%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET881+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 : n014.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 5.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 11 unt; 0 def)
% Number of atoms : 24 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 12 ~; 5 |; 0 &)
% ( 3 <=>; 0 =>; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 4 sgn 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_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(l36_zfmisc_1,axiom,
! [A,B] :
( set_difference(singleton(A),B) = empty_set
<=> in(A,B) ),
file('theBenchmark.p',l36_zfmisc_1) ).
fof(t22_zfmisc_1,conjecture,
! [A,B] : set_difference(singleton(A),unordered_pair(A,B)) = empty_set,
file('theBenchmark.p',t22_zfmisc_1) ).
fof(t22_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] : set_difference(singleton(A),unordered_pair(A,B)) = empty_set,
inference(assume_negation,[status(cth)],[t22_zfmisc_1]) ).
cnf(c_9,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_12,plain,
( D != B
| in(D,C)
| unordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d2_tarski]) ).
cnf(c_18,plain,
( ~ in(A,B)
| set_difference(singleton(A),B) = empty_set ),
inference(clausify,[status(thm)],[l36_zfmisc_1]) ).
fof(nnf_7,plain,
? [A,B] : set_difference(singleton(A),unordered_pair(A,B)) != empty_set,
inference(fof_nnf,[status(thm)],[t22_zfmisc_1_neg]) ).
fof(sk_t22_zfmisc_1_neg,plain,
set_difference(singleton(sK0),unordered_pair(sK0,sK1)) != empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_7]) ).
cnf(c_21,negated_conjecture,
set_difference(singleton(sK0),unordered_pair(sK0,sK1)) != empty_set,
inference(split_conjunct,[status(thm)],[sk_t22_zfmisc_1_neg]) ).
cnf(c_50,negated_conjecture,
~ in(sK0,unordered_pair(sK0,sK1)),
inference(resolve,[status(thm)],[c_18,c_21]) ).
cnf(c_63,plain,
( sK0 != B
| unordered_pair(A,B) != unordered_pair(sK0,sK1) ),
inference(resolve,[status(thm)],[c_12,c_50]) ).
cnf(c_64,plain,
unordered_pair(A,sK0) != unordered_pair(sK0,sK1),
inference(xxres,[status(thm)],[c_63]) ).
cnf(c_61,plain,
unordered_pair(sK0,sK1) != unordered_pair(A,sK0),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_62,plain,
$false,
inference(resolve,[status(thm)],[c_61,c_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET881+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/5.41 % Computer : n014.cluster.edu
% 0.14/5.41 % Model : x86_64 x86_64
% 0.14/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.41 % Memory : 8046.5625MB
% 0.14/5.41 % OS : Linux 6.8.0-71-generic
% 0.14/5.41 % CPULimit : 300
% 0.14/5.41 % WCLimit : 300
% 0.14/5.41 % DateTime : Sat Sep 26 08:24:08 UTC 2026
% 0.14/5.41 % CPUTime :
% 0.14/5.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/5.42 % Process 2638058 was started by sandbox2 on n014,
% 0.14/5.42 % Sat Sep 26 08:24:08 2026
% 0.14/5.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/5.42
% 0.14/5.42 % From the command line: assign(max_seconds, 300).
% 0.14/5.43
% 0.14/5.43 % SZS status Theorem for theBenchmark
% 0.14/5.43
% 0.14/5.43 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/5.43 % Length of proof is 11.
% 0.14/5.43 % Level of proof is 4.
% 0.14/5.43 % Maximum clause weight is 11.000.
% 0.14/5.43 % Given clauses 19.
% 0.14/5.43
% 0.14/5.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------