%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET940+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 : n007.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 08:37:20 AM UTC 2026
% Result : Theorem 0.09s 0.37s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 10 unt; 0 def)
% Number of atoms : 10 ( 9 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 6 !; 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(t93_zfmisc_1,conjecture,
! [A,B] : union(unordered_pair(A,B)) = set_union2(A,B),
file('theBenchmark.p',t93_zfmisc_1) ).
fof(t93_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] : union(unordered_pair(A,B)) = set_union2(A,B),
inference(assume_negation,[status(cth)],[t93_zfmisc_1]) ).
cnf(c_17,plain,
union(unordered_pair(A,B)) = set_union2(A,B),
inference(clausify,[status(thm)],[l52_zfmisc_1]) ).
cnf(c_18,plain,
set_union2(A,B) = union(unordered_pair(A,B)),
inference(copy,[status(thm)],[c_17]) ).
fof(nnf_9,plain,
? [A,B] : union(unordered_pair(A,B)) != set_union2(A,B),
inference(fof_nnf,[status(thm)],[t93_zfmisc_1_neg]) ).
fof(sk_t93_zfmisc_1_neg,plain,
union(unordered_pair(sK0,sK1)) != set_union2(sK0,sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_9]) ).
cnf(c_19,negated_conjecture,
union(unordered_pair(sK0,sK1)) != set_union2(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t93_zfmisc_1_neg]) ).
cnf(c_21,negated_conjecture,
union(unordered_pair(sK0,sK1)) != union(unordered_pair(sK0,sK1)),
inference(paramod,[status(thm)],[c_18,c_19]) ).
cnf(c_20,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET940+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 08:24:23 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3291122 was started by sandbox2 on n007,
% 0.09/0.36 % Sat Sep 26 08:24:23 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.09/0.37
% 0.09/0.37 % SZS status Theorem for theBenchmark
% 0.09/0.37
% 0.09/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.37 % Length of proof is 6.
% 0.09/0.37 % Level of proof is 3.
% 0.09/0.37 % Maximum clause weight is 8.000.
% 0.09/0.37 % Given clauses 0.
% 0.09/0.37
% 0.09/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------