0,sK1) = empty_set,
inference(resolve,[status(thm)],[c_91,c_113]) ).
cnf(c_114,plain,
( C != B
| unordered_pair(A,B) != empty_set ),
inference(resolve,[status(thm)],[c_18,c_43]) ).
cnf(c_107,plain,
unordered_pair(A,B) != empty_set,
inference(xxres,[status(thm)],[c_114]) ).
cnf(c_108,plain,
$false,
inference(resolve,[status(thm)],[c_107,c_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET887+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n004.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sat Sep 26 08:23:51 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.46 % Process 1232789 was started by sandbox2 on n004,
% 0.20/0.46 % Sat Sep 26 08:23:51 2026
% 0.20/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.20/0.46
% 0.20/0.46 % From the command line: assign(max_seconds, 300).
% 0.20/0.49
% 0.20/0.49 % SZS status Theorem for theBenchmark
% 0.20/0.49
% 0.20/0.49 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.20/0.49 % Length of proof is 23.
% 0.20/0.49 % Level of proof is 5.
% 0.20/0.49 % Maximum clause weight is 34.000.
% 0.20/0.49 % Given clauses 30.
% 0.20/0.49
% 0.20/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------