%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET918+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 : n010.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 0.19s 0.53s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 10 unt; 0 def)
% Number of atoms : 52 ( 26 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 51 ( 23 ~; 13 |; 9 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 3 sgn 19 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
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_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(t59_zfmisc_1,conjecture,
! [A,B,C] :
~ ( A != B
& in(B,C)
& set_intersection2(unordered_pair(A,B),C) = singleton(A) ),
file('theBenchmark.p',t59_zfmisc_1) ).
fof(t59_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] :
~ ( A != B
& in(B,C)
& set_intersection2(unordered_pair(A,B),C) = singleton(A) ),
inference(assume_negation,[status(cth)],[t59_zfmisc_1]) ).
cnf(c_12,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_14,plain,
( C = A
| ~ in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_19,plain,
( D != A
| in(D,C)
| unordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d2_tarski]) ).
cnf(c_26,plain,
( ~ in(D,B)
| ~ in(D,A)
| in(D,C)
| set_intersection2(A,B) != C ),
inference(clausify,[status(thm)],[d3_xboole_0]) ).
fof(nnf_10,plain,
? [A,B,C] :
( B != A
& in(B,C)
& singleton(A) = set_intersection2(unordered_pair(A,B),C) ),
inference(fof_nnf,[status(thm)],[t59_zfmisc_1_neg]) ).
fof(sk_t59_zfmisc_1_neg,plain,
( sK1 != sK0
& in(sK1,sK2)
& singleton(sK0) = set_intersection2(unordered_pair(sK0,sK1),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_10]) ).
cnf(c_33,negated_conjecture,
singleton(sK0) = set_intersection2(unordered_pair(sK0,sK1),sK2),
inference(split_conjunct,[status(thm)],[sk_t59_zfmisc_1_neg]) ).
cnf(c_34,negated_conjecture,
in(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t59_zfmisc_1_neg]) ).
cnf(c_35,negated_conjecture,
sK1 != sK0,
inference(split_conjunct,[status(thm)],[sk_t59_zfmisc_1_neg]) ).
cnf(c_66,plain,
( A != C
| in(A,unordered_pair(B,C)) ),
inference(resolve,[status(thm)],[c_19,c_12]) ).
cnf(c_730,plain,
( A = B
| ~ in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_14]) ).
cnf(c_282,negated_conjecture,
~ in(sK1,singleton(sK0)),
inference(resolve,[status(thm)],[c_730,c_35]) ).
cnf(c_731,negated_conjecture,
set_intersection2(unordered_pair(sK0,sK1),sK2) = singleton(sK0),
inference(copy,[status(thm)],[c_33]) ).
cnf(c_732,negated_conjecture,
( ~ in(A,sK2)
| ~ in(A,unordered_pair(sK0,sK1))
| in(A,singleton(sK0)) ),
inference(resolve,[status(thm)],[c_26,c_731]) ).
cnf(c_733,negated_conjecture,
( ~ in(sK1,sK2)
| ~ in(sK1,unordered_pair(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_732,c_282]) ).
cnf(c_433,negated_conjecture,
~ in(sK1,unordered_pair(sK0,sK1)),
inference(resolve,[status(thm)],[c_733,c_34]) ).
cnf(c_728,plain,
in(A,unordered_pair(B,A)),
inference(xxres,[status(thm)],[c_66]) ).
cnf(c_729,plain,
$false,
inference(resolve,[status(thm)],[c_728,c_433]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET918+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n010.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 08:26:16 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.44 % Process 2898894 was started by sandbox on n010,
% 0.19/0.44 % Sat Sep 26 08:26:16 2026
% 0.19/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 0.19/0.53
% 0.19/0.53 % SZS status Theorem for theBenchmark
% 0.19/0.53
% 0.19/0.53 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.19/0.53 % Length of proof is 17.
% 0.19/0.53 % Level of proof is 4.
% 0.19/0.53 % Maximum clause weight is 24.000.
% 0.19/0.53 % Given clauses 53.
% 0.19/0.53
% 0.19/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------