%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET927+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 02:44:19 PM UTC 2026
% Result : Theorem 4.76s 1.09s
% Output : Proof 4.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 2
% Syntax : Number of formulae : 34 ( 5 unt; 0 def)
% Number of atoms : 107 ( 57 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 107 ( 34 ~; 53 |; 17 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 1 sgn 15 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
<=> ( ( A = B
| in(B,C) )
& ~ in(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(f5_nnf,plain,
! [A,B,C] :
( ( ( A != B
& ~ in(B,C) )
| in(A,C)
| set_difference(unordered_pair(A,B),C) = singleton(A) )
& ( ( ( A = B
| in(B,C) )
& ~ in(A,C) )
| set_difference(unordered_pair(A,B),C) != singleton(A) ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C] :
( ( ( A != B
& ~ in(B,C) )
| in(A,C)
| set_difference(unordered_pair(A,B),C) = singleton(A) )
& ( ( ( A = B
| in(B,C) )
& ~ in(A,C) )
| set_difference(unordered_pair(A,B),C) != singleton(A) ) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c16,plain,
( X0 != X1
| in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(c15,plain,
( ~ in(X1,X2)
| in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(c14,plain,
( X0 = X1
| in(X1,X2)
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f4,conjecture,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
<=> ( ( A = B
| in(B,C) )
& ~ in(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_zfmisc_1) ).
fof(f4_neg,negated_conjecture,
~ ! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
<=> ( ( A = B
| in(B,C) )
& ~ in(A,C) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f4_nnf,plain,
? [A,B,C] :
( ( ( A = B
| in(B,C) )
& ~ in(A,C)
& set_difference(unordered_pair(A,B),C) != singleton(A) )
| ( ( ( A != B
& ~ in(B,C) )
| in(A,C) )
& set_difference(unordered_pair(A,B),C) = singleton(A) ) ),
inference(nnf_transformation,[status(thm)],[f4_neg]) ).
fof(f4_sk,plain,
( ( ( sk2 = sk3
| in(sk3,sk4) )
& ~ in(sk2,sk4)
& set_difference(unordered_pair(sk2,sk3),sk4) != singleton(sk2) )
| ( ( ( sk2 != sk3
& ~ in(sk3,sk4) )
| in(sk2,sk4) )
& set_difference(unordered_pair(sk2,sk3),sk4) = singleton(sk2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f4_nnf]) ).
cnf(c6,plain,
( sk2 = sk3
| in(sk3,sk4)
| set_difference(unordered_pair(sk2,sk3),sk4) = singleton(sk2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p20,plain,
( sk2 = sk3
| in(sk3,sk4)
| sk2 = sk3
| in(sk3,sk4) ),
inference(resolution,[status(thm)],[c14,c6]) ).
cnf(p22,plain,
( sk2 = sk3
| sk2 = sk3
| in(sk3,sk4) ),
inference(factoring,[status(thm)],[p20]) ).
cnf(p24,plain,
( sk2 = sk3
| in(sk3,sk4) ),
inference(factoring,[status(thm)],[p22]) ).
cnf(p27,plain,
( sk2 = sk3
| in(X0,sk4)
| set_difference(unordered_pair(X0,sk3),sk4) = singleton(X0) ),
inference(resolution,[status(thm)],[c15,p24]) ).
cnf(c7,plain,
( set_difference(unordered_pair(sk2,sk3),sk4) != singleton(sk2)
| ~ in(sk3,sk4)
| in(sk2,sk4) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p25,plain,
( set_difference(unordered_pair(sk2,sk3),sk4) != singleton(sk2)
| in(sk2,sk4)
| sk2 = sk3 ),
inference(resolution,[status(thm)],[p24,c7]) ).
cnf(p30,plain,
( in(sk2,sk4)
| sk2 = sk3
| sk2 = sk3
| in(sk2,sk4) ),
inference(resolution,[status(thm)],[p27,p25]) ).
cnf(p31,plain,
( sk2 = sk3
| sk2 = sk3
| in(sk2,sk4) ),
inference(factoring,[status(thm)],[p30]) ).
cnf(p33,plain,
( sk2 = sk3
| in(sk2,sk4) ),
inference(factoring,[status(thm)],[p31]) ).
cnf(c5,plain,
( ~ in(sk2,sk4)
| set_difference(unordered_pair(sk2,sk3),sk4) = singleton(sk2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p34,plain,
( set_difference(unordered_pair(sk2,sk3),sk4) = singleton(sk2)
| sk2 = sk3 ),
inference(resolution,[status(thm)],[p33,c5]) ).
cnf(c13,plain,
( ~ in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p37,plain,
( ~ in(sk2,sk4)
| sk2 = sk3 ),
inference(resolution,[status(thm)],[p34,c13]) ).
cnf(p39,plain,
( sk2 = sk3
| sk2 = sk3 ),
inference(resolution,[status(thm)],[p37,p33]) ).
cnf(p40,plain,
sk2 = sk3,
inference(factoring,[status(thm)],[p39]) ).
cnf(p46,plain,
( in(sk2,X0)
| set_difference(unordered_pair(sk2,sk3),X0) = singleton(sk2) ),
inference(resolution,[status(thm)],[c16,p40]) ).
cnf(c10,plain,
( set_difference(unordered_pair(sk2,sk3),sk4) != singleton(sk2)
| sk2 != sk3
| in(sk2,sk4) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p41,plain,
( set_difference(unordered_pair(sk2,sk3),sk4) != singleton(sk2)
| in(sk2,sk4) ),
inference(resolution,[status(thm)],[p40,c10]) ).
cnf(p48,plain,
( in(sk2,sk4)
| in(sk2,sk4) ),
inference(resolution,[status(thm)],[p46,p41]) ).
cnf(p50,plain,
in(sk2,sk4),
inference(factoring,[status(thm)],[p48]) ).
cnf(p51,plain,
set_difference(unordered_pair(sk2,sk3),sk4) = singleton(sk2),
inference(resolution,[status(thm)],[p50,c5]) ).
cnf(p54,plain,
~ in(sk2,sk4),
inference(resolution,[status(thm)],[p51,c13]) ).
cnf(p57,plain,
$false,
inference(resolution,[status(thm)],[p54,p50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET927+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n005.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
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 12:23:32 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.76/1.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.76/1.09 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------