%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET016-6 : 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 : 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 08:35:19 AM UTC 2026
% Result : Unsatisfiable 4.50s 1.05s
% Output : CNFRefutation 4.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 44 ( 33 unt; 0 def)
% Number of atoms : 59 ( 30 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 23 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 47 ( 12 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_ordered_pair_determines_components1_3,axiom,
w != y,
file('theBenchmark.p',prove_ordered_pair_determines_components1_3) ).
cnf(c_34,plain,
w != y,
inference(clausify,[status(thm)],[prove_ordered_pair_determines_components1_3]) ).
cnf(c_35,plain,
y != w,
inference(copy,[status(thm)],[c_34]) ).
fof(prove_ordered_pair_determines_components1_2,axiom,
member(w,universal_class),
file('theBenchmark.p',prove_ordered_pair_determines_components1_2) ).
cnf(c_36,plain,
member(w,universal_class),
inference(clausify,[status(thm)],[prove_ordered_pair_determines_components1_2]) ).
fof(prove_ordered_pair_determines_components1_1,axiom,
ordered_pair(w,x) = ordered_pair(y,z),
file('theBenchmark.p',prove_ordered_pair_determines_components1_1) ).
cnf(c_37,plain,
ordered_pair(w,x) = ordered_pair(y,z),
inference(clausify,[status(thm)],[prove_ordered_pair_determines_components1_1]) ).
cnf(c_38,plain,
ordered_pair(y,z) = ordered_pair(w,x),
inference(copy,[status(thm)],[c_37]) ).
fof(ordered_pair,axiom,
! [VAR_0,VAR_1] : unordered_pair(singleton(VAR_0),unordered_pair(VAR_0,singleton(VAR_1))) = ordered_pair(VAR_0,VAR_1),
file('theBenchmark.p',ordered_pair) ).
cnf(c_110,plain,
unordered_pair(singleton(A),unordered_pair(A,singleton(B))) = ordered_pair(A,B),
inference(clausify,[status(thm)],[ordered_pair]) ).
cnf(c_111,plain,
ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,singleton(B))),
inference(copy,[status(thm)],[c_110]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_112,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_113,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_112]) ).
fof(unordered_pairs_in_universal,axiom,
! [VAR_0,VAR_1] : member(unordered_pair(VAR_0,VAR_1),universal_class),
file('theBenchmark.p',unordered_pairs_in_universal) ).
cnf(c_114,plain,
member(unordered_pair(A,B),universal_class),
inference(clausify,[status(thm)],[unordered_pairs_in_universal]) ).
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_subclass1,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',equal_implies_subclass1) ).
cnf(c_120,plain,
( subclass(A,B)
| A != B ),
inference(clausify,[status(thm)],[equal_implies_subclass1]) ).
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_3691,plain,
unordered_pair(singleton(y),unordered_pair(y,singleton(z))) = ordered_pair(w,x),
inference(paramod,[status(thm)],[c_111,c_38]) ).
cnf(c_3692,plain,
unordered_pair(unordered_pair(y,y),unordered_pair(y,singleton(z))) = ordered_pair(w,x),
inference(paramod,[status(thm)],[c_113,c_3691]) ).
cnf(c_3693,plain,
unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))) = ordered_pair(w,x),
inference(paramod,[status(thm)],[c_113,c_3692]) ).
cnf(c_3694,plain,
unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))) = unordered_pair(singleton(w),unordered_pair(w,singleton(x))),
inference(paramod,[status(thm)],[c_111,c_3693]) ).
cnf(c_3695,plain,
unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))) = unordered_pair(unordered_pair(w,w),unordered_pair(w,singleton(x))),
inference(paramod,[status(thm)],[c_113,c_3694]) ).
cnf(c_198,plain,
unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))) = unordered_pair(unordered_pair(w,w),unordered_pair(w,unordered_pair(x,x))),
inference(paramod,[status(thm)],[c_113,c_3695]) ).
cnf(c_233,plain,
member(unordered_pair(A,B),unordered_pair(unordered_pair(A,B),C)),
inference(resolve,[status(thm)],[c_116,c_114]) ).
cnf(c_236,plain,
member(w,unordered_pair(w,A)),
inference(resolve,[status(thm)],[c_116,c_36]) ).
cnf(c_3696,plain,
w != y,
inference(copy,[status(thm)],[c_35]) ).
cnf(c_3697,plain,
( w = A
| ~ member(w,unordered_pair(y,A)) ),
inference(resolve,[status(thm)],[c_117,c_3696]) ).
cnf(c_3698,plain,
w != y,
inference(copy,[status(thm)],[c_35]) ).
cnf(c_239,plain,
~ member(w,unordered_pair(y,y)),
inference(resolve,[status(thm)],[c_3697,c_3698]) ).
cnf(c_3699,plain,
( member(w,B)
| ~ subclass(unordered_pair(w,A),B) ),
inference(resolve,[status(thm)],[c_124,c_236]) ).
cnf(c_562,plain,
~ subclass(unordered_pair(w,A),unordered_pair(y,y)),
inference(resolve,[status(thm)],[c_3699,c_239]) ).
cnf(c_1093,plain,
member(unordered_pair(y,y),unordered_pair(unordered_pair(w,w),unordered_pair(w,unordered_pair(x,x)))),
inference(paramod,[status(thm)],[c_198,c_233]) ).
cnf(c_3700,plain,
unordered_pair(w,A) != unordered_pair(y,y),
inference(resolve,[status(thm)],[c_120,c_562]) ).
cnf(c_1988,plain,
unordered_pair(y,y) != unordered_pair(w,A),
inference(copy,[status(thm)],[c_3700]) ).
cnf(c_3701,plain,
( unordered_pair(y,y) = B
| ~ member(unordered_pair(y,y),unordered_pair(unordered_pair(w,A),B)) ),
inference(resolve,[status(thm)],[c_117,c_1988]) ).
cnf(c_3689,plain,
~ member(unordered_pair(y,y),unordered_pair(unordered_pair(w,A),unordered_pair(w,B))),
inference(resolve,[status(thm)],[c_3701,c_1988]) ).
cnf(c_3690,plain,
$false,
inference(resolve,[status(thm)],[c_3689,c_1093]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET016-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n016.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 06:56:00 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 226302 was started by sandbox on n016,
% 0.15/0.42 % Sat Sep 26 06:56:00 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 4.50/1.05
% 4.50/1.05 % given #500 (T,wt=20): 1253 identity_relation = null_class | -subclass(universal_class,A) | member(regular(identity_relation),A). [resolve(1009,b,124,b)].
% 4.50/1.05
% 4.50/1.05 % SZS status Unsatisfiable for theBenchmark
% 4.50/1.05
% 4.50/1.05 % Proof 1 at 0.50 (+ 0.10) seconds.
% 4.50/1.05 % Length of proof is 23.
% 4.50/1.05 % Level of proof is 6.
% 4.50/1.05 % Maximum clause weight is 69.000.
% 4.50/1.05 % Given clauses 532.
% 4.50/1.05
% 4.50/1.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------