%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU151+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 16.04s 2.48s
% Output : Proof 16.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 11 unt; 0 def)
% Number of atoms : 73 ( 57 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 84 ( 35 ~; 27 |; 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 : 49 ( 3 sgn 26 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,conjecture,
! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(f5_neg,negated_conjecture,
~ ! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f5_nnf,plain,
? [A,B,C,D] :
( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
inference(nnf_transformation,[status(thm)],[f5_neg]) ).
fof(f5_sk,plain,
( sk3 != sk6
& sk3 != sk5
& unordered_pair(sk3,sk4) = unordered_pair(sk5,sk6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4,sk5,sk6])],[f5_nnf]) ).
cnf(c13,plain,
unordered_pair(sk3,sk4) = unordered_pair(sk5,sk6),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f1,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox/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(p17,plain,
unordered_pair(sk5,sk6) = unordered_pair(sk3,sk4),
inference(superposition,[status(thm)],[c13,c1]) ).
fof(f2,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(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(p44,plain,
( X1 = sk6
| X1 = sk5
| ~ in(X1,X0)
| X0 != unordered_pair(sk3,sk4) ),
inference(superposition,[status(thm)],[p17,c2]) ).
cnf(p45,plain,
( X0 = sk6
| X0 = sk5
| ~ in(X0,unordered_pair(sk3,sk4)) ),
inference(equality_resolution,[status(thm)],[p44]) ).
cnf(c3,plain,
( X3 != X0
| in(X3,X2)
| X2 != unordered_pair(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p18,plain,
( X0 != X1
| in(X0,unordered_pair(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c3]) ).
cnf(p26,plain,
in(X0,unordered_pair(X0,X1)),
inference(equality_resolution,[status(thm)],[p18]) ).
cnf(p50,plain,
( sk3 = sk6
| sk3 = sk5 ),
inference(resolution,[status(thm)],[p45,p26]) ).
cnf(c15,plain,
sk3 != sk6,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p54,plain,
sk3 = sk5,
inference(resolution,[status(thm)],[p50,c15]) ).
cnf(c14,plain,
sk3 != sk5,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p55,plain,
$false,
inference(resolution,[status(thm)],[p54,c14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU151+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.34 % Computer : n008.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Thu Sep 24 12:58:40 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 16.04/2.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.04/2.48 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------