%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET072-6 : 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 : n007.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 08:35:37 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.51s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 21 unt; 0 def)
% Number of atoms : 57 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 23 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 9 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_right_cancellation_3,axiom,
x != y,
file('theBenchmark.p',prove_right_cancellation_3) ).
cnf(c_34,plain,
x != y,
inference(clausify,[status(thm)],[prove_right_cancellation_3]) ).
cnf(c_35,plain,
y != x,
inference(copy,[status(thm)],[c_34]) ).
fof(prove_right_cancellation_2,axiom,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
file('theBenchmark.p',prove_right_cancellation_2) ).
cnf(c_36,plain,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
inference(clausify,[status(thm)],[prove_right_cancellation_2]) ).
fof(prove_right_cancellation_1,axiom,
unordered_pair(x,z) = unordered_pair(y,z),
file('theBenchmark.p',prove_right_cancellation_1) ).
cnf(c_37,plain,
unordered_pair(x,z) = unordered_pair(y,z),
inference(clausify,[status(thm)],[prove_right_cancellation_1]) ).
cnf(c_38,plain,
unordered_pair(y,z) = unordered_pair(x,z),
inference(copy,[status(thm)],[c_37]) ).
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_108,plain,
( member(B,D)
| ~ member(ordered_pair(A,B),cross_product(C,D)) ),
inference(clausify,[status(thm)],[cartesian_product2]) ).
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_109,plain,
( member(A,C)
| ~ member(ordered_pair(A,B),cross_product(C,D)) ),
inference(clausify,[status(thm)],[cartesian_product1]) ).
fof(unordered_pair2,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,unordered_pair(VAR_0,VAR_1))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',unordered_pair2) ).
cnf(c_116,plain,
( member(A,unordered_pair(A,B))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair2]) ).
fof(unordered_pair_member,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| VAR_0 = VAR_1
| ~ member(VAR_0,unordered_pair(VAR_1,VAR_2)) ),
file('theBenchmark.p',unordered_pair_member) ).
cnf(c_117,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_member]) ).
fof(equal_implies_subclass2,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_1,VAR_0)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',equal_implies_subclass2) ).
cnf(c_119,plain,
( subclass(B,A)
| A != B ),
inference(clausify,[status(thm)],[equal_implies_subclass2]) ).
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_124,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_222,plain,
member(y,universal_class),
inference(resolve,[status(thm)],[c_108,c_36]) ).
cnf(c_223,plain,
member(x,universal_class),
inference(resolve,[status(thm)],[c_109,c_36]) ).
cnf(c_1396,plain,
x != y,
inference(copy,[status(thm)],[c_35]) ).
cnf(c_1397,plain,
( x = A
| ~ member(x,unordered_pair(y,A)) ),
inference(resolve,[status(thm)],[c_117,c_1396]) ).
cnf(c_1398,plain,
x != y,
inference(copy,[status(thm)],[c_35]) ).
cnf(c_270,plain,
~ member(x,unordered_pair(y,y)),
inference(resolve,[status(thm)],[c_1397,c_1398]) ).
cnf(c_301,plain,
subclass(unordered_pair(x,z),unordered_pair(y,z)),
inference(resolve,[status(thm)],[c_119,c_38]) ).
cnf(c_434,plain,
member(y,unordered_pair(y,A)),
inference(resolve,[status(thm)],[c_222,c_116]) ).
cnf(c_450,plain,
member(x,unordered_pair(x,A)),
inference(resolve,[status(thm)],[c_223,c_116]) ).
cnf(c_858,plain,
member(y,unordered_pair(x,z)),
inference(paramod,[status(thm)],[c_38,c_434]) ).
cnf(c_1399,plain,
( member(x,B)
| ~ subclass(unordered_pair(x,A),B) ),
inference(resolve,[status(thm)],[c_124,c_450]) ).
cnf(c_900,plain,
~ subclass(unordered_pair(x,A),unordered_pair(y,y)),
inference(resolve,[status(thm)],[c_1399,c_270]) ).
cnf(c_1400,plain,
( y = z
| y = x ),
inference(resolve,[status(thm)],[c_858,c_117]) ).
cnf(c_1401,plain,
( z = y
| y = x ),
inference(copy,[status(thm)],[c_1400]) ).
cnf(c_1005,plain,
z = y,
inference(resolve,[status(thm)],[c_35,c_1401]) ).
cnf(c_1402,plain,
subclass(unordered_pair(x,z),unordered_pair(y,y)),
inference(paramod,[status(thm)],[c_1005,c_301]) ).
cnf(c_1395,plain,
$false,
inference(resolve,[status(thm)],[c_900,c_1402]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET072-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n007.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % 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 07:00:53 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 3070440 was started by sandbox2 on n007,
% 0.10/0.36 % Sat Sep 26 07:00:53 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.51
% 0.14/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.51
% 0.14/0.51 % Proof 1 at 0.09 (+ 0.03) seconds.
% 0.14/0.51 % Length of proof is 21.
% 0.14/0.51 % Level of proof is 5.
% 0.14/0.51 % Maximum clause weight is 21.000.
% 0.14/0.51 % Given clauses 226.
% 0.14/0.51
% 0.14/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------