%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET085-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 02:42:09 PM UTC 2026
% Result : Unsatisfiable 23.42s 3.93s
% Output : Proof 23.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 23 unt; 0 def)
% Number of atoms : 48 ( 29 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 18 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 3 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f11,axiom,
unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
fof(f11_nnf,plain,
! [X] : unordered_pair(X,X) = singleton(X),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X] : unordered_pair(X,X) = singleton(X),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(f8,axiom,
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f8_nnf,plain,
! [X,Y] :
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y] :
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(f129,negated_conjecture,
member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair3_2) ).
fof(f129_nnf,plain,
member(x,universal_class),
inference(nnf_transformation,[status(thm)],[f129]) ).
cnf(c129,plain,
member(x,universal_class),
inference(cnf_transformation,[status(esa)],[f129_nnf]) ).
cnf(p154,plain,
member(x,unordered_pair(x,X0)),
inference(resolution,[status(thm)],[c8,c129]) ).
cnf(p160,plain,
member(x,singleton(x)),
inference(superposition,[status(thm)],[c11,p154]) ).
cnf(f128,negated_conjecture,
unordered_pair(y,z) = singleton(x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair3_1) ).
fof(f128_nnf,plain,
unordered_pair(y,z) = singleton(x),
inference(nnf_transformation,[status(thm)],[f128]) ).
cnf(c128,plain,
unordered_pair(y,z) = singleton(x),
inference(cnf_transformation,[status(esa)],[f128_nnf]) ).
cnf(f7,axiom,
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f7_nnf,plain,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p147,plain,
( X0 = z
| X0 = y
| ~ member(X0,singleton(x)) ),
inference(superposition,[status(thm)],[c128,c7]) ).
cnf(p161,plain,
( x = z
| x = y ),
inference(resolution,[status(thm)],[p160,p147]) ).
cnf(f131,negated_conjecture,
x != z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair3_4) ).
fof(f131_nnf,plain,
x != z,
inference(nnf_transformation,[status(thm)],[f131]) ).
fof(f131_sk,plain,
x != z,
inference(skolemisation,[status(esa)],[f131_nnf]) ).
cnf(c131,plain,
x != z,
inference(cnf_transformation,[status(esa)],[f131_sk]) ).
cnf(p166,plain,
x = y,
inference(resolution,[status(thm)],[p161,c131]) ).
cnf(f130,negated_conjecture,
x != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair3_3) ).
fof(f130_nnf,plain,
x != y,
inference(nnf_transformation,[status(thm)],[f130]) ).
fof(f130_sk,plain,
x != y,
inference(skolemisation,[status(esa)],[f130_nnf]) ).
cnf(c130,plain,
x != y,
inference(cnf_transformation,[status(esa)],[f130_sk]) ).
cnf(p169,plain,
y != y,
inference(demodulation,[status(thm)],[p166,c130]) ).
cnf(p181,plain,
$false,
inference(equality_resolution,[status(thm)],[p169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET085-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.37 % Computer : n009.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Thu Sep 24 09:41:30 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 23.42/3.93 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.42/3.93 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------