%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU151+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 02:51:07 PM UTC 2026
% Result : Theorem 21.65s 3.24s
% Output : Proof 21.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 33 ( 13 unt; 0 def)
% Number of atoms : 90 ( 72 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 96 ( 39 ~; 35 |; 20 &)
% ( 2 <=>; 0 =>; 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 : 6 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 50 ( 2 sgn 26 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,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(f2_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)],[f2]) ).
fof(f2_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])],[f2_nnf]) ).
cnf(c2,plain,
( X3 = X1
| X3 = X0
| ~ in(X3,X2)
| X2 != unordered_pair(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p22,plain,
( X0 = X2
| X0 = X1
| ~ in(X0,unordered_pair(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c2]) ).
fof(f4,conjecture,
! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(f4_neg,negated_conjecture,
~ ! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f4_nnf,plain,
? [A,B,C,D] :
( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
inference(nnf_transformation,[status(thm)],[f4_neg]) ).
fof(f4_sk,plain,
( sk1 != sk4
& sk1 != sk3
& unordered_pair(sk1,sk2) = unordered_pair(sk3,sk4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3,sk4])],[f4_nnf]) ).
cnf(c12,plain,
unordered_pair(sk1,sk2) = unordered_pair(sk3,sk4),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f1,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f1_nnf,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p16,plain,
unordered_pair(sk3,sk4) = unordered_pair(sk1,sk2),
inference(superposition,[status(thm)],[c12,c1]) ).
cnf(c3,plain,
( X3 != X0
| in(X3,X2)
| X2 != unordered_pair(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p20,plain,
( X1 != sk3
| in(X1,X0)
| X0 != unordered_pair(sk1,sk2) ),
inference(superposition,[status(thm)],[p16,c3]) ).
cnf(p26,plain,
( X0 != sk3
| in(X0,unordered_pair(sk1,sk2)) ),
inference(equality_resolution,[status(thm)],[p20]) ).
cnf(p28,plain,
in(sk3,unordered_pair(sk1,sk2)),
inference(equality_resolution,[status(thm)],[p26]) ).
cnf(p264,plain,
( sk3 = sk2
| sk3 = sk1 ),
inference(resolution,[status(thm)],[p22,p28]) ).
cnf(p282,plain,
( unordered_pair(sk2,sk4) = unordered_pair(sk1,sk2)
| sk3 = sk1 ),
inference(superposition,[status(thm)],[p264,p16]) ).
cnf(p18,plain,
( in(X1,X0)
| X0 != unordered_pair(X1,X2) ),
inference(equality_resolution,[status(thm)],[c3]) ).
cnf(p423,plain,
( in(sk1,unordered_pair(sk2,sk4))
| sk3 = sk1 ),
inference(resolution,[status(thm)],[p282,p18]) ).
cnf(p431,plain,
( sk1 = sk4
| sk1 = sk2
| sk3 = sk1 ),
inference(resolution,[status(thm)],[p423,p22]) ).
cnf(c13,plain,
sk1 != sk3,
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p501,plain,
( sk1 != sk1
| sk1 = sk4
| sk1 = sk2 ),
inference(superposition,[status(thm)],[p431,c13]) ).
cnf(p690,plain,
( sk1 = sk4
| sk1 = sk2 ),
inference(equality_resolution,[status(thm)],[p501]) ).
cnf(c14,plain,
sk1 != sk4,
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p693,plain,
sk1 = sk2,
inference(resolution,[status(thm)],[p690,c14]) ).
cnf(p280,plain,
( sk1 != sk2
| sk3 = sk1 ),
inference(equality_factoring,[status(thm)],[p264]) ).
cnf(p1131,plain,
sk3 = sk1,
inference(resolution,[status(thm)],[p693,p280]) ).
cnf(p1132,plain,
sk1 != sk1,
inference(demodulation,[status(thm)],[p1131,c13]) ).
cnf(p1287,plain,
$false,
inference(equality_resolution,[status(thm)],[p1132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU151+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.38 % Computer : n015.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 13:01:13 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 21.65/3.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.65/3.24 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------