TSTP Solution File: SEU408+2 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU408+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:36:58 EDT 2023
% Result : Theorem 19.20s 3.12s
% Output : CNFRefutation 20.05s
% 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,A)
| r2_hidden(D,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f444,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4433,axiom,
! [A,B] :
( ( l1_orders_2(A)
& l1_orders_2(B) )
=> ( v1_orders_2(k1_latsum_1(A,B))
& l1_orders_2(k1_latsum_1(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4436,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( ( v1_orders_2(C)
& l1_orders_2(C) )
=> ( C = k1_latsum_1(A,B)
<=> ( u1_struct_0(C) = k2_xboole_0(u1_struct_0(A),u1_struct_0(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))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4448,conjecture,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( r2_hidden(C,u1_struct_0(B))
=> m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4449,negated_conjecture,
~ ! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& l1_orders_2(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] :
( ( C != k2_xboole_0(A,B)
| ! [D] :
( ( ~ r2_hidden(D,C)
| r2_hidden(D,A)
| r2_hidden(D,B) )
& ( r2_hidden(D,C)
| ( ~ r2_hidden(D,A)
& ~ r2_hidden(D,B) ) ) ) )
& ( C = k2_xboole_0(A,B)
| ? [D] :
( ( ~ r2_hidden(D,C)
| ( ~ r2_hidden(D,A)
& ~ r2_hidden(D,B) ) )
& ( r2_hidden(D,C)
| r2_hidden(D,A)
| r2_hidden(D,B) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f30]) ).
fof(f4545,plain,
( ! [A,B,C] :
( C != k2_xboole_0(A,B)
| ( ! [D] :
( ~ r2_hidden(D,C)
| r2_hidden(D,A)
| r2_hidden(D,B) )
& ! [D] :
( r2_hidden(D,C)
| ( ~ r2_hidden(D,A)
& ~ r2_hidden(D,B) ) ) ) )
& ! [A,B,C] :
( C = k2_xboole_0(A,B)
| ? [D] :
( ( ~ r2_hidden(D,C)
| ( ~ r2_hidden(D,A)
& ~ r2_hidden(D,B) ) )
& ( r2_hidden(D,C)
| r2_hidden(D,A)
| r2_hidden(D,B) ) ) ) ),
inference(miniscoping,[status(esa)],[f4544]) ).
fof(f4546,plain,
( ! [A,B,C] :
( C != k2_xboole_0(A,B)
| ( ! [D] :
( ~ r2_hidden(D,C)
| r2_hidden(D,A)
| r2_hidden(D,B) )
& ! [D] :
( r2_hidden(D,C)
| ( ~ r2_hidden(D,A)
& ~ r2_hidden(D,B) ) ) ) )
& ! [A,B,C] :
( C = k2_xboole_0(A,B)
| ( ( ~ r2_hidden(sk0_23(C,B,A),C)
| ( ~ r2_hidden(sk0_23(C,B,A),A)
& ~ r2_hidden(sk0_23(C,B,A),B) ) )
& ( r2_hidden(sk0_23(C,B,A),C)
| r2_hidden(sk0_23(C,B,A),A)
| r2_hidden(sk0_23(C,B,A),B) ) ) ) ),
inference(skolemization,[status(esa)],[f4545]) ).
fof(f4549,plain,
! [X0,X1,X2,X3] :
( X0 != k2_xboole_0(X1,X2)
| r2_hidden(X3,X0)
| ~ r2_hidden(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f4546]) ).
fof(f5554,plain,
! [A,B] :
( ~ r2_hidden(A,B)
| m1_subset_1(A,B) ),
inference(pre_NNF_transformation,[status(esa)],[f444]) ).
fof(f5555,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5554]) ).
fof(f18505,plain,
! [A,B] :
( ~ l1_orders_2(A)
| ~ l1_orders_2(B)
| ( v1_orders_2(k1_latsum_1(A,B))
& l1_orders_2(k1_latsum_1(A,B)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4433]) ).
fof(f18506,plain,
! [X0,X1] :
( ~ l1_orders_2(X0)
| ~ l1_orders_2(X1)
| v1_orders_2(k1_latsum_1(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f18505]) ).
fof(f18507,plain,
! [X0,X1] :
( ~ l1_orders_2(X0)
| ~ l1_orders_2(X1)
| l1_orders_2(k1_latsum_1(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f18505]) ).
fof(f18524,plain,
! [A] :
( ~ l1_orders_2(A)
| ! [B] :
( ~ l1_orders_2(B)
| ! [C] :
( ~ v1_orders_2(C)
| ~ l1_orders_2(C)
| ( C = k1_latsum_1(A,B)
<=> ( u1_struct_0(C) = k2_xboole_0(u1_struct_0(A),u1_struct_0(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))) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4436]) ).
fof(f18525,plain,
! [A] :
( ~ l1_orders_2(A)
| ! [B] :
( ~ l1_orders_2(B)
| ! [C] :
( ~ v1_orders_2(C)
| ~ l1_orders_2(C)
| ( ( C != k1_latsum_1(A,B)
| ( u1_struct_0(C) = k2_xboole_0(u1_struct_0(A),u1_struct_0(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))) ) )
& ( C = k1_latsum_1(A,B)
| u1_struct_0(C) != k2_xboole_0(u1_struct_0(A),u1_struct_0(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))) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f18524]) ).
fof(f18526,plain,
! [X0,X1,X2] :
( ~ l1_orders_2(X0)
| ~ l1_orders_2(X1)
| ~ v1_orders_2(X2)
| ~ l1_orders_2(X2)
| X2 != k1_latsum_1(X0,X1)
| u1_struct_0(X2) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) ),
inference(cnf_transformation,[status(esa)],[f18525]) ).
fof(f18560,plain,
? [A] :
( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A)
& ? [B] :
( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& l1_orders_2(B)
& ? [C] :
( r2_hidden(C,u1_struct_0(B))
& ~ m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B))) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4449]) ).
fof(f18561,plain,
( ~ v3_struct_0(sk0_1191)
& v2_orders_2(sk0_1191)
& v3_orders_2(sk0_1191)
& v4_orders_2(sk0_1191)
& v1_lattice3(sk0_1191)
& l1_orders_2(sk0_1191)
& ~ v3_struct_0(sk0_1192)
& v2_orders_2(sk0_1192)
& v3_orders_2(sk0_1192)
& v4_orders_2(sk0_1192)
& v1_lattice3(sk0_1192)
& l1_orders_2(sk0_1192)
& r2_hidden(sk0_1193,u1_struct_0(sk0_1192))
& ~ m1_subset_1(sk0_1193,u1_struct_0(k1_latsum_1(sk0_1191,sk0_1192))) ),
inference(skolemization,[status(esa)],[f18560]) ).
fof(f18567,plain,
l1_orders_2(sk0_1191),
inference(cnf_transformation,[status(esa)],[f18561]) ).
fof(f18573,plain,
l1_orders_2(sk0_1192),
inference(cnf_transformation,[status(esa)],[f18561]) ).
fof(f18574,plain,
r2_hidden(sk0_1193,u1_struct_0(sk0_1192)),
inference(cnf_transformation,[status(esa)],[f18561]) ).
fof(f18575,plain,
~ m1_subset_1(sk0_1193,u1_struct_0(k1_latsum_1(sk0_1191,sk0_1192))),
inference(cnf_transformation,[status(esa)],[f18561]) ).
fof(f21906,plain,
! [X0,X1,X2] :
( r2_hidden(X0,k2_xboole_0(X1,X2))
| ~ r2_hidden(X0,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f4549]) ).
fof(f22765,plain,
! [X0,X1] :
( ~ l1_orders_2(X0)
| ~ l1_orders_2(X1)
| ~ v1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(k1_latsum_1(X0,X1))
| u1_struct_0(k1_latsum_1(X0,X1)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) ),
inference(destructive_equality_resolution,[status(esa)],[f18526]) ).
fof(f22827,plain,
~ r2_hidden(sk0_1193,u1_struct_0(k1_latsum_1(sk0_1191,sk0_1192))),
inference(resolution,[status(thm)],[f5555,f18575]) ).
fof(f23050,plain,
! [X0,X1] :
( ~ l1_orders_2(X0)
| ~ l1_orders_2(X1)
| ~ l1_orders_2(k1_latsum_1(X0,X1))
| u1_struct_0(k1_latsum_1(X0,X1)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f22765,f18506]) ).
fof(f23051,plain,
! [X0,X1] :
( ~ l1_orders_2(X0)
| ~ l1_orders_2(X1)
| u1_struct_0(k1_latsum_1(X0,X1)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))
| ~ l1_orders_2(X0)
| ~ l1_orders_2(X1) ),
inference(resolution,[status(thm)],[f23050,f18507]) ).
fof(f23052,plain,
! [X0,X1] :
( ~ l1_orders_2(X0)
| ~ l1_orders_2(X1)
| u1_struct_0(k1_latsum_1(X0,X1)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) ),
inference(duplicate_literals_removal,[status(esa)],[f23051]) ).
fof(f23054,plain,
! [X0] :
( ~ l1_orders_2(X0)
| u1_struct_0(k1_latsum_1(X0,sk0_1192)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(sk0_1192)) ),
inference(resolution,[status(thm)],[f23052,f18573]) ).
fof(f23109,plain,
u1_struct_0(k1_latsum_1(sk0_1191,sk0_1192)) = k2_xboole_0(u1_struct_0(sk0_1191),u1_struct_0(sk0_1192)),
inference(resolution,[status(thm)],[f23054,f18567]) ).
fof(f26789,plain,
! [X0] : r2_hidden(sk0_1193,k2_xboole_0(X0,u1_struct_0(sk0_1192))),
inference(resolution,[status(thm)],[f21906,f18574]) ).
fof(f27382,plain,
r2_hidden(sk0_1193,u1_struct_0(k1_latsum_1(sk0_1191,sk0_1192))),
inference(paramodulation,[status(thm)],[f23109,f26789]) ).
fof(f27586,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f27382,f22827]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SEU408+2 : TPTP v8.1.2. Released v3.4.0.
% 0.09/0.15 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.36 % Computer : n021.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue May 30 09:17:23 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.49/0.68 % Drodi V3.5.1
% 19.20/3.12 % Refutation found
% 19.20/3.12 % SZS status Theorem for theBenchmark: Theorem is valid
% 19.20/3.12 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 20.05/3.20 % Elapsed time: 2.833454 seconds
% 20.05/3.20 % CPU time: 19.890283 seconds
% 20.05/3.20 % Memory used: 757.056 MB
%------------------------------------------------------------------------------