%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU408+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Thu Sep 24 02:20:27 PM UTC 2026
% Result : Theorem 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 15 unt; 0 def)
% Number of atoms : 188 ( 33 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 220 ( 73 ~; 63 |; 69 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-6 aty)
% Number of variables : 81 ( 76 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A] :
( ( l1_orders_2(A)
& v1_lattice3(A)
& v4_orders_2(A)
& v3_orders_2(A)
& v2_orders_2(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_orders_2(B)
& v1_lattice3(B)
& v4_orders_2(B)
& v3_orders_2(B)
& v2_orders_2(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( r2_hidden(C,u1_struct_0(B))
=> m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A] :
( ( l1_orders_2(A)
& v1_lattice3(A)
& v4_orders_2(A)
& v3_orders_2(A)
& v2_orders_2(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_orders_2(B)
& v1_lattice3(B)
& v4_orders_2(B)
& v3_orders_2(B)
& v2_orders_2(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( r2_hidden(C,u1_struct_0(B))
=> m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B))) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f6,axiom,
! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( ( l1_orders_2(C)
& v1_orders_2(C) )
=> ( C = k1_latsum_1(A,B)
<=> ( u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A),u1_orders_2(B)),k7_relset_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_orders_2(A),u1_orders_2(B)))
& u1_struct_0(C) = k2_xboole_0(u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] :
( C = k2_xboole_0(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ( r2_hidden(D,B)
| r2_hidden(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B)))
& r2_hidden(C,u1_struct_0(B)) )
& l1_orders_2(B)
& v1_lattice3(B)
& v4_orders_2(B)
& v3_orders_2(B)
& v2_orders_2(B)
& ~ v3_struct_0(B) )
& l1_orders_2(A)
& v1_lattice3(A)
& v4_orders_2(A)
& v3_orders_2(A)
& v2_orders_2(A)
& ~ v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f54,plain,
( ~ m1_subset_1(sK2_skl,u1_struct_0(k1_latsum_1(sK0_skl,sK1_skl)))
& r2_hidden(sK2_skl,u1_struct_0(sK1_skl))
& l1_orders_2(sK1_skl)
& v1_lattice3(sK1_skl)
& v4_orders_2(sK1_skl)
& v3_orders_2(sK1_skl)
& v2_orders_2(sK1_skl)
& ~ v3_struct_0(sK1_skl)
& l1_orders_2(sK0_skl)
& v1_lattice3(sK0_skl)
& v4_orders_2(sK0_skl)
& v3_orders_2(sK0_skl)
& v2_orders_2(sK0_skl)
& ~ v3_struct_0(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(C,sK2_skl)],[f53]) ).
fof(f60,plain,
l1_orders_2(sK0_skl),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f66,plain,
l1_orders_2(sK1_skl),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f67,plain,
r2_hidden(sK2_skl,u1_struct_0(sK1_skl)),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f68,plain,
~ m1_subset_1(sK2_skl,u1_struct_0(k1_latsum_1(sK0_skl,sK1_skl))),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f76,plain,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f77,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( C = k1_latsum_1(A,B)
<=> ( u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A),u1_orders_2(B)),k7_relset_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_orders_2(A),u1_orders_2(B)))
& u1_struct_0(C) = k2_xboole_0(u1_struct_0(A),u1_struct_0(B)) ) )
| ~ l1_orders_2(C)
| ~ v1_orders_2(C) )
| ~ l1_orders_2(B) )
| ~ l1_orders_2(A) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f78,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( u1_orders_2(C) != k2_xboole_0(k2_xboole_0(u1_orders_2(A),u1_orders_2(B)),k7_relset_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_orders_2(A),u1_orders_2(B)))
| u1_struct_0(C) != k2_xboole_0(u1_struct_0(A),u1_struct_0(B))
| C = k1_latsum_1(A,B) )
& ( ( u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A),u1_orders_2(B)),k7_relset_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_orders_2(A),u1_orders_2(B)))
& u1_struct_0(C) = k2_xboole_0(u1_struct_0(A),u1_struct_0(B)) )
| C != k1_latsum_1(A,B) ) )
| ~ l1_orders_2(C)
| ~ v1_orders_2(C) )
| ~ l1_orders_2(B) )
| ~ l1_orders_2(A) ),
inference(NNF_transformation,[status(thm)],[f77]) ).
fof(f79,plain,
! [X0,X1,X2] :
( u1_struct_0(X2) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))
| X2 != k1_latsum_1(X0,X1)
| ~ l1_orders_2(X2)
| ~ v1_orders_2(X2)
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f82,plain,
! [A,B,C] :
( ( ? [D] :
( ( r2_hidden(D,B)
| r2_hidden(D,A)
| r2_hidden(D,C) )
& ( ( ~ r2_hidden(D,B)
& ~ r2_hidden(D,A) )
| ~ r2_hidden(D,C) ) )
| C = k2_xboole_0(A,B) )
& ( ! [D] :
( ( ( ~ r2_hidden(D,B)
& ~ r2_hidden(D,A) )
| r2_hidden(D,C) )
& ( r2_hidden(D,B)
| r2_hidden(D,A)
| ~ r2_hidden(D,C) ) )
| C != k2_xboole_0(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f83,plain,
( ! [A,B,C] :
( ? [D] :
( ( r2_hidden(D,B)
| r2_hidden(D,A)
| r2_hidden(D,C) )
& ( ( ~ r2_hidden(D,B)
& ~ r2_hidden(D,A) )
| ~ r2_hidden(D,C) ) )
| C = k2_xboole_0(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( ~ r2_hidden(D,B)
& ~ r2_hidden(D,A) )
| r2_hidden(D,C) )
& ! [D] :
( r2_hidden(D,B)
| r2_hidden(D,A)
| ~ r2_hidden(D,C) ) )
| C != k2_xboole_0(A,B) ) ),
inference(miniscoping,[status(thm)],[f82]) ).
fof(f84,plain,
( ! [A,B,C] :
( ( ( r2_hidden(sK3_skl(C,B,A),B)
| r2_hidden(sK3_skl(C,B,A),A)
| r2_hidden(sK3_skl(C,B,A),C) )
& ( ( ~ r2_hidden(sK3_skl(C,B,A),B)
& ~ r2_hidden(sK3_skl(C,B,A),A) )
| ~ r2_hidden(sK3_skl(C,B,A),C) ) )
| C = k2_xboole_0(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( ~ r2_hidden(D,B)
& ~ r2_hidden(D,A) )
| r2_hidden(D,C) )
& ! [D] :
( r2_hidden(D,B)
| r2_hidden(D,A)
| ~ r2_hidden(D,C) ) )
| C != k2_xboole_0(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(D,sK3_skl(C,B,A))],[f83]) ).
fof(f86,plain,
! [X0,X1,X2,X3] :
( ~ r2_hidden(X3,X1)
| r2_hidden(X3,X0)
| X0 != k2_xboole_0(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f94,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)],[f10]) ).
fof(f95,plain,
! [X0,X1] :
( v1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f96,plain,
! [X0,X1] :
( l1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f157,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f158,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f179,plain,
! [X0,X1] :
( u1_struct_0(k1_latsum_1(X0,X1)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))
| ~ l1_orders_2(k1_latsum_1(X0,X1))
| ~ v1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f79]) ).
fof(f182,plain,
! [X0,X1,X2] :
( ~ r2_hidden(X0,X1)
| r2_hidden(X0,k2_xboole_0(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f86]) ).
fof(f185,plain,
! [X0,X1] :
( u1_struct_0(k1_latsum_1(X0,X1)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))
| ~ l1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f179,f95]) ).
fof(f187,plain,
! [X0,X1] :
( u1_struct_0(k1_latsum_1(X0,X1)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f185,f96]) ).
fof(f190,plain,
~ r2_hidden(sK2_skl,u1_struct_0(k1_latsum_1(sK0_skl,sK1_skl))),
inference(resolution,[status(thm)],[f68,f158]) ).
fof(f218,plain,
! [X0] :
( u1_struct_0(k1_latsum_1(X0,sK1_skl)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(sK1_skl))
| ~ l1_orders_2(X0) ),
inference(resolution,[status(thm)],[f187,f66]) ).
fof(f219,plain,
! [X0] :
( u1_struct_0(k1_latsum_1(X0,sK0_skl)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(sK0_skl))
| ~ l1_orders_2(X0) ),
inference(resolution,[status(thm)],[f187,f60]) ).
fof(f223,plain,
u1_struct_0(k1_latsum_1(sK0_skl,sK1_skl)) = k2_xboole_0(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)),
inference(resolution,[status(thm)],[f218,f60]) ).
fof(f227,plain,
u1_struct_0(k1_latsum_1(sK1_skl,sK0_skl)) = k2_xboole_0(u1_struct_0(sK1_skl),u1_struct_0(sK0_skl)),
inference(resolution,[status(thm)],[f219,f66]) ).
fof(f234,plain,
u1_struct_0(k1_latsum_1(sK0_skl,sK1_skl)) = k2_xboole_0(u1_struct_0(sK1_skl),u1_struct_0(sK0_skl)),
inference(paramodulation,[status(thm)],[f76,f223]) ).
fof(f239,plain,
~ r2_hidden(sK2_skl,u1_struct_0(k1_latsum_1(sK1_skl,sK0_skl))),
inference(backward_demodulation,[status(thm)],[f241,f190]) ).
fof(f241,plain,
u1_struct_0(k1_latsum_1(sK0_skl,sK1_skl)) = u1_struct_0(k1_latsum_1(sK1_skl,sK0_skl)),
inference(forward_demodulation,[status(thm)],[f227,f234]) ).
fof(f317,plain,
! [X0] : r2_hidden(sK2_skl,k2_xboole_0(u1_struct_0(sK1_skl),X0)),
inference(resolution,[status(thm)],[f182,f67]) ).
fof(f331,plain,
r2_hidden(sK2_skl,u1_struct_0(k1_latsum_1(sK1_skl,sK0_skl))),
inference(paramodulation,[status(thm)],[f227,f317]) ).
fof(f336,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f331,f239]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU408+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n015.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Mon Sep 21 06:24:21 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.46 % Elapsed time: 0.085345 seconds
% 0.14/0.46 % CPU time: 0.393193 seconds
% 0.14/0.46 % Total memory used: 110.866 MB
% 0.14/0.46 % Net memory used: 110.398 MB
%------------------------------------------------------------------------------