%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET891+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 : n018.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 08:37:14 AM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 13 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l52_zfmisc_1,axiom,
! [A,B] : union(unordered_pair(A,B)) = set_union2(A,B),
file('theBenchmark.p',l52_zfmisc_1) ).
fof(t41_enumset1,axiom,
! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
file('theBenchmark.p',t41_enumset1) ).
fof(t32_zfmisc_1,conjecture,
! [A,B] : union(unordered_pair(singleton(A),singleton(B))) = unordered_pair(A,B),
file('theBenchmark.p',t32_zfmisc_1) ).
fof(t32_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] : union(unordered_pair(singleton(A),singleton(B))) = unordered_pair(A,B),
inference(assume_negation,[status(cth)],[t32_zfmisc_1]) ).
cnf(c_16,plain,
union(unordered_pair(A,B)) = set_union2(A,B),
inference(clausify,[status(thm)],[l52_zfmisc_1]) ).
cnf(c_19,plain,
set_union2(singleton(A),singleton(B)) = unordered_pair(A,B),
inference(clausify,[status(thm)],[t41_enumset1]) ).
cnf(c_20,plain,
unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
inference(copy,[status(thm)],[c_19]) ).
fof(nnf_10,plain,
? [A,B] : union(unordered_pair(singleton(A),singleton(B))) != unordered_pair(A,B),
inference(fof_nnf,[status(thm)],[t32_zfmisc_1_neg]) ).
fof(sk_t32_zfmisc_1_neg,plain,
union(unordered_pair(singleton(sK0),singleton(sK1))) != unordered_pair(sK0,sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_10]) ).
cnf(c_21,negated_conjecture,
union(unordered_pair(singleton(sK0),singleton(sK1))) != unordered_pair(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t32_zfmisc_1_neg]) ).
cnf(c_25,negated_conjecture,
union(set_union2(singleton(singleton(sK0)),singleton(singleton(sK1)))) != unordered_pair(sK0,sK1),
inference(paramod,[status(thm)],[c_20,c_21]) ).
cnf(c_22,negated_conjecture,
union(set_union2(singleton(singleton(sK0)),singleton(singleton(sK1)))) != set_union2(singleton(sK0),singleton(sK1)),
inference(paramod,[status(thm)],[c_20,c_25]) ).
cnf(c_23,plain,
union(set_union2(singleton(A),singleton(B))) = set_union2(A,B),
inference(paramod,[status(thm)],[c_20,c_16]) ).
cnf(c_24,plain,
$false,
inference(resolve,[status(thm)],[c_23,c_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET891+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n018.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 08:26:38 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 4188193 was started by sandbox on n018,
% 0.16/0.44 % Sat Sep 26 08:26:38 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 0.16/0.46
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46
% 0.16/0.46 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/0.46 % Length of proof is 10.
% 0.16/0.46 % Level of proof is 4.
% 0.16/0.46 % Maximum clause weight is 14.000.
% 0.16/0.46 % Given clauses 0.
% 0.16/0.46
% 0.16/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------