%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU150+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 35.52s 5.66s
% Output : Proof 35.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 14 unt; 0 def)
% Number of atoms : 98 ( 69 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 109 ( 43 ~; 38 |; 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 : 59 ( 2 sgn 33 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f72,conjecture,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
fof(f72_neg,negated_conjecture,
~ ! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
inference(negated_conjecture,[status(cth)],[f72]) ).
fof(f72_nnf,plain,
? [A,B,C] :
( B != C
& singleton(A) = unordered_pair(B,C) ),
inference(nnf_transformation,[status(thm)],[f72_neg]) ).
fof(f72_sk,plain,
( sk14 != sk15
& singleton(sk13) = unordered_pair(sk14,sk15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13,sk14,sk15])],[f72_nnf]) ).
cnf(c134,plain,
singleton(sk13) = unordered_pair(sk14,sk15),
inference(cnf_transformation,[status(esa)],[f72_sk]) ).
fof(f2,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox2/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(p137,plain,
unordered_pair(sk14,sk15) = singleton(sk13),
inference(superposition,[status(thm)],[c134,c2]) ).
fof(f9,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(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(c24,plain,
( X3 != X1
| in(X3,X2)
| X2 != unordered_pair(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p266,plain,
( X1 != sk15
| in(X1,X0)
| X0 != singleton(sk13) ),
inference(superposition,[status(thm)],[p137,c24]) ).
cnf(p451,plain,
( X0 != sk15
| in(X0,singleton(sk13)) ),
inference(equality_resolution,[status(thm)],[p266]) ).
cnf(p456,plain,
in(sk15,singleton(sk13)),
inference(equality_resolution,[status(thm)],[p451]) ).
fof(f6,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/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(p154,plain,
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c8]) ).
cnf(p462,plain,
sk15 = sk13,
inference(resolution,[status(thm)],[p456,p154]) ).
cnf(c23,plain,
( X3 != X0
| in(X3,X2)
| X2 != unordered_pair(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p258,plain,
( X1 != sk14
| in(X1,X0)
| X0 != singleton(sk13) ),
inference(superposition,[status(thm)],[p137,c23]) ).
cnf(p426,plain,
( X0 != sk14
| in(X0,singleton(sk13)) ),
inference(equality_resolution,[status(thm)],[p258]) ).
cnf(p431,plain,
in(sk14,singleton(sk13)),
inference(equality_resolution,[status(thm)],[p426]) ).
cnf(p438,plain,
sk14 = sk13,
inference(resolution,[status(thm)],[p431,p154]) ).
cnf(c135,plain,
sk14 != sk15,
inference(cnf_transformation,[status(esa)],[f72_sk]) ).
cnf(p439,plain,
sk13 != sk15,
inference(demodulation,[status(thm)],[p438,c135]) ).
cnf(p463,plain,
sk13 != sk13,
inference(demodulation,[status(thm)],[p462,p439]) ).
cnf(p473,plain,
$false,
inference(equality_resolution,[status(thm)],[p463]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU150+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n013.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 12:57:14 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 35.52/5.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.52/5.66 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------