%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET120-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 08:35:51 AM UTC 2026
% Result : Unsatisfiable 6.67s 21.41s
% Output : CNFRefutation 6.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 8 unt; 0 def)
% Number of atoms : 22 ( 10 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 6 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 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 : 12 ( 2 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_2_to_OP_determines_components1_2,axiom,
second(ordered_pair(x,y)) != ordered_pair(x,y),
file('theBenchmark.p',prove_corollary_2_to_OP_determines_components1_2) ).
cnf(c_33,plain,
second(ordered_pair(x,y)) != ordered_pair(x,y),
inference(clausify,[status(thm)],[prove_corollary_2_to_OP_determines_components1_2]) ).
fof(prove_corollary_2_to_OP_determines_components1_1,axiom,
~ member(x,universal_class),
file('theBenchmark.p',prove_corollary_2_to_OP_determines_components1_1) ).
cnf(c_34,plain,
~ member(x,universal_class),
inference(clausify,[status(thm)],[prove_corollary_2_to_OP_determines_components1_1]) ).
fof(unique_1st_and_2nd_in_pair_of_non_sets4,axiom,
! [VAR_0] :
( second(VAR_0) = VAR_0
| ordered_pair(first(VAR_0),second(VAR_0)) = VAR_0 ),
file('theBenchmark.p',unique_1st_and_2nd_in_pair_of_non_sets4) ).
cnf(c_37,plain,
( second(A) = A
| ordered_pair(first(A),second(A)) = A ),
inference(clausify,[status(thm)],[unique_1st_and_2nd_in_pair_of_non_sets4]) ).
fof(unique_1st_and_2nd_in_pair_of_non_sets2,axiom,
! [VAR_0] :
( second(VAR_0) = VAR_0
| member(ordered_pair(first(VAR_0),second(VAR_0)),cross_product(universal_class,universal_class)) ),
file('theBenchmark.p',unique_1st_and_2nd_in_pair_of_non_sets2) ).
cnf(c_39,plain,
( second(A) = A
| member(ordered_pair(first(A),second(A)),cross_product(universal_class,universal_class)) ),
inference(clausify,[status(thm)],[unique_1st_and_2nd_in_pair_of_non_sets2]) ).
fof(cartesian_product1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_0,VAR_2)
| ~ member(ordered_pair(VAR_0,VAR_1),cross_product(VAR_2,VAR_3)) ),
file('theBenchmark.p',cartesian_product1) ).
cnf(c_181,plain,
( member(A,C)
| ~ member(ordered_pair(A,B),cross_product(C,D)) ),
inference(clausify,[status(thm)],[cartesian_product1]) ).
cnf(c_224,plain,
ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))) = ordered_pair(x,y),
inference(resolve,[status(thm)],[c_37,c_33]) ).
cnf(c_3823,plain,
( second(ordered_pair(x,y)) = ordered_pair(x,y)
| member(ordered_pair(x,y),cross_product(universal_class,universal_class)) ),
inference(paramod,[status(thm)],[c_224,c_39]) ).
cnf(c_1470,plain,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
inference(resolve,[status(thm)],[c_33,c_3823]) ).
cnf(c_3824,plain,
member(x,universal_class),
inference(resolve,[status(thm)],[c_1470,c_181]) ).
cnf(c_3822,plain,
$false,
inference(resolve,[status(thm)],[c_34,c_3824]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET120-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/20.43 % Computer : n004.cluster.edu
% 0.14/20.43 % Model : x86_64 x86_64
% 0.14/20.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/20.43 % Memory : 8046.5625MB
% 0.14/20.43 % OS : Linux 6.8.0-71-generic
% 0.14/20.43 % CPULimit : 300
% 0.14/20.43 % WCLimit : 300
% 0.14/20.43 % DateTime : Sat Sep 26 07:11:14 UTC 2026
% 0.14/20.44 % CPUTime :
% 0.14/20.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/20.44 % Process 1082206 was started by sandbox2 on n004,
% 0.14/20.44 % Sat Sep 26 07:11:14 2026
% 0.14/20.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/20.45
% 0.14/20.45 % From the command line: assign(max_seconds, 300).
% 6.67/21.41
% 6.67/21.41 % SZS status Unsatisfiable for theBenchmark
% 6.67/21.41
% 6.67/21.41 % Proof 1 at 0.78 (+ 0.15) seconds.
% 6.67/21.41 % Length of proof is 8.
% 6.67/21.41 % Level of proof is 3.
% 6.67/21.41 % Maximum clause weight is 33.000.
% 6.67/21.41 % Given clauses 374.
% 6.67/21.41
% 6.67/21.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------