%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET885+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 22.31s 4.34s
% Output : Proof 22.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 6 unt; 0 def)
% Number of atoms : 99 ( 49 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 117 ( 43 ~; 40 |; 26 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 60 ( 3 sgn 36 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('/export/starexec/sandbox/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] :
( ( ( ( sk1(A,B,C) = B
| sk1(A,B,C) = A )
& ~ in(sk1(A,B,C),C) )
| ( sk1(A,B,C) != B
& sk1(A,B,C) != A
& in(sk1(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,[sk1])],[f3_nnf]) ).
cnf(c9,plain,
( X3 != X0
| in(X3,X2)
| X2 != unordered_pair(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p57,plain,
( X0 != X1
| in(X0,unordered_pair(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c9]) ).
cnf(p61,plain,
in(X0,unordered_pair(X0,X1)),
inference(equality_resolution,[status(thm)],[p57]) ).
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f4_nnf,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk2(A,B),B)
& in(sk2(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f4_nnf]) ).
cnf(c17,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f8,conjecture,
! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> A = C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_zfmisc_1) ).
fof(f8_neg,negated_conjecture,
~ ! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> A = C ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [A,B,C] :
( A != C
& subset(unordered_pair(A,B),singleton(C)) ),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
( sk5 != sk7
& subset(unordered_pair(sk5,sk6),singleton(sk7)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5,sk6,sk7])],[f8_nnf]) ).
cnf(c23,plain,
subset(unordered_pair(sk5,sk6),singleton(sk7)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p27,plain,
( in(X0,singleton(sk7))
| ~ in(X0,unordered_pair(sk5,sk6)) ),
inference(resolution,[status(thm)],[c17,c23]) ).
cnf(p83,plain,
in(sk5,singleton(sk7)),
inference(resolution,[status(thm)],[p61,p27]) ).
fof(f2,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f2_nnf,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
& ~ in(C,B) )
| ( C != A
& in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,A,C] :
( ( ( sk0(A,B) = A
& ~ in(sk0(A,B),B) )
| ( sk0(A,B) != A
& in(sk0(A,B),B) )
| B = singleton(A) )
& ( ( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c2,plain,
( X2 = X0
| ~ in(X2,X1)
| X1 != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p30,plain,
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(p88,plain,
sk5 = sk7,
inference(resolution,[status(thm)],[p83,p30]) ).
cnf(c24,plain,
sk5 != sk7,
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p89,plain,
$false,
inference(resolution,[status(thm)],[p88,c24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET885+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.42 % Computer : n006.cluster.edu
% 0.08/0.42 % Model : x86_64 x86_64
% 0.08/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.42 % Memory : 8046.5625MB
% 0.08/0.42 % OS : Linux 6.8.0-71-generic
% 0.08/0.42 % CPULimit : 300
% 0.08/0.42 % WCLimit : 300
% 0.08/0.42 % DateTime : Thu Sep 24 12:19:44 UTC 2026
% 0.08/0.42 % CPUTime :
% 0.08/0.42 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 22.31/4.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.31/4.34 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------