%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET021-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 08:35:22 AM UTC 2026
% Result : Unsatisfiable 116.86s 31.02s
% Output : CNFRefutation 116.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 9 unt; 0 def)
% Number of atoms : 27 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 11 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_unique_1st_and_2nd_in_pair_of_sets2_2,axiom,
second(ordered_pair(u,v)) != v,
file('theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets2_2) ).
cnf(c_33,plain,
second(ordered_pair(u,v)) != v,
inference(clausify,[status(thm)],[prove_unique_1st_and_2nd_in_pair_of_sets2_2]) ).
fof(prove_unique_1st_and_2nd_in_pair_of_sets2_1,axiom,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
file('theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets2_1) ).
cnf(c_34,plain,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
inference(clausify,[status(thm)],[prove_unique_1st_and_2nd_in_pair_of_sets2_1]) ).
fof(ordered_pair_determines_components2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_1 = VAR_3
| ~ member(VAR_1,universal_class)
| ordered_pair(VAR_0,VAR_1) != ordered_pair(VAR_2,VAR_3) ),
file('theBenchmark.p',ordered_pair_determines_components2) ).
cnf(c_40,plain,
( B = D
| ~ member(B,universal_class)
| ordered_pair(A,B) != ordered_pair(C,D) ),
inference(clausify,[status(thm)],[ordered_pair_determines_components2]) ).
fof(corollary_2_to_cartesian_product,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_1,universal_class)
| ~ member(ordered_pair(VAR_0,VAR_1),cross_product(VAR_2,VAR_3)) ),
file('theBenchmark.p',corollary_2_to_cartesian_product) ).
cnf(c_108,plain,
( member(B,universal_class)
| ~ member(ordered_pair(A,B),cross_product(C,D)) ),
inference(clausify,[status(thm)],[corollary_2_to_cartesian_product]) ).
fof(cartesian_product4,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ordered_pair(first(VAR_0),second(VAR_0)) = VAR_0
| ~ member(VAR_0,cross_product(VAR_1,VAR_2)) ),
file('theBenchmark.p',cartesian_product4) ).
cnf(c_175,plain,
( ordered_pair(first(A),second(A)) = A
| ~ member(A,cross_product(B,C)) ),
inference(clausify,[status(thm)],[cartesian_product4]) ).
cnf(c_575,plain,
member(v,universal_class),
inference(resolve,[status(thm)],[c_108,c_34]) ).
cnf(c_754,plain,
ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))) = ordered_pair(u,v),
inference(resolve,[status(thm)],[c_175,c_34]) ).
cnf(c_1316,plain,
( v = C
| ordered_pair(A,v) != ordered_pair(B,C) ),
inference(resolve,[status(thm)],[c_575,c_40]) ).
cnf(c_20224,plain,
( v = C
| ordered_pair(B,C) != ordered_pair(A,v) ),
inference(copy,[status(thm)],[c_1316]) ).
cnf(c_20225,plain,
v = second(ordered_pair(u,v)),
inference(resolve,[status(thm)],[c_754,c_20224]) ).
cnf(c_20226,plain,
second(ordered_pair(u,v)) = v,
inference(copy,[status(thm)],[c_20225]) ).
cnf(c_20223,plain,
$false,
inference(resolve,[status(thm)],[c_33,c_20226]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET021-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.43 % Computer : n014.cluster.edu
% 0.08/0.43 % Model : x86_64 x86_64
% 0.08/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.43 % Memory : 8046.5625MB
% 0.08/0.43 % OS : Linux 6.8.0-71-generic
% 0.08/0.43 % CPULimit : 300
% 0.08/0.43 % WCLimit : 300
% 0.08/0.43 % DateTime : Sat Sep 26 06:52:47 UTC 2026
% 0.08/0.43 % CPUTime :
% 0.08/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.43 % Process 2430025 was started by sandbox on n014,
% 0.08/0.43 % Sat Sep 26 06:52:47 2026
% 0.08/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.44
% 0.08/0.44 % From the command line: assign(max_seconds, 300).
% 116.86/31.02
% 116.86/31.02 % given #500 (W,wt=19): 4085 successor(u) != null_class | member(ordered_pair(u,null_class),successor_relation). [resolve(4026,a,139,b)].
% 116.86/31.02
% 116.86/31.02 % given #1000 (T,wt=20): 13318 member_of(universal_class) = universal_class | subclass(singleton(omega),intersection(omega,omega)). [resolve(12863,b,61,a)].
% 116.86/31.02
% 116.86/31.02 % SZS status Unsatisfiable for theBenchmark
% 116.86/31.02
% 116.86/31.02 % Proof 1 at 3.52 (+ 0.95) seconds.
% 116.86/31.02 % Length of proof is 9.
% 116.86/31.02 % Level of proof is 3.
% 116.86/31.02 % Maximum clause weight is 33.000.
% 116.86/31.02 % Given clauses 1417.
% 116.86/31.02
% 116.86/31.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------