%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET884+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 : n020.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 0.18s 0.50s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 9 unt; 0 def)
% Number of atoms : 50 ( 26 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 53 ( 26 ~; 13 |; 8 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 16 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
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(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(t25_zfmisc_1,conjecture,
! [A,B,C] :
~ ( A != C
& A != B
& subset(singleton(A),unordered_pair(B,C)) ),
file('theBenchmark.p',t25_zfmisc_1) ).
fof(t25_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] :
~ ( A != C
& A != B
& subset(singleton(A),unordered_pair(B,C)) ),
inference(assume_negation,[status(cth)],[t25_zfmisc_1]) ).
cnf(c_11,plain,
( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[d3_tarski]) ).
fof(nnf_9,plain,
? [A,B,C] :
( C != A
& B != A
& subset(singleton(A),unordered_pair(B,C)) ),
inference(fof_nnf,[status(thm)],[t25_zfmisc_1_neg]) ).
fof(sk_t25_zfmisc_1_neg,plain,
( sK2 != sK0
& sK1 != sK0
& subset(singleton(sK0),unordered_pair(sK1,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_9]) ).
cnf(c_14,negated_conjecture,
subset(singleton(sK0),unordered_pair(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_t25_zfmisc_1_neg]) ).
cnf(c_15,negated_conjecture,
( in(A,unordered_pair(sK1,sK2))
| ~ in(A,singleton(sK0)) ),
inference(resolve,[status(thm)],[c_14,c_11]) ).
cnf(c_18,negated_conjecture,
sK2 != sK0,
inference(split_conjunct,[status(thm)],[sk_t25_zfmisc_1_neg]) ).
cnf(c_19,negated_conjecture,
sK1 != sK0,
inference(split_conjunct,[status(thm)],[sk_t25_zfmisc_1_neg]) ).
cnf(c_27,plain,
( D = B
| D = A
| ~ in(D,C)
| unordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d2_tarski]) ).
cnf(c_30,plain,
( C != A
| in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_166,plain,
( A = C
| A = B
| ~ in(A,unordered_pair(B,C)) ),
inference(xxres,[status(thm)],[c_27]) ).
cnf(c_167,negated_conjecture,
sK0 != sK1,
inference(copy,[status(thm)],[c_19]) ).
cnf(c_168,negated_conjecture,
( sK0 = A
| ~ in(sK0,unordered_pair(sK1,A)) ),
inference(resolve,[status(thm)],[c_166,c_167]) ).
cnf(c_169,negated_conjecture,
sK0 != sK2,
inference(copy,[status(thm)],[c_18]) ).
cnf(c_54,negated_conjecture,
~ in(sK0,unordered_pair(sK1,sK2)),
inference(resolve,[status(thm)],[c_168,c_169]) ).
cnf(c_76,plain,
( A != B
| in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_30]) ).
cnf(c_158,plain,
in(A,singleton(A)),
inference(xxres,[status(thm)],[c_76]) ).
cnf(c_170,negated_conjecture,
in(sK0,unordered_pair(sK1,sK2)),
inference(resolve,[status(thm)],[c_158,c_15]) ).
cnf(c_165,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_54,c_170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET884+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n020.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 08:25:04 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 1078573 was started by sandbox2 on n020,
% 0.18/0.45 % Sat Sep 26 08:25:04 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 0.18/0.50
% 0.18/0.50 % SZS status Theorem for theBenchmark
% 0.18/0.50
% 0.18/0.50 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.18/0.50 % Length of proof is 15.
% 0.18/0.50 % Level of proof is 4.
% 0.18/0.50 % Maximum clause weight is 14.000.
% 0.18/0.50 % Given clauses 32.
% 0.18/0.50
% 0.18/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------