%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET920+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 : n019.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 08:37:17 AM UTC 2026
% Result : Theorem 0.18s 0.68s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 5 unt; 0 def)
% Number of atoms : 31 ( 13 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 27 ( 11 ~; 7 |; 3 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 31 ( 4 sgn 14 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d3_xboole_0) ).
fof(t63_zfmisc_1,conjecture,
! [A,B,C] :
( set_intersection2(unordered_pair(A,B),C) = unordered_pair(A,B)
=> in(A,C) ),
file('theBenchmark.p',t63_zfmisc_1) ).
fof(t63_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] :
( set_intersection2(unordered_pair(A,B),C) = unordered_pair(A,B)
=> in(A,C) ),
inference(assume_negation,[status(cth)],[t63_zfmisc_1]) ).
cnf(c_14,plain,
( D != A
| in(D,C)
| unordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d2_tarski]) ).
cnf(c_20,plain,
( in(D,B)
| ~ in(D,C)
| set_intersection2(A,B) != C ),
inference(clausify,[status(thm)],[d3_xboole_0]) ).
fof(nnf_9,plain,
? [A,B,C] :
( ~ in(A,C)
& set_intersection2(unordered_pair(A,B),C) = unordered_pair(A,B) ),
inference(fof_nnf,[status(thm)],[t63_zfmisc_1_neg]) ).
fof(sk_t63_zfmisc_1_neg,plain,
( ~ in(sK0,sK2)
& set_intersection2(unordered_pair(sK0,sK1),sK2) = unordered_pair(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_9]) ).
cnf(c_28,negated_conjecture,
set_intersection2(unordered_pair(sK0,sK1),sK2) = unordered_pair(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t63_zfmisc_1_neg]) ).
cnf(c_29,negated_conjecture,
~ in(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_t63_zfmisc_1_neg]) ).
cnf(c_42,plain,
( A != B
| in(A,unordered_pair(B,C)) ),
inference(xxres,[status(thm)],[c_14]) ).
cnf(c_208,negated_conjecture,
( in(A,sK2)
| ~ in(A,unordered_pair(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_20,c_28]) ).
cnf(c_131,negated_conjecture,
~ in(sK0,unordered_pair(sK0,sK1)),
inference(resolve,[status(thm)],[c_208,c_29]) ).
cnf(c_206,plain,
in(A,unordered_pair(A,B)),
inference(xxres,[status(thm)],[c_42]) ).
cnf(c_207,plain,
$false,
inference(resolve,[status(thm)],[c_206,c_131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET920+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.61 % Computer : n019.cluster.edu
% 0.13/0.61 % Model : x86_64 x86_64
% 0.13/0.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.61 % Memory : 8046.5625MB
% 0.13/0.61 % OS : Linux 6.8.0-71-generic
% 0.13/0.62 % CPULimit : 300
% 0.13/0.62 % WCLimit : 300
% 0.13/0.62 % DateTime : Sat Sep 26 08:25:50 UTC 2026
% 0.13/0.62 % CPUTime :
% 0.13/0.62 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.62 % Process 849343 was started by sandbox2 on n019,
% 0.13/0.62 % Sat Sep 26 08:25:50 2026
% 0.13/0.62 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.63
% 0.13/0.63 % From the command line: assign(max_seconds, 300).
% 0.18/0.68
% 0.18/0.68 % SZS status Theorem for theBenchmark
% 0.18/0.68
% 0.18/0.68 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.18/0.68 % Length of proof is 11.
% 0.18/0.68 % Level of proof is 4.
% 0.18/0.68 % Maximum clause weight is 24.000.
% 0.18/0.68 % Given clauses 31.
% 0.18/0.68
% 0.18/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------