%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET020+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 : n020.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 08:35:21 AM UTC 2026
% Result : Theorem 0.22s 0.59s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 12 unt; 0 def)
% Number of atoms : 84 ( 53 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 91 ( 44 ~; 30 |; 14 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 11 !; 3 ?)
% 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(first_second,axiom,
! [X,Y] :
( ( member(Y,universal_class)
& member(X,universal_class) )
=> ( second(ordered_pair(X,Y)) = Y
& first(ordered_pair(X,Y)) = X ) ),
file('theBenchmark.p',first_second) ).
fof(unique_1st_and_2nd_in_pair_of_sets1,conjecture,
! [U,V,X] :
( ( X = ordered_pair(U,V)
& member(V,universal_class)
& member(U,universal_class) )
=> ( second(X) = V
& first(X) = U ) ),
file('theBenchmark.p',unique_1st_and_2nd_in_pair_of_sets1) ).
fof(unique_1st_and_2nd_in_pair_of_sets1_neg,negated_conjecture,
~ ! [U,V,X] :
( ( X = ordered_pair(U,V)
& member(V,universal_class)
& member(U,universal_class) )
=> ( second(X) = V
& first(X) = U ) ),
inference(assume_negation,[status(cth)],[unique_1st_and_2nd_in_pair_of_sets1]) ).
fof(nnf_42,plain,
? [U,V,X] :
( ( second(X) != V
| first(X) != U )
& ordered_pair(U,V) = X
& member(V,universal_class)
& member(U,universal_class) ),
inference(fof_nnf,[status(thm)],[unique_1st_and_2nd_in_pair_of_sets1_neg]) ).
fof(sk_unique_1st_and_2nd_in_pair_of_sets1_neg,plain,
( ( second(sK0) != sK2
| first(sK0) != sK1 )
& ordered_pair(sK1,sK2) = sK0
& member(sK2,universal_class)
& member(sK1,universal_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK0]),skolemize(U,sK1),skolemize(V,sK2),skolemize(X,sK0)],[nnf_42]) ).
cnf(c_64,negated_conjecture,
( second(sK0) != sK2
| first(sK0) != sK1 ),
inference(split_conjunct,[status(thm)],[sk_unique_1st_and_2nd_in_pair_of_sets1_neg]) ).
cnf(c_65,negated_conjecture,
ordered_pair(sK1,sK2) = sK0,
inference(split_conjunct,[status(thm)],[sk_unique_1st_and_2nd_in_pair_of_sets1_neg]) ).
cnf(c_66,negated_conjecture,
sK0 = ordered_pair(sK1,sK2),
inference(copy,[status(thm)],[c_65]) ).
cnf(c_67,negated_conjecture,
member(sK2,universal_class),
inference(split_conjunct,[status(thm)],[sk_unique_1st_and_2nd_in_pair_of_sets1_neg]) ).
cnf(c_68,negated_conjecture,
member(sK1,universal_class),
inference(split_conjunct,[status(thm)],[sk_unique_1st_and_2nd_in_pair_of_sets1_neg]) ).
cnf(c_125,plain,
( second(ordered_pair(A,B)) = B
| ~ member(B,universal_class)
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[first_second]) ).
cnf(c_126,plain,
( first(ordered_pair(A,B)) = A
| ~ member(B,universal_class)
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[first_second]) ).
cnf(c_130,plain,
ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,singleton(B))),
inference(clausify,[status(thm)],[ordered_pair_defn]) ).
cnf(c_131,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[singleton_set_defn]) ).
cnf(c_619,negated_conjecture,
( second(sK0) != sK2
| first(ordered_pair(sK1,sK2)) != sK1 ),
inference(paramod,[status(thm)],[c_66,c_64]) ).
cnf(c_620,negated_conjecture,
( second(sK0) != sK2
| first(unordered_pair(singleton(sK1),unordered_pair(sK1,singleton(sK2)))) != sK1 ),
inference(paramod,[status(thm)],[c_130,c_619]) ).
cnf(c_621,negated_conjecture,
( second(sK0) != sK2
| first(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,singleton(sK2)))) != sK1 ),
inference(paramod,[status(thm)],[c_131,c_620]) ).
cnf(c_622,negated_conjecture,
( second(sK0) != sK2
| first(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK2,sK2)))) != sK1 ),
inference(paramod,[status(thm)],[c_131,c_621]) ).
cnf(c_623,negated_conjecture,
( second(ordered_pair(sK1,sK2)) != sK2
| first(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK2,sK2)))) != sK1 ),
inference(paramod,[status(thm)],[c_66,c_622]) ).
cnf(c_624,negated_conjecture,
( second(unordered_pair(singleton(sK1),unordered_pair(sK1,singleton(sK2)))) != sK2
| first(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK2,sK2)))) != sK1 ),
inference(paramod,[status(thm)],[c_130,c_623]) ).
cnf(c_625,negated_conjecture,
( second(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,singleton(sK2)))) != sK2
| first(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK2,sK2)))) != sK1 ),
inference(paramod,[status(thm)],[c_131,c_624]) ).
cnf(c_152,negated_conjecture,
( second(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK2,sK2)))) != sK2
| first(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK2,sK2)))) != sK1 ),
inference(paramod,[status(thm)],[c_131,c_625]) ).
cnf(c_626,plain,
( first(unordered_pair(singleton(A),unordered_pair(A,singleton(B)))) = A
| ~ member(B,universal_class)
| ~ member(A,universal_class) ),
inference(paramod,[status(thm)],[c_130,c_126]) ).
cnf(c_627,plain,
( first(unordered_pair(unordered_pair(A,A),unordered_pair(A,singleton(B)))) = A
| ~ member(B,universal_class)
| ~ member(A,universal_class) ),
inference(paramod,[status(thm)],[c_131,c_626]) ).
cnf(c_178,plain,
( first(unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B)))) = A
| ~ member(B,universal_class)
| ~ member(A,universal_class) ),
inference(paramod,[status(thm)],[c_131,c_627]) ).
cnf(c_628,plain,
( second(unordered_pair(singleton(A),unordered_pair(A,singleton(B)))) = B
| ~ member(B,universal_class)
| ~ member(A,universal_class) ),
inference(paramod,[status(thm)],[c_130,c_125]) ).
cnf(c_629,plain,
( second(unordered_pair(unordered_pair(A,A),unordered_pair(A,singleton(B)))) = B
| ~ member(B,universal_class)
| ~ member(A,universal_class) ),
inference(paramod,[status(thm)],[c_131,c_628]) ).
cnf(c_179,plain,
( second(unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B)))) = B
| ~ member(B,universal_class)
| ~ member(A,universal_class) ),
inference(paramod,[status(thm)],[c_131,c_629]) ).
cnf(c_630,negated_conjecture,
( first(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(A,A)))) = sK1
| ~ member(A,universal_class) ),
inference(resolve,[status(thm)],[c_178,c_68]) ).
cnf(c_585,negated_conjecture,
first(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK2,sK2)))) = sK1,
inference(resolve,[status(thm)],[c_630,c_67]) ).
cnf(c_631,negated_conjecture,
( second(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK2,sK2)))) != sK2
| sK1 != sK1 ),
inference(paramod,[status(thm)],[c_585,c_152]) ).
cnf(c_590,negated_conjecture,
second(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK2,sK2)))) != sK2,
inference(copy,[status(thm)],[c_631]) ).
cnf(c_632,negated_conjecture,
( second(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(A,A)))) = A
| ~ member(A,universal_class) ),
inference(resolve,[status(thm)],[c_179,c_68]) ).
cnf(c_633,negated_conjecture,
second(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK2,sK2)))) = sK2,
inference(resolve,[status(thm)],[c_632,c_67]) ).
cnf(c_618,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_590,c_633]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET020+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n020.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 06:53:33 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 897508 was started by sandbox on n020,
% 0.18/0.44 % Sat Sep 26 06:53:33 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 0.22/0.59
% 0.22/0.59 % SZS status Theorem for theBenchmark
% 0.22/0.59
% 0.22/0.59 % Proof 1 at 0.08 (+ 0.03) seconds.
% 0.22/0.59 % Length of proof is 19.
% 0.22/0.59 % Level of proof is 5.
% 0.22/0.59 % Maximum clause weight is 79.000.
% 0.22/0.59 % Given clauses 83.
% 0.22/0.59
% 0.22/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------