%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET117-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 08:35:50 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 8 unt; 0 def)
% Number of atoms : 8 ( 2 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 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 : 4 ( 2 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_1_to_ordered_pairs_are_sets_2,axiom,
~ member(x,universal_class),
file('theBenchmark.p',prove_corollary_1_to_ordered_pairs_are_sets_2) ).
cnf(c_33,plain,
~ member(x,universal_class),
inference(clausify,[status(thm)],[prove_corollary_1_to_ordered_pairs_are_sets_2]) ).
fof(prove_corollary_1_to_ordered_pairs_are_sets_1,axiom,
ordered_pair(first(x),second(x)) = x,
file('theBenchmark.p',prove_corollary_1_to_ordered_pairs_are_sets_1) ).
cnf(c_34,plain,
ordered_pair(first(x),second(x)) = x,
inference(clausify,[status(thm)],[prove_corollary_1_to_ordered_pairs_are_sets_1]) ).
fof(ordered_pair_is_set,axiom,
! [VAR_0,VAR_1] : member(ordered_pair(VAR_0,VAR_1),universal_class),
file('theBenchmark.p',ordered_pair_is_set) ).
cnf(c_52,plain,
member(ordered_pair(A,B),universal_class),
inference(clausify,[status(thm)],[ordered_pair_is_set]) ).
cnf(c_322,plain,
member(x,universal_class),
inference(paramod,[status(thm)],[c_34,c_52]) ).
cnf(c_321,plain,
$false,
inference(resolve,[status(thm)],[c_33,c_322]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET117-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.40 % Computer : n008.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8046.5625MB
% 0.16/0.40 % OS : Linux 6.8.0-71-generic
% 0.16/0.40 % CPULimit : 300
% 0.16/0.40 % WCLimit : 300
% 0.16/0.40 % DateTime : Sat Sep 26 07:10:40 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.41 % Process 3040668 was started by sandbox on n008,
% 0.16/0.41 % Sat Sep 26 07:10:40 2026
% 0.16/0.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.42
% 0.16/0.42 % From the command line: assign(max_seconds, 300).
% 0.16/0.46
% 0.16/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.46
% 0.16/0.46 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.16/0.46 % Length of proof is 4.
% 0.16/0.46 % Level of proof is 1.
% 0.16/0.46 % Maximum clause weight is 22.000.
% 0.16/0.46 % Given clauses 20.
% 0.16/0.46
% 0.16/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------