%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET885+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 : n006.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 0.14s 5.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 41 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 39 ( 19 ~; 10 |; 2 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 36 ( 4 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(t26_zfmisc_1,conjecture,
! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> A = C ),
file('theBenchmark.p',t26_zfmisc_1) ).
fof(t26_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> A = C ),
inference(assume_negation,[status(cth)],[t26_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
& subset(unordered_pair(A,B),singleton(C)) ),
inference(fof_nnf,[status(thm)],[t26_zfmisc_1_neg]) ).
fof(sk_t26_zfmisc_1_neg,plain,
( sK2 != sK0
& subset(unordered_pair(sK0,sK1),singleton(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(unordered_pair(sK0,sK1),singleton(sK2)),
inference(split_conjunct,[status(thm)],[sk_t26_zfmisc_1_neg]) ).
cnf(c_15,negated_conjecture,
( in(A,singleton(sK2))
| ~ in(A,unordered_pair(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_14,c_11]) ).
cnf(c_18,negated_conjecture,
sK2 != sK0,
inference(split_conjunct,[status(thm)],[sk_t26_zfmisc_1_neg]) ).
cnf(c_25,plain,
( 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_313,plain,
( A = B
| ~ in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_30]) ).
cnf(c_314,negated_conjecture,
sK0 != sK2,
inference(copy,[status(thm)],[c_18]) ).
cnf(c_77,negated_conjecture,
~ in(sK0,singleton(sK2)),
inference(resolve,[status(thm)],[c_313,c_314]) ).
cnf(c_175,negated_conjecture,
~ in(sK0,unordered_pair(sK0,sK1)),
inference(resolve,[status(thm)],[c_15,c_77]) ).
cnf(c_315,plain,
( sK0 != A
| unordered_pair(A,B) != unordered_pair(sK0,sK1) ),
inference(resolve,[status(thm)],[c_25,c_175]) ).
cnf(c_316,plain,
unordered_pair(sK0,A) != unordered_pair(sK0,sK1),
inference(xxres,[status(thm)],[c_315]) ).
cnf(c_317,plain,
unordered_pair(sK0,sK1) != unordered_pair(sK0,A),
inference(copy,[status(thm)],[c_316]) ).
cnf(c_312,plain,
$false,
inference(copy,[status(thm)],[c_317]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET885+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.37 % Computer : n006.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Sat Sep 26 08:24:05 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.38 % Process 809954 was started by sandbox on n006,
% 0.08/5.38 % Sat Sep 26 08:24:05 2026
% 0.08/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/5.38
% 0.08/5.38 % From the command line: assign(max_seconds, 300).
% 0.14/5.41
% 0.14/5.41 % SZS status Theorem for theBenchmark
% 0.14/5.41
% 0.14/5.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.14/5.41 % Length of proof is 13.
% 0.14/5.41 % Level of proof is 4.
% 0.14/5.41 % Maximum clause weight is 21.000.
% 0.14/5.41 % Given clauses 44.
% 0.14/5.41
% 0.14/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------