%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET878+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 : n011.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 02:44:12 PM UTC 2026
% Result : Theorem 25.18s 4.09s
% Output : Proof 25.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 9 unt; 0 def)
% Number of atoms : 54 ( 37 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 61 ( 25 ~; 21 |; 12 &)
% ( 2 <=>; 1 =>; 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 : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 38 ( 4 sgn 22 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,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(f3_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)],[f3]) ).
fof(f3_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])],[f3_nnf]) ).
cnf(c4,plain,
( X3 != X0
| in(X3,X2)
| X2 != unordered_pair(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p18,plain,
( X0 != X1
| in(X0,unordered_pair(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c4]) ).
cnf(p21,plain,
in(X0,unordered_pair(X0,X1)),
inference(equality_resolution,[status(thm)],[p18]) ).
fof(f5,axiom,
! [A,B] :
( in(A,B)
=> set_intersection2(B,singleton(A)) = singleton(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_zfmisc_1) ).
fof(f5_nnf,plain,
! [A,B] :
( set_intersection2(B,singleton(A)) = singleton(A)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B] :
( set_intersection2(B,singleton(A)) = singleton(A)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c13,plain,
( set_intersection2(X1,singleton(X0)) = singleton(X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p26,plain,
set_intersection2(singleton(X0),unordered_pair(X0,X1)) = singleton(X0),
inference(resolution,[status(thm)],[p21,c13]) ).
fof(f8,conjecture,
! [A,B] : set_intersection2(singleton(A),unordered_pair(A,B)) = singleton(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_zfmisc_1) ).
fof(f8_neg,negated_conjecture,
~ ! [A,B] : set_intersection2(singleton(A),unordered_pair(A,B)) = singleton(A),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [A,B] : set_intersection2(singleton(A),unordered_pair(A,B)) != singleton(A),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
set_intersection2(singleton(sk3),unordered_pair(sk3,sk4)) != singleton(sk3),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f8_nnf]) ).
cnf(c16,plain,
set_intersection2(singleton(sk3),unordered_pair(sk3,sk4)) != singleton(sk3),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p27,plain,
singleton(sk3) != singleton(sk3),
inference(demodulation,[status(thm)],[p26,c16]) ).
cnf(p28,plain,
$false,
inference(equality_resolution,[status(thm)],[p27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET878+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.32 % Computer : n011.cluster.edu
% 0.07/0.32 % Model : x86_64 x86_64
% 0.07/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.32 % Memory : 8046.5625MB
% 0.07/0.32 % OS : Linux 6.8.0-71-generic
% 0.07/0.32 % CPULimit : 300
% 0.07/0.32 % WCLimit : 300
% 0.07/0.32 % DateTime : Thu Sep 24 12:18:57 UTC 2026
% 0.07/0.33 % CPUTime :
% 0.07/0.33 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 25.18/4.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.18/4.09 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------