%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET051-6 : 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 : n016.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 08:35:30 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.53s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 10 unt; 0 def)
% Number of atoms : 26 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 23 ( 6 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_2_to_unordered_pair_2,axiom,
~ member(y,unordered_pair(x,y)),
file('theBenchmark.p',prove_corollary_2_to_unordered_pair_2) ).
cnf(c_34,plain,
~ member(y,unordered_pair(x,y)),
inference(clausify,[status(thm)],[prove_corollary_2_to_unordered_pair_2]) ).
fof(prove_corollary_2_to_unordered_pair_1,axiom,
member(ordered_pair(x,y),cross_product(u,v)),
file('theBenchmark.p',prove_corollary_2_to_unordered_pair_1) ).
cnf(c_35,plain,
member(ordered_pair(x,y),cross_product(u,v)),
inference(clausify,[status(thm)],[prove_corollary_2_to_unordered_pair_1]) ).
fof(cartesian_product2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_1,VAR_3)
| ~ member(ordered_pair(VAR_0,VAR_1),cross_product(VAR_2,VAR_3)) ),
file('theBenchmark.p',cartesian_product2) ).
cnf(c_105,plain,
( member(B,D)
| ~ member(ordered_pair(A,B),cross_product(C,D)) ),
inference(clausify,[status(thm)],[cartesian_product2]) ).
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_112,plain,
( member(A,unordered_pair(B,A))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair3]) ).
fof(class_elements_are_sets,axiom,
! [VAR_0] : subclass(VAR_0,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
cnf(c_118,plain,
subclass(A,universal_class),
inference(clausify,[status(thm)],[class_elements_are_sets]) ).
fof(subclass_members,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ subclass(VAR_0,VAR_1) ),
file('theBenchmark.p',subclass_members) ).
cnf(c_121,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_208,plain,
member(y,v),
inference(resolve,[status(thm)],[c_105,c_35]) ).
cnf(c_232,plain,
~ member(y,universal_class),
inference(resolve,[status(thm)],[c_112,c_34]) ).
cnf(c_366,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_121,c_118]) ).
cnf(c_364,plain,
~ member(y,A),
inference(resolve,[status(thm)],[c_366,c_232]) ).
cnf(c_365,plain,
$false,
inference(resolve,[status(thm)],[c_364,c_208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET051-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.46 % Computer : n016.cluster.edu
% 0.22/0.46 % Model : x86_64 x86_64
% 0.22/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.46 % Memory : 8046.5625MB
% 0.22/0.46 % OS : Linux 6.8.0-71-generic
% 0.22/0.46 % CPULimit : 300
% 0.22/0.46 % WCLimit : 300
% 0.22/0.46 % DateTime : Sat Sep 26 07:04:47 UTC 2026
% 0.22/0.46 % CPUTime :
% 0.22/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.22/0.46 % Process 245534 was started by sandbox2 on n016,
% 0.22/0.46 % Sat Sep 26 07:04:47 2026
% 0.22/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.22/0.47
% 0.22/0.47 % From the command line: assign(max_seconds, 300).
% 0.23/0.53
% 0.23/0.53 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.53
% 0.23/0.53 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.23/0.53 % Length of proof is 10.
% 0.23/0.53 % Level of proof is 3.
% 0.23/0.53 % Maximum clause weight is 20.000.
% 0.23/0.53 % Given clauses 102.
% 0.23/0.53
% 0.23/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------