%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET878+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 : n016.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 08:37:12 AM UTC 2026
% Result : Theorem 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 19 unt; 0 def)
% Number of atoms : 34 ( 27 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 25 ( 16 ~; 6 |; 0 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 6 sgn 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_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(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
fof(l32_zfmisc_1,axiom,
! [A,B] :
( in(A,B)
=> set_intersection2(B,singleton(A)) = singleton(A) ),
file('theBenchmark.p',l32_zfmisc_1) ).
fof(t19_zfmisc_1,conjecture,
! [A,B] : set_intersection2(singleton(A),unordered_pair(A,B)) = singleton(A),
file('theBenchmark.p',t19_zfmisc_1) ).
fof(t19_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] : set_intersection2(singleton(A),unordered_pair(A,B)) = singleton(A),
inference(assume_negation,[status(cth)],[t19_zfmisc_1]) ).
cnf(c_11,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_12,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(clausify,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_15,plain,
( D != B
| in(D,C)
| unordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d2_tarski]) ).
cnf(c_19,plain,
set_intersection2(A,A) = A,
inference(clausify,[status(thm)],[idempotence_k3_xboole_0]) ).
cnf(c_20,plain,
( singleton(A) = set_intersection2(B,singleton(A))
| ~ in(A,B) ),
inference(clausify,[status(thm)],[l32_zfmisc_1]) ).
cnf(c_21,plain,
( set_intersection2(B,singleton(A)) = singleton(A)
| ~ in(A,B) ),
inference(copy,[status(thm)],[c_20]) ).
fof(nnf_9,plain,
? [A,B] : singleton(A) != set_intersection2(singleton(A),unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[t19_zfmisc_1_neg]) ).
fof(sk_t19_zfmisc_1_neg,plain,
singleton(sK0) != set_intersection2(singleton(sK0),unordered_pair(sK0,sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_9]) ).
cnf(c_24,negated_conjecture,
singleton(sK0) != set_intersection2(singleton(sK0),unordered_pair(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_t19_zfmisc_1_neg]) ).
cnf(c_71,negated_conjecture,
singleton(sK0) != set_intersection2(unordered_pair(sK0,sK1),singleton(sK0)),
inference(paramod,[status(thm)],[c_12,c_24]) ).
cnf(c_25,negated_conjecture,
set_intersection2(unordered_pair(sK0,sK1),singleton(sK0)) != singleton(sK0),
inference(copy,[status(thm)],[c_71]) ).
cnf(c_56,negated_conjecture,
~ in(sK0,unordered_pair(sK0,sK1)),
inference(resolve,[status(thm)],[c_21,c_25]) ).
cnf(c_72,plain,
( sK0 != B
| unordered_pair(A,B) != unordered_pair(sK0,sK1) ),
inference(resolve,[status(thm)],[c_15,c_56]) ).
cnf(c_73,plain,
A = set_intersection2(A,A),
inference(copy,[status(thm)],[c_19]) ).
cnf(c_74,plain,
unordered_pair(A,set_intersection2(sK0,sK0)) != unordered_pair(sK0,sK1),
inference(resolve,[status(thm)],[c_72,c_73]) ).
cnf(c_75,plain,
unordered_pair(A,sK0) != unordered_pair(sK0,sK1),
inference(paramod,[status(thm)],[c_19,c_74]) ).
cnf(c_69,plain,
unordered_pair(sK0,sK1) != unordered_pair(A,sK0),
inference(copy,[status(thm)],[c_75]) ).
cnf(c_70,plain,
$false,
inference(resolve,[status(thm)],[c_69,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET878+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 08:28:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 421406 was started by sandbox on n016,
% 0.10/0.37 % Sat Sep 26 08:28:45 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SZS status Theorem for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/0.39 % Length of proof is 17.
% 0.10/0.39 % Level of proof is 5.
% 0.10/0.39 % Maximum clause weight is 11.000.
% 0.10/0.39 % Given clauses 19.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------