%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET881+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 02:44:13 PM UTC 2026
% Result : Theorem 11.41s 2.50s
% Output : Proof 11.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 9 unt; 0 def)
% Number of atoms : 58 ( 39 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 67 ( 27 ~; 23 |; 14 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 38 ( 4 sgn 22 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f2_nnf,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( D = B
| D = A )
& ~ in(D,C) )
| ( D != B
& D != A
& in(D,C) ) )
| C = unordered_pair(A,B) )
& ( ! [D] :
( ( ( D != B
& D != A )
| in(D,C) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [C,A,B,D] :
( ( ( ( sk0(A,B,C) = B
| sk0(A,B,C) = A )
& ~ in(sk0(A,B,C),C) )
| ( sk0(A,B,C) != B
& sk0(A,B,C) != A
& in(sk0(A,B,C),C) )
| C = unordered_pair(A,B) )
& ( ( ( ( D != B
& D != A )
| in(D,C) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c3,plain,
( X3 != X0
| in(X3,X2)
| X2 != unordered_pair(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p22,plain,
( X0 != X1
| in(X0,unordered_pair(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c3]) ).
cnf(p25,plain,
in(X0,unordered_pair(X0,X1)),
inference(equality_resolution,[status(thm)],[p22]) ).
fof(f4,axiom,
! [A,B] :
( set_difference(singleton(A),B) = empty_set
<=> in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).
fof(f4_nnf,plain,
! [A,B] :
( ( ~ in(A,B)
| set_difference(singleton(A),B) = empty_set )
& ( in(A,B)
| set_difference(singleton(A),B) != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] :
( ( ~ in(A,B)
| set_difference(singleton(A),B) = empty_set )
& ( in(A,B)
| set_difference(singleton(A),B) != empty_set ) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c13,plain,
( ~ in(X0,X1)
| set_difference(singleton(X0),X1) = empty_set ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p29,plain,
set_difference(singleton(X0),unordered_pair(X0,X1)) = empty_set,
inference(resolution,[status(thm)],[p25,c13]) ).
fof(f7,conjecture,
! [A,B] : set_difference(singleton(A),unordered_pair(A,B)) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_zfmisc_1) ).
fof(f7_neg,negated_conjecture,
~ ! [A,B] : set_difference(singleton(A),unordered_pair(A,B)) = empty_set,
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f7_nnf,plain,
? [A,B] : set_difference(singleton(A),unordered_pair(A,B)) != empty_set,
inference(nnf_transformation,[status(thm)],[f7_neg]) ).
fof(f7_sk,plain,
set_difference(singleton(sk3),unordered_pair(sk3,sk4)) != empty_set,
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f7_nnf]) ).
cnf(c16,plain,
set_difference(singleton(sk3),unordered_pair(sk3,sk4)) != empty_set,
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p30,plain,
empty_set != empty_set,
inference(demodulation,[status(thm)],[p29,c16]) ).
cnf(p31,plain,
$false,
inference(equality_resolution,[status(thm)],[p30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET881+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.04/0.52 % Computer : n012.cluster.edu
% 0.04/0.52 % Model : x86_64 x86_64
% 0.04/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.52 % Memory : 8046.5625MB
% 0.04/0.52 % OS : Linux 6.8.0-71-generic
% 0.04/0.52 % CPULimit : 300
% 0.04/0.52 % WCLimit : 300
% 0.04/0.52 % DateTime : Thu Sep 24 12:19:21 UTC 2026
% 0.04/0.53 % CPUTime :
% 0.04/0.53 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 11.41/2.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.41/2.50 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------