%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU142+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 02:51:04 PM UTC 2026
% Result : Theorem 81.34s 12.35s
% Output : Proof 81.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 8 unt; 0 def)
% Number of atoms : 97 ( 66 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 111 ( 41 ~; 46 |; 20 &)
% ( 4 <=>; 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 : 5 ( 5 usr; 1 con; 0-3 aty)
% Number of variables : 56 ( 3 sgn 23 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(c5,plain,
( sk0(X0,X1) = X0
| in(sk0(X0,X1),X1)
| X1 = singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
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(p32,plain,
( X0 != X1
| in(X0,unordered_pair(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c9]) ).
cnf(p55,plain,
( in(sk0(X1,X0),unordered_pair(X1,X2))
| in(sk0(X1,X0),X0)
| X0 = singleton(X1) ),
inference(resolution,[status(thm)],[c5,p32]) ).
cnf(p159,plain,
( in(sk0(X0,unordered_pair(X0,X1)),unordered_pair(X0,X1))
| unordered_pair(X0,X1) = singleton(X0) ),
inference(factoring,[status(thm)],[p55]) ).
cnf(c8,plain,
( X3 = X1
| X3 = X0
| ~ in(X3,X2)
| X2 != unordered_pair(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p61,plain,
( X2 = X1
| ~ in(X2,X0)
| X0 != unordered_pair(X1,X1) ),
inference(factoring,[status(thm)],[c8]) ).
cnf(p66,plain,
( X0 = X1
| ~ in(X0,unordered_pair(X1,X1)) ),
inference(equality_resolution,[status(thm)],[p61]) ).
cnf(p171,plain,
( sk0(X0,unordered_pair(X0,X0)) = X0
| unordered_pair(X0,X0) = singleton(X0) ),
inference(resolution,[status(thm)],[p159,p66]) ).
cnf(c6,plain,
( ~ in(sk0(X0,X1),X1)
| sk0(X0,X1) != X0
| X1 = singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p185,plain,
( ~ in(sk0(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0))
| unordered_pair(X0,X0) = singleton(X0)
| unordered_pair(X0,X0) = singleton(X0) ),
inference(resolution,[status(thm)],[p171,c6]) ).
cnf(p6026,plain,
( ~ in(sk0(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0))
| unordered_pair(X0,X0) = singleton(X0) ),
inference(factoring,[status(thm)],[p185]) ).
cnf(p6027,plain,
( unordered_pair(X0,X0) = singleton(X0)
| unordered_pair(X0,X0) = singleton(X0) ),
inference(resolution,[status(thm)],[p6026,p159]) ).
cnf(p6030,plain,
unordered_pair(X0,X0) = singleton(X0),
inference(factoring,[status(thm)],[p6027]) ).
fof(f7,conjecture,
! [A] : unordered_pair(A,A) = singleton(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f7_neg,negated_conjecture,
~ ! [A] : unordered_pair(A,A) = singleton(A),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f7_nnf,plain,
? [A] : unordered_pair(A,A) != singleton(A),
inference(nnf_transformation,[status(thm)],[f7_neg]) ).
fof(f7_sk,plain,
unordered_pair(sk3,sk3) != singleton(sk3),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f7_nnf]) ).
cnf(c23,plain,
unordered_pair(sk3,sk3) != singleton(sk3),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p6031,plain,
singleton(sk3) != singleton(sk3),
inference(demodulation,[status(thm)],[p6030,c23]) ).
cnf(p6059,plain,
$false,
inference(equality_resolution,[status(thm)],[p6031]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU142+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.38 % Computer : n002.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Thu Sep 24 12:58:04 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 81.34/12.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 81.34/12.35 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------