%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET074-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 08:35:38 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 10 unt; 0 def)
% Number of atoms : 14 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 8 ( 4 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_to_unordered_pair_axiom2_2,axiom,
unordered_pair(x,y) = null_class,
file('theBenchmark.p',prove_corollary_to_unordered_pair_axiom2_2) ).
cnf(c_33,plain,
unordered_pair(x,y) = null_class,
inference(clausify,[status(thm)],[prove_corollary_to_unordered_pair_axiom2_2]) ).
cnf(c_34,plain,
null_class = unordered_pair(x,y),
inference(copy,[status(thm)],[c_33]) ).
fof(prove_corollary_to_unordered_pair_axiom2_1,axiom,
member(y,universal_class),
file('theBenchmark.p',prove_corollary_to_unordered_pair_axiom2_1) ).
cnf(c_35,plain,
member(y,universal_class),
inference(clausify,[status(thm)],[prove_corollary_to_unordered_pair_axiom2_1]) ).
fof(existence_of_null_class,axiom,
! [VAR_0] : ~ member(VAR_0,null_class),
file('theBenchmark.p',existence_of_null_class) ).
cnf(c_50,plain,
~ member(A,null_class),
inference(clausify,[status(thm)],[existence_of_null_class]) ).
fof(unordered_pair3,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,unordered_pair(VAR_1,VAR_0))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',unordered_pair3) ).
cnf(c_138,plain,
( member(A,unordered_pair(B,A))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair3]) ).
cnf(c_178,plain,
~ member(A,unordered_pair(x,y)),
inference(paramod,[status(thm)],[c_34,c_50]) ).
cnf(c_428,plain,
member(y,unordered_pair(A,y)),
inference(resolve,[status(thm)],[c_138,c_35]) ).
cnf(c_429,plain,
$false,
inference(resolve,[status(thm)],[c_428,c_178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET074-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n001.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 07:09:27 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.35 % Process 1192980 was started by sandbox2 on n001,
% 0.10/0.35 % Sat Sep 26 07:09:27 2026
% 0.10/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.36
% 0.10/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.38
% 0.12/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.38
% 0.12/0.38 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.12/0.38 % Length of proof is 8.
% 0.12/0.38 % Level of proof is 3.
% 0.12/0.38 % Maximum clause weight is 18.000.
% 0.12/0.38 % Given clauses 88.
% 0.12/0.38
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------