%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU149+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 02:51:06 PM UTC 2026
% Result : Theorem 26.81s 4.33s
% Output : Proof 26.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 12 unt; 0 def)
% Number of atoms : 85 ( 60 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 94 ( 35 ~; 31 |; 22 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 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 : 54 ( 3 sgn 33 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f71,conjecture,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(f71_neg,negated_conjecture,
~ ! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
inference(negated_conjecture,[status(cth)],[f71]) ).
fof(f71_nnf,plain,
? [A,B,C] :
( A != B
& singleton(A) = unordered_pair(B,C) ),
inference(nnf_transformation,[status(thm)],[f71_neg]) ).
fof(f71_sk,plain,
( sk13 != sk14
& singleton(sk13) = unordered_pair(sk14,sk15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13,sk14,sk15])],[f71_nnf]) ).
cnf(c133,plain,
singleton(sk13) = unordered_pair(sk14,sk15),
inference(cnf_transformation,[status(esa)],[f71_sk]) ).
fof(f2,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f2_nnf,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p152,plain,
unordered_pair(sk14,sk15) = singleton(sk13),
inference(superposition,[status(thm)],[c133,c2]) ).
fof(f9,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(f9_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)],[f9]) ).
fof(f9_sk,plain,
! [C,A,B,D] :
( ( ( ( sk3(A,B,C) = B
| sk3(A,B,C) = A )
& ~ in(sk3(A,B,C),C) )
| ( sk3(A,B,C) != B
& sk3(A,B,C) != A
& in(sk3(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,[sk3])],[f9_nnf]) ).
cnf(c23,plain,
( X3 != X0
| in(X3,X2)
| X2 != unordered_pair(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p246,plain,
( X0 != X1
| in(X0,unordered_pair(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c23]) ).
cnf(p671,plain,
in(X0,unordered_pair(X0,X1)),
inference(equality_resolution,[status(thm)],[p246]) ).
cnf(p681,plain,
in(sk14,singleton(sk13)),
inference(superposition,[status(thm)],[p152,p671]) ).
fof(f6,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f6_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)],[f6]) ).
fof(f6_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])],[f6_nnf]) ).
cnf(c8,plain,
( X2 = X0
| ~ in(X2,X1)
| X1 != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p153,plain,
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c8]) ).
cnf(p686,plain,
sk14 = sk13,
inference(resolution,[status(thm)],[p681,p153]) ).
cnf(c134,plain,
sk13 != sk14,
inference(cnf_transformation,[status(esa)],[f71_sk]) ).
cnf(p687,plain,
sk13 != sk13,
inference(demodulation,[status(thm)],[p686,c134]) ).
cnf(p689,plain,
$false,
inference(equality_resolution,[status(thm)],[p687]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU149+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.01/0.36 % WCLimit : 300
% 0.01/0.36 % DateTime : Thu Sep 24 12:57:17 UTC 2026
% 0.01/0.36 % CPUTime :
% 0.01/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 26.81/4.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.81/4.33 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------