%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU408+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 60.34s 8.51s
% Output : CNFRefutation 61.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 9 unt; 0 def)
% Number of atoms : 185 ( 28 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 225 ( 75 ~; 66 |; 69 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 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 : 78 ( 73 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f30,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(f444,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4433,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(f4436,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(f4448,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(f4449,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)],[f4448]) ).
fof(f4544,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)],[f30]) ).
fof(f4545,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)],[f4544]) ).
fof(f4546,plain,
( ! [A,B,C] :
( ( ( r2_hidden(sK23_skl(C,B,A),B)
| r2_hidden(sK23_skl(C,B,A),A)
| r2_hidden(sK23_skl(C,B,A),C) )
& ( ( ~ r2_hidden(sK23_skl(C,B,A),B)
& ~ r2_hidden(sK23_skl(C,B,A),A) )
| ~ r2_hidden(sK23_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,[sK23_skl]),skolemize(D,sK23_skl(C,B,A))],[f4545]) ).
fof(f4549,plain,
! [X0,X1,X2,X3] :
( ~ r2_hidden(X3,X2)
| r2_hidden(X3,X0)
| X0 != k2_xboole_0(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f4546]) ).
fof(f5554,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f444]) ).
fof(f5555,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f5554]) ).
fof(f18505,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)],[f4433]) ).
fof(f18506,plain,
! [X0,X1] :
( v1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[status(thm)],[f18505]) ).
fof(f18507,plain,
! [X0,X1] :
( ~ l1_orders_2(X1)
| l1_orders_2(k1_latsum_1(X1,X0))
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[status(thm)],[f18505]) ).
fof(f18524,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)],[f4436]) ).
fof(f18525,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)],[f18524]) ).
fof(f18526,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)],[f18525]) ).
fof(f18560,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)],[f4449]) ).
fof(f18561,plain,
( ~ m1_subset_1(sK1193_skl,u1_struct_0(k1_latsum_1(sK1191_skl,sK1192_skl)))
& r2_hidden(sK1193_skl,u1_struct_0(sK1192_skl))
& l1_orders_2(sK1192_skl)
& v1_lattice3(sK1192_skl)
& v4_orders_2(sK1192_skl)
& v3_orders_2(sK1192_skl)
& v2_orders_2(sK1192_skl)
& ~ v3_struct_0(sK1192_skl)
& l1_orders_2(sK1191_skl)
& v1_lattice3(sK1191_skl)
& v4_orders_2(sK1191_skl)
& v3_orders_2(sK1191_skl)
& v2_orders_2(sK1191_skl)
& ~ v3_struct_0(sK1191_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1191_skl,sK1192_skl,sK1193_skl]),skolemize(A,sK1191_skl),skolemize(B,sK1192_skl),skolemize(C,sK1193_skl)],[f18560]) ).
fof(f18567,plain,
l1_orders_2(sK1191_skl),
inference(cnf_transformation,[status(thm)],[f18561]) ).
fof(f18573,plain,
l1_orders_2(sK1192_skl),
inference(cnf_transformation,[status(thm)],[f18561]) ).
fof(f18574,plain,
r2_hidden(sK1193_skl,u1_struct_0(sK1192_skl)),
inference(cnf_transformation,[status(thm)],[f18561]) ).
fof(f18575,plain,
~ m1_subset_1(sK1193_skl,u1_struct_0(k1_latsum_1(sK1191_skl,sK1192_skl))),
inference(cnf_transformation,[status(thm)],[f18561]) ).
fof(f22156,plain,
! [X0,X1,X2] :
( r2_hidden(X0,k2_xboole_0(X2,X1))
| ~ r2_hidden(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f4549]) ).
fof(f22430,plain,
! [X0,X1] :
( k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) = u1_struct_0(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X0)
| ~ l1_orders_2(X1)
| ~ l1_orders_2(k1_latsum_1(X0,X1))
| ~ v1_orders_2(k1_latsum_1(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f18526]) ).
fof(f23177,plain,
~ r2_hidden(sK1193_skl,u1_struct_0(k1_latsum_1(sK1191_skl,sK1192_skl))),
inference(resolution,[status(thm)],[f18575,f5555]) ).
fof(f23429,plain,
! [X0,X1] :
( ~ l1_orders_2(k1_latsum_1(X0,X1))
| k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) = u1_struct_0(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f22430,f18506]) ).
fof(f23430,plain,
! [X0,X1] :
( ~ l1_orders_2(X0)
| ~ l1_orders_2(X1)
| k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) = u1_struct_0(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(resolution,[status(thm)],[f23429,f18507]) ).
fof(f23431,plain,
! [X0,X1] :
( ~ l1_orders_2(X1)
| ~ l1_orders_2(X0)
| k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) = u1_struct_0(k1_latsum_1(X0,X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f23430]) ).
fof(f23613,plain,
! [X0] :
( u1_struct_0(k1_latsum_1(X0,sK1192_skl)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(sK1192_skl))
| ~ l1_orders_2(X0) ),
inference(resolution,[status(thm)],[f23431,f18573]) ).
fof(f23615,plain,
u1_struct_0(k1_latsum_1(sK1191_skl,sK1192_skl)) = k2_xboole_0(u1_struct_0(sK1191_skl),u1_struct_0(sK1192_skl)),
inference(resolution,[status(thm)],[f23613,f18567]) ).
fof(f24273,plain,
! [X0] : r2_hidden(sK1193_skl,k2_xboole_0(X0,u1_struct_0(sK1192_skl))),
inference(resolution,[status(thm)],[f18574,f22156]) ).
fof(f25396,plain,
r2_hidden(sK1193_skl,u1_struct_0(k1_latsum_1(sK1191_skl,sK1192_skl))),
inference(paramodulation,[status(thm)],[f23615,f24273]) ).
fof(f25409,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f25396,f23177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU408+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n014.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 06:21:07 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.56/0.82 % Drodi V4.1.1
% 60.34/8.51 % Refutation found
% 60.34/8.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 60.34/8.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.42/8.62 % Elapsed time: 8.247477 seconds
% 4.42/8.62 % CPU time: 61.476109 seconds
% 4.42/8.62 % Total memory used: 999.204 MB
% 4.42/8.62 % Net memory used: 948.167 MB
%------------------------------------------------------------------------------