%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU413+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 02:20:28 PM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 12 unt; 0 def)
% Number of atoms : 153 ( 0 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 193 ( 77 ~; 68 |; 29 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 56 ( 52 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k1_latsum_1(A,B)))
=> ( ( r2_hidden(D,u1_struct_0(A))
& r1_orders_2(k1_latsum_1(A,B),C,D)
& m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B) )
=> r2_hidden(C,u1_struct_0(A)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k1_latsum_1(A,B)))
=> ( ( r2_hidden(D,u1_struct_0(A))
& r1_orders_2(k1_latsum_1(A,B),C,D)
& m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B) )
=> r2_hidden(C,u1_struct_0(A)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f7,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_orders_2(A,B,C)
<=> r2_hidden(k4_tarski(B,C),u1_orders_2(A)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] :
( ( l1_orders_2(B)
& l1_orders_2(A) )
=> ( l1_orders_2(k1_latsum_1(A,B))
& v1_orders_2(k1_latsum_1(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C,D] :
( ( r2_hidden(D,u1_struct_0(A))
& r2_hidden(k4_tarski(C,D),u1_orders_2(k1_latsum_1(A,B)))
& m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B) )
=> r2_hidden(C,u1_struct_0(A)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,plain,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ~ r2_hidden(C,u1_struct_0(A))
& r2_hidden(D,u1_struct_0(A))
& r1_orders_2(k1_latsum_1(A,B),C,D)
& m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B)
& m1_subset_1(D,u1_struct_0(k1_latsum_1(A,B))) )
& m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B))) )
& l1_orders_2(B) )
& l1_orders_2(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f45,plain,
( ~ r2_hidden(sK2_skl,u1_struct_0(sK0_skl))
& r2_hidden(sK3_skl,u1_struct_0(sK0_skl))
& r1_orders_2(k1_latsum_1(sK0_skl,sK1_skl),sK2_skl,sK3_skl)
& m1_subset_1(k3_xboole_0(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)),k1_zfmisc_1(u1_struct_0(sK1_skl)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)),sK1_skl)
& m1_subset_1(sK3_skl,u1_struct_0(k1_latsum_1(sK0_skl,sK1_skl)))
& m1_subset_1(sK2_skl,u1_struct_0(k1_latsum_1(sK0_skl,sK1_skl)))
& l1_orders_2(sK1_skl)
& l1_orders_2(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(C,sK2_skl),skolemize(D,sK3_skl)],[f44]) ).
fof(f46,plain,
l1_orders_2(sK0_skl),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
l1_orders_2(sK1_skl),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f48,plain,
m1_subset_1(sK2_skl,u1_struct_0(k1_latsum_1(sK0_skl,sK1_skl))),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f49,plain,
m1_subset_1(sK3_skl,u1_struct_0(k1_latsum_1(sK0_skl,sK1_skl))),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f50,plain,
v12_waybel_0(k3_xboole_0(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)),sK1_skl),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f51,plain,
m1_subset_1(k3_xboole_0(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)),k1_zfmisc_1(u1_struct_0(sK1_skl))),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f52,plain,
r1_orders_2(k1_latsum_1(sK0_skl,sK1_skl),sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f53,plain,
r2_hidden(sK3_skl,u1_struct_0(sK0_skl)),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f54,plain,
~ r2_hidden(sK2_skl,u1_struct_0(sK0_skl)),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f63,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( r1_orders_2(A,B,C)
<=> r2_hidden(k4_tarski(B,C),u1_orders_2(A)) )
| ~ m1_subset_1(C,u1_struct_0(A)) )
| ~ m1_subset_1(B,u1_struct_0(A)) )
| ~ l1_orders_2(A) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f64,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ~ r2_hidden(k4_tarski(B,C),u1_orders_2(A))
| r1_orders_2(A,B,C) )
& ( r2_hidden(k4_tarski(B,C),u1_orders_2(A))
| ~ r1_orders_2(A,B,C) ) )
| ~ m1_subset_1(C,u1_struct_0(A)) )
| ~ m1_subset_1(B,u1_struct_0(A)) )
| ~ l1_orders_2(A) ),
inference(NNF_transformation,[status(thm)],[f63]) ).
fof(f65,plain,
! [X0,X1,X2] :
( r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0))
| ~ r1_orders_2(X0,X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f70,plain,
! [A,B] :
( ( l1_orders_2(k1_latsum_1(A,B))
& v1_orders_2(k1_latsum_1(A,B)) )
| ~ l1_orders_2(B)
| ~ l1_orders_2(A) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f72,plain,
! [X0,X1] :
( l1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f107,plain,
! [A] :
( ! [B] :
( ! [C,D] :
( r2_hidden(C,u1_struct_0(A))
| ~ r2_hidden(D,u1_struct_0(A))
| ~ r2_hidden(k4_tarski(C,D),u1_orders_2(k1_latsum_1(A,B)))
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B) )
| ~ l1_orders_2(B) )
| ~ l1_orders_2(A) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f108,plain,
! [A] :
( ! [B] :
( ! [C] :
( r2_hidden(C,u1_struct_0(A))
| ! [D] :
( ~ r2_hidden(D,u1_struct_0(A))
| ~ r2_hidden(k4_tarski(C,D),u1_orders_2(k1_latsum_1(A,B)))
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B) ) )
| ~ l1_orders_2(B) )
| ~ l1_orders_2(A) ),
inference(miniscoping,[status(thm)],[f107]) ).
fof(f109,plain,
! [X0,X1,X2,X3] :
( r2_hidden(X2,u1_struct_0(X0))
| ~ r2_hidden(X3,u1_struct_0(X0))
| ~ r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f146,plain,
! [X0,X1] :
( r2_hidden(X0,u1_struct_0(sK0_skl))
| ~ r2_hidden(X1,u1_struct_0(sK0_skl))
| ~ r2_hidden(k4_tarski(X0,X1),u1_orders_2(k1_latsum_1(sK0_skl,sK1_skl)))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)),sK1_skl)
| ~ l1_orders_2(sK1_skl)
| ~ l1_orders_2(sK0_skl) ),
inference(resolution,[status(thm)],[f109,f51]) ).
fof(f150,plain,
! [X0,X1] :
( r2_hidden(X0,u1_struct_0(sK0_skl))
| ~ r2_hidden(X1,u1_struct_0(sK0_skl))
| ~ r2_hidden(k4_tarski(X0,X1),u1_orders_2(k1_latsum_1(sK0_skl,sK1_skl)))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)),sK1_skl)
| ~ l1_orders_2(sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f146,f46]) ).
fof(f172,plain,
! [X0,X1] :
( r2_hidden(X0,u1_struct_0(sK0_skl))
| ~ r2_hidden(X1,u1_struct_0(sK0_skl))
| ~ r2_hidden(k4_tarski(X0,X1),u1_orders_2(k1_latsum_1(sK0_skl,sK1_skl)))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)),sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f150,f47]) ).
fof(f173,plain,
! [X0,X1] :
( ~ r1_orders_2(k1_latsum_1(sK0_skl,sK1_skl),X1,X0)
| ~ m1_subset_1(X0,u1_struct_0(k1_latsum_1(sK0_skl,sK1_skl)))
| ~ m1_subset_1(X1,u1_struct_0(k1_latsum_1(sK0_skl,sK1_skl)))
| ~ l1_orders_2(k1_latsum_1(sK0_skl,sK1_skl))
| r2_hidden(X1,u1_struct_0(sK0_skl))
| ~ r2_hidden(X0,u1_struct_0(sK0_skl))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)),sK1_skl) ),
inference(resolution,[status(thm)],[f172,f65]) ).
fof(f174,plain,
! [X0,X1] :
( ~ r1_orders_2(k1_latsum_1(sK0_skl,sK1_skl),X1,X0)
| ~ m1_subset_1(X0,u1_struct_0(k1_latsum_1(sK0_skl,sK1_skl)))
| ~ m1_subset_1(X1,u1_struct_0(k1_latsum_1(sK0_skl,sK1_skl)))
| ~ l1_orders_2(k1_latsum_1(sK0_skl,sK1_skl))
| r2_hidden(X1,u1_struct_0(sK0_skl))
| ~ r2_hidden(X0,u1_struct_0(sK0_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f173,f50]) ).
fof(f175,plain,
( ~ m1_subset_1(sK3_skl,u1_struct_0(k1_latsum_1(sK0_skl,sK1_skl)))
| ~ m1_subset_1(sK2_skl,u1_struct_0(k1_latsum_1(sK0_skl,sK1_skl)))
| ~ l1_orders_2(k1_latsum_1(sK0_skl,sK1_skl))
| r2_hidden(sK2_skl,u1_struct_0(sK0_skl))
| ~ r2_hidden(sK3_skl,u1_struct_0(sK0_skl)) ),
inference(resolution,[status(thm)],[f174,f52]) ).
fof(f176,plain,
( ~ m1_subset_1(sK3_skl,u1_struct_0(k1_latsum_1(sK0_skl,sK1_skl)))
| ~ m1_subset_1(sK2_skl,u1_struct_0(k1_latsum_1(sK0_skl,sK1_skl)))
| ~ l1_orders_2(k1_latsum_1(sK0_skl,sK1_skl))
| r2_hidden(sK2_skl,u1_struct_0(sK0_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f175,f53]) ).
fof(f177,plain,
( ~ m1_subset_1(sK3_skl,u1_struct_0(k1_latsum_1(sK0_skl,sK1_skl)))
| ~ m1_subset_1(sK2_skl,u1_struct_0(k1_latsum_1(sK0_skl,sK1_skl)))
| ~ l1_orders_2(k1_latsum_1(sK0_skl,sK1_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f176,f54]) ).
fof(f178,plain,
( ~ m1_subset_1(sK2_skl,u1_struct_0(k1_latsum_1(sK0_skl,sK1_skl)))
| ~ l1_orders_2(k1_latsum_1(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f177,f49]) ).
fof(f179,plain,
~ l1_orders_2(k1_latsum_1(sK0_skl,sK1_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f178,f48]) ).
fof(f180,plain,
( ~ l1_orders_2(sK1_skl)
| ~ l1_orders_2(sK0_skl) ),
inference(resolution,[status(thm)],[f179,f72]) ).
fof(f181,plain,
~ l1_orders_2(sK1_skl),
inference(forward_subsumption_resolution,[status(thm)],[f180,f46]) ).
fof(f182,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f181,f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU413+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.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 : Mon Sep 21 06:24:00 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.43 % Elapsed time: 0.060864 seconds
% 0.09/0.43 % CPU time: 0.156309 seconds
% 0.09/0.43 % Total memory used: 103.534 MB
% 0.09/0.43 % Net memory used: 103.444 MB
%------------------------------------------------------------------------------