%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET108+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 08:35:48 AM UTC 2026
% Result : Theorem 0.14s 5.52s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 10 unt; 0 def)
% Number of atoms : 107 ( 67 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 134 ( 62 ~; 51 |; 21 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 17 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(singleton_set_defn,axiom,
! [X] : singleton(X) = unordered_pair(X,X),
file('theBenchmark.p',singleton_set_defn) ).
fof(ordered_pair_defn,axiom,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),
file('theBenchmark.p',ordered_pair_defn) ).
fof(existence_of_first_and_second,conjecture,
! [X] :
? [U,V] :
( ( V = X
& U = X
& ~ ? [Y,Z] :
( X = ordered_pair(Y,Z)
& member(Z,universal_class)
& member(Y,universal_class) ) )
| ( X = ordered_pair(U,V)
& member(V,universal_class)
& member(U,universal_class) ) ),
file('theBenchmark.p',existence_of_first_and_second) ).
fof(existence_of_first_and_second_neg,negated_conjecture,
~ ! [X] :
? [U,V] :
( ( V = X
& U = X
& ~ ? [Y,Z] :
( X = ordered_pair(Y,Z)
& member(Z,universal_class)
& member(Y,universal_class) ) )
| ( X = ordered_pair(U,V)
& member(V,universal_class)
& member(U,universal_class) ) ),
inference(assume_negation,[status(cth)],[existence_of_first_and_second]) ).
fof(nnf_42,plain,
? [X] :
! [U,V] :
( ( V != X
| U != X
| ? [Y,Z] :
( ordered_pair(Y,Z) = X
& member(Z,universal_class)
& member(Y,universal_class) ) )
& ( ordered_pair(U,V) != X
| ~ member(V,universal_class)
| ~ member(U,universal_class) ) ),
inference(fof_nnf,[status(thm)],[existence_of_first_and_second_neg]) ).
fof(sk_existence_of_first_and_second_neg_sk,plain,
! [U,V] :
( ( V != sK2
| U != sK2
| ( ordered_pair(sK0(U,V),sK1(U,V)) = sK2
& member(sK1(U,V),universal_class)
& member(sK0(U,V),universal_class) ) )
& ( ordered_pair(U,V) != sK2
| ~ member(V,universal_class)
| ~ member(U,universal_class) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK1]),skolemize(X,sK2),skolemize(Y,sK0(U,V)),skolemize(Z,sK1(U,V))],[nnf_42]) ).
fof(sk_existence_of_first_and_second_neg,plain,
( ! [VAR_0,VAR_1] :
( VAR_1 != sK2
| VAR_0 != sK2
| ordered_pair(sK0(VAR_0,VAR_1),sK1(VAR_0,VAR_1)) = sK2 )
& ! [VAR_0,VAR_1] :
( VAR_1 != sK2
| VAR_0 != sK2
| member(sK1(VAR_0,VAR_1),universal_class) )
& ! [VAR_0,VAR_1] :
( VAR_1 != sK2
| VAR_0 != sK2
| member(sK0(VAR_0,VAR_1),universal_class) )
& ! [VAR_0,VAR_1] :
( ordered_pair(VAR_0,VAR_1) != sK2
| ~ member(VAR_1,universal_class)
| ~ member(VAR_0,universal_class) ) ),
inference(cnf_transformation,[status(thm)],[sk_existence_of_first_and_second_neg_sk]) ).
cnf(c_64,negated_conjecture,
( B != sK2
| A != sK2
| ordered_pair(sK0(A,B),sK1(A,B)) = sK2 ),
inference(split_conjunct,[status(thm)],[sk_existence_of_first_and_second_neg]) ).
cnf(c_1146,negated_conjecture,
( B != sK2
| sK2 != A
| ordered_pair(sK0(A,B),sK1(A,B)) = sK2 ),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_65,negated_conjecture,
( sK2 != B
| sK2 != A
| ordered_pair(sK0(A,B),sK1(A,B)) = sK2 ),
inference(copy,[status(thm)],[c_1146]) ).
cnf(c_66,negated_conjecture,
( B != sK2
| A != sK2
| member(sK1(A,B),universal_class) ),
inference(split_conjunct,[status(thm)],[sk_existence_of_first_and_second_neg]) ).
cnf(c_1147,negated_conjecture,
( B != sK2
| sK2 != A
| member(sK1(A,B),universal_class) ),
inference(copy,[status(thm)],[c_66]) ).
cnf(c_67,negated_conjecture,
( sK2 != B
| sK2 != A
| member(sK1(A,B),universal_class) ),
inference(copy,[status(thm)],[c_1147]) ).
cnf(c_68,negated_conjecture,
( B != sK2
| A != sK2
| member(sK0(A,B),universal_class) ),
inference(split_conjunct,[status(thm)],[sk_existence_of_first_and_second_neg]) ).
cnf(c_1148,negated_conjecture,
( B != sK2
| sK2 != A
| member(sK0(A,B),universal_class) ),
inference(copy,[status(thm)],[c_68]) ).
cnf(c_69,negated_conjecture,
( sK2 != B
| sK2 != A
| member(sK0(A,B),universal_class) ),
inference(copy,[status(thm)],[c_1148]) ).
cnf(c_70,negated_conjecture,
( ordered_pair(A,B) != sK2
| ~ member(B,universal_class)
| ~ member(A,universal_class) ),
inference(split_conjunct,[status(thm)],[sk_existence_of_first_and_second_neg]) ).
cnf(c_132,plain,
ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,singleton(B))),
inference(clausify,[status(thm)],[ordered_pair_defn]) ).
cnf(c_133,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[singleton_set_defn]) ).
cnf(c_1149,plain,
( sK2 != A
| ordered_pair(sK0(A,A),sK1(A,A)) = sK2 ),
inference(factor,[status(thm)],[c_65]) ).
cnf(c_1150,plain,
( sK2 != A
| unordered_pair(singleton(sK0(A,A)),unordered_pair(sK0(A,A),singleton(sK1(A,A)))) = sK2 ),
inference(paramod,[status(thm)],[c_132,c_1149]) ).
cnf(c_1151,plain,
( sK2 != A
| unordered_pair(unordered_pair(sK0(A,A),sK0(A,A)),unordered_pair(sK0(A,A),singleton(sK1(A,A)))) = sK2 ),
inference(paramod,[status(thm)],[c_133,c_1150]) ).
cnf(c_154,plain,
( sK2 != A
| unordered_pair(unordered_pair(sK0(A,A),sK0(A,A)),unordered_pair(sK0(A,A),unordered_pair(sK1(A,A),sK1(A,A)))) = sK2 ),
inference(paramod,[status(thm)],[c_133,c_1151]) ).
cnf(c_155,plain,
( sK2 != A
| member(sK1(A,A),universal_class) ),
inference(factor,[status(thm)],[c_67]) ).
cnf(c_156,plain,
( sK2 != A
| member(sK0(A,A),universal_class) ),
inference(factor,[status(thm)],[c_69]) ).
cnf(c_1152,negated_conjecture,
( unordered_pair(singleton(A),unordered_pair(A,singleton(B))) != sK2
| ~ member(B,universal_class)
| ~ member(A,universal_class) ),
inference(paramod,[status(thm)],[c_132,c_70]) ).
cnf(c_1153,negated_conjecture,
( unordered_pair(unordered_pair(A,A),unordered_pair(A,singleton(B))) != sK2
| ~ member(B,universal_class)
| ~ member(A,universal_class) ),
inference(paramod,[status(thm)],[c_133,c_1152]) ).
cnf(c_200,negated_conjecture,
( unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B))) != sK2
| ~ member(B,universal_class)
| ~ member(A,universal_class) ),
inference(paramod,[status(thm)],[c_133,c_1153]) ).
cnf(c_368,plain,
unordered_pair(unordered_pair(sK0(sK2,sK2),sK0(sK2,sK2)),unordered_pair(sK0(sK2,sK2),unordered_pair(sK1(sK2,sK2),sK1(sK2,sK2)))) = sK2,
inference(xxres,[status(thm)],[c_154]) ).
cnf(c_369,plain,
member(sK1(sK2,sK2),universal_class),
inference(xxres,[status(thm)],[c_155]) ).
cnf(c_370,plain,
member(sK0(sK2,sK2),universal_class),
inference(xxres,[status(thm)],[c_156]) ).
cnf(c_1154,negated_conjecture,
( unordered_pair(unordered_pair(sK0(sK2,sK2),sK0(sK2,sK2)),unordered_pair(sK0(sK2,sK2),unordered_pair(A,A))) != sK2
| ~ member(A,universal_class) ),
inference(resolve,[status(thm)],[c_200,c_370]) ).
cnf(c_1155,negated_conjecture,
unordered_pair(unordered_pair(sK0(sK2,sK2),sK0(sK2,sK2)),unordered_pair(sK0(sK2,sK2),unordered_pair(sK1(sK2,sK2),sK1(sK2,sK2)))) != sK2,
inference(resolve,[status(thm)],[c_1154,c_369]) ).
cnf(c_1156,negated_conjecture,
sK2 != sK2,
inference(paramod,[status(thm)],[c_368,c_1155]) ).
cnf(c_1145,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_1156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET108+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n008.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 26 07:08:59 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 3037903 was started by sandbox on n008,
% 0.10/5.38 % Sat Sep 26 07:08:59 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.39
% 0.10/5.39 % From the command line: assign(max_seconds, 300).
% 0.14/5.52
% 0.14/5.52 % SZS status Theorem for theBenchmark
% 0.14/5.52
% 0.14/5.52 % Proof 1 at 0.09 (+ 0.03) seconds.
% 0.14/5.52 % Length of proof is 20.
% 0.14/5.52 % Level of proof is 5.
% 0.14/5.52 % Maximum clause weight is 55.000.
% 0.14/5.52 % Given clauses 155.
% 0.14/5.52
% 0.14/5.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------