%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN966+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 : Thu Sep 24 03:18:35 PM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 21 ( 6 unt; 0 def)
% Number of atoms : 80 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 97 ( 38 ~; 32 |; 17 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 48 ( 40 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) )
=> ! [A,B] :
( eq(A,B)
=> eq(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) )
=> ! [A,B] :
( eq(A,B)
=> eq(B,A) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( ( ? [Z] :
( ( a_member_of(Z,Y)
| a_member_of(Z,X) )
& ( ~ a_member_of(Z,Y)
| ~ a_member_of(Z,X) ) )
| eq(X,Y) )
& ( ! [Z] :
( ( ~ a_member_of(Z,Y)
| a_member_of(Z,X) )
& ( a_member_of(Z,Y)
| ~ a_member_of(Z,X) ) )
| ~ eq(X,Y) ) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f5,plain,
( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( ? [Z] :
( ( a_member_of(Z,Y)
| a_member_of(Z,X) )
& ( ~ a_member_of(Z,Y)
| ~ a_member_of(Z,X) ) )
| eq(X,Y) )
& ! [X,Y] :
( ( ! [Z] :
( ~ a_member_of(Z,Y)
| a_member_of(Z,X) )
& ! [Z] :
( a_member_of(Z,Y)
| ~ a_member_of(Z,X) ) )
| ~ eq(X,Y) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f6,plain,
( ~ eq(sK2_skl,sK1_skl)
& eq(sK1_skl,sK2_skl)
& ! [X,Y] :
( ( ( a_member_of(sK0_skl(Y,X),Y)
| a_member_of(sK0_skl(Y,X),X) )
& ( ~ a_member_of(sK0_skl(Y,X),Y)
| ~ a_member_of(sK0_skl(Y,X),X) ) )
| eq(X,Y) )
& ! [X,Y] :
( ( ! [Z] :
( ~ a_member_of(Z,Y)
| a_member_of(Z,X) )
& ! [Z] :
( a_member_of(Z,Y)
| ~ a_member_of(Z,X) ) )
| ~ eq(X,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(Z,sK0_skl(Y,X)),skolemize(A,sK1_skl),skolemize(B,sK2_skl)],[f5]) ).
fof(f7,plain,
! [X0,X1,X2] :
( a_member_of(X2,X1)
| ~ a_member_of(X2,X0)
| ~ eq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0,X1,X2] :
( ~ a_member_of(X2,X1)
| a_member_of(X2,X0)
| ~ eq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f9,plain,
! [X0,X1] :
( ~ a_member_of(sK0_skl(X1,X0),X1)
| ~ a_member_of(sK0_skl(X1,X0),X0)
| eq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f10,plain,
! [X0,X1] :
( a_member_of(sK0_skl(X1,X0),X1)
| a_member_of(sK0_skl(X1,X0),X0)
| eq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f11,plain,
eq(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f12,plain,
~ eq(sK2_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f13,plain,
( ~ a_member_of(sK0_skl(sK1_skl,sK2_skl),sK1_skl)
| ~ a_member_of(sK0_skl(sK1_skl,sK2_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f9,f12]) ).
fof(f15,plain,
! [X0] :
( ~ a_member_of(sK0_skl(sK1_skl,sK2_skl),X0)
| ~ eq(X0,sK2_skl)
| ~ a_member_of(sK0_skl(sK1_skl,sK2_skl),sK1_skl) ),
inference(resolution,[status(thm)],[f13,f7]) ).
fof(f17,plain,
( ~ a_member_of(sK0_skl(sK1_skl,sK2_skl),sK1_skl)
| ~ a_member_of(sK0_skl(sK1_skl,sK2_skl),sK1_skl) ),
inference(resolution,[status(thm)],[f15,f11]) ).
fof(f19,plain,
~ a_member_of(sK0_skl(sK1_skl,sK2_skl),sK1_skl),
inference(duplicate_literals_removal,[status(thm)],[f17]) ).
fof(f20,plain,
( a_member_of(sK0_skl(sK1_skl,sK2_skl),sK2_skl)
| eq(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f19,f10]) ).
fof(f21,plain,
! [X0] :
( ~ a_member_of(sK0_skl(sK1_skl,sK2_skl),X0)
| ~ eq(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f19,f8]) ).
fof(f23,plain,
a_member_of(sK0_skl(sK1_skl,sK2_skl),sK2_skl),
inference(forward_subsumption_resolution,[status(thm)],[f20,f12]) ).
fof(f24,plain,
~ a_member_of(sK0_skl(sK1_skl,sK2_skl),sK2_skl),
inference(resolution,[status(thm)],[f21,f11]) ).
fof(f26,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f24,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN966+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 11:31:25 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.042569 seconds
% 0.12/0.40 % CPU time: 0.117210 seconds
% 0.12/0.40 % Total memory used: 16.676 MB
% 0.12/0.40 % Net memory used: 16.152 MB
%------------------------------------------------------------------------------