%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET072+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 : Theorem 8.19s 1.48s
% Output : CNFRefutation 8.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 16 unt; 0 def)
% Number of atoms : 65 ( 28 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 18 ~; 14 |; 12 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 38 ( 7 sgn 14 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subclass_defn,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('theBenchmark.p',subclass_defn) ).
fof(extensionality,axiom,
! [X,Y] :
( X = Y
<=> ( subclass(Y,X)
& subclass(X,Y) ) ),
file('theBenchmark.p',extensionality) ).
fof(unordered_pair_defn,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( ( U = Y
| U = X )
& member(U,universal_class) ) ),
file('theBenchmark.p',unordered_pair_defn) ).
fof(right_cancellation,conjecture,
! [X,Y,Z] :
( ( unordered_pair(X,Z) = unordered_pair(Y,Z)
& member(Y,universal_class)
& member(X,universal_class) )
=> X = Y ),
file('theBenchmark.p',right_cancellation) ).
fof(right_cancellation_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( unordered_pair(X,Z) = unordered_pair(Y,Z)
& member(Y,universal_class)
& member(X,universal_class) )
=> X = Y ),
inference(assume_negation,[status(cth)],[right_cancellation]) ).
fof(nnf_42,plain,
? [X,Y,Z] :
( Y != X
& unordered_pair(Y,Z) = unordered_pair(X,Z)
& member(Y,universal_class)
& member(X,universal_class) ),
inference(fof_nnf,[status(thm)],[right_cancellation_neg]) ).
fof(sk_right_cancellation_neg,plain,
( sK0 != sK1
& unordered_pair(sK0,sK2) = unordered_pair(sK1,sK2)
& member(sK0,universal_class)
& member(sK1,universal_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK2]),skolemize(X,sK1),skolemize(Y,sK0),skolemize(Z,sK2)],[nnf_42]) ).
cnf(c_64,negated_conjecture,
sK0 != sK1,
inference(split_conjunct,[status(thm)],[sk_right_cancellation_neg]) ).
cnf(c_65,negated_conjecture,
unordered_pair(sK0,sK2) = unordered_pair(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_right_cancellation_neg]) ).
cnf(c_66,negated_conjecture,
member(sK0,universal_class),
inference(split_conjunct,[status(thm)],[sk_right_cancellation_neg]) ).
cnf(c_67,negated_conjecture,
member(sK1,universal_class),
inference(split_conjunct,[status(thm)],[sk_right_cancellation_neg]) ).
cnf(c_133,plain,
( A != B
| ~ member(A,universal_class)
| member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_defn]) ).
cnf(c_134,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_defn]) ).
cnf(c_137,plain,
( subclass(A,B)
| A != B ),
inference(clausify,[status(thm)],[extensionality]) ).
cnf(c_142,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_defn]) ).
cnf(c_375,plain,
( sK1 != A
| member(sK1,unordered_pair(A,B)) ),
inference(resolve,[status(thm)],[c_133,c_67]) ).
cnf(c_376,plain,
( sK0 != A
| member(sK0,unordered_pair(A,B)) ),
inference(resolve,[status(thm)],[c_133,c_66]) ).
cnf(c_18949,negated_conjecture,
sK1 != sK0,
inference(copy,[status(thm)],[c_64]) ).
cnf(c_18950,negated_conjecture,
( sK1 = A
| ~ member(sK1,unordered_pair(sK0,A)) ),
inference(resolve,[status(thm)],[c_134,c_18949]) ).
cnf(c_18951,negated_conjecture,
sK1 != sK0,
inference(copy,[status(thm)],[c_64]) ).
cnf(c_379,negated_conjecture,
~ member(sK1,unordered_pair(sK0,sK0)),
inference(resolve,[status(thm)],[c_18950,c_18951]) ).
cnf(c_18952,negated_conjecture,
unordered_pair(sK1,sK2) = unordered_pair(sK0,sK2),
inference(copy,[status(thm)],[c_65]) ).
cnf(c_409,negated_conjecture,
subclass(unordered_pair(sK1,sK2),unordered_pair(sK0,sK2)),
inference(resolve,[status(thm)],[c_137,c_18952]) ).
cnf(c_18329,plain,
member(sK1,unordered_pair(sK1,A)),
inference(xxres,[status(thm)],[c_375]) ).
cnf(c_18670,plain,
member(sK0,unordered_pair(sK0,A)),
inference(xxres,[status(thm)],[c_376]) ).
cnf(c_18953,plain,
( member(sK1,B)
| ~ subclass(unordered_pair(sK1,A),B) ),
inference(resolve,[status(thm)],[c_142,c_18329]) ).
cnf(c_18870,plain,
~ subclass(unordered_pair(sK1,A),unordered_pair(sK0,sK0)),
inference(resolve,[status(thm)],[c_18953,c_379]) ).
cnf(c_18913,plain,
member(sK0,unordered_pair(sK1,sK2)),
inference(paramod,[status(thm)],[c_65,c_18670]) ).
cnf(c_18954,plain,
( sK0 = sK2
| sK0 = sK1 ),
inference(resolve,[status(thm)],[c_18913,c_134]) ).
cnf(c_18955,plain,
( sK2 = sK0
| sK0 = sK1 ),
inference(copy,[status(thm)],[c_18954]) ).
cnf(c_18927,negated_conjecture,
sK2 = sK0,
inference(resolve,[status(thm)],[c_64,c_18955]) ).
cnf(c_18956,plain,
subclass(unordered_pair(sK1,sK2),unordered_pair(sK0,sK0)),
inference(paramod,[status(thm)],[c_18927,c_409]) ).
cnf(c_18948,plain,
$false,
inference(resolve,[status(thm)],[c_18870,c_18956]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET072+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 07:02:59 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 3629364 was started by sandbox2 on n009,
% 0.11/0.36 % Sat Sep 26 07:02:59 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 8.19/1.48
% 8.19/1.48 % given #500 (T,wt=14): 7541 complement(universal_class) = null_class. [resolve(270,a,71,b),flip(b),merge(b)].
% 8.19/1.48
% 8.19/1.48 % SZS status Theorem for theBenchmark
% 8.19/1.48
% 8.19/1.48 % Proof 1 at 0.76 (+ 0.32) seconds.
% 8.19/1.48 % Length of proof is 22.
% 8.19/1.48 % Level of proof is 6.
% 8.19/1.48 % Maximum clause weight is 21.000.
% 8.19/1.48 % Given clauses 920.
% 8.19/1.48
% 8.19/1.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------