TSTP Solution File: SEU408+3 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU408+3 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n011.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 : Tue Apr 30 20:42:14 EDT 2024
% Result : Theorem 26.90s 6.04s
% Output : CNFRefutation 29.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 11 unt; 0 def)
% Number of atoms : 205 ( 27 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 236 ( 78 ~; 71 |; 69 &)
% ( 7 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-6 aty)
% Number of variables : 75 ( 70 !; 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(f675,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19022,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(f19025,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(f19037,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(f19038,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)],[f19037]) ).
fof(f19133,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(f19134,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)],[f19133]) ).
fof(f19135,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)],[f19134]) ).
fof(f19138,plain,
! [X0,X1,X2,X3] :
( X0 != k2_xboole_0(X1,X2)
| r2_hidden(X3,X0)
| ~ r2_hidden(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f19135]) ).
fof(f20501,plain,
! [A,B] :
( ~ r2_hidden(A,B)
| m1_subset_1(A,B) ),
inference(pre_NNF_transformation,[status(esa)],[f675]) ).
fof(f20502,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f20501]) ).
fof(f89021,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)],[f19022]) ).
fof(f89022,plain,
! [X0,X1] :
( ~ l1_orders_2(X0)
| ~ l1_orders_2(X1)
| v1_orders_2(k1_latsum_1(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f89021]) ).
fof(f89023,plain,
! [X0,X1] :
( ~ l1_orders_2(X0)
| ~ l1_orders_2(X1)
| l1_orders_2(k1_latsum_1(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f89021]) ).
fof(f89040,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)],[f19025]) ).
fof(f89041,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)],[f89040]) ).
fof(f89042,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)],[f89041]) ).
fof(f89076,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)],[f19038]) ).
fof(f89077,plain,
( ~ v3_struct_0(sk0_6519)
& v2_orders_2(sk0_6519)
& v3_orders_2(sk0_6519)
& v4_orders_2(sk0_6519)
& v1_lattice3(sk0_6519)
& l1_orders_2(sk0_6519)
& ~ v3_struct_0(sk0_6520)
& v2_orders_2(sk0_6520)
& v3_orders_2(sk0_6520)
& v4_orders_2(sk0_6520)
& v1_lattice3(sk0_6520)
& l1_orders_2(sk0_6520)
& r2_hidden(sk0_6521,u1_struct_0(sk0_6520))
& ~ m1_subset_1(sk0_6521,u1_struct_0(k1_latsum_1(sk0_6519,sk0_6520))) ),
inference(skolemization,[status(esa)],[f89076]) ).
fof(f89083,plain,
l1_orders_2(sk0_6519),
inference(cnf_transformation,[status(esa)],[f89077]) ).
fof(f89089,plain,
l1_orders_2(sk0_6520),
inference(cnf_transformation,[status(esa)],[f89077]) ).
fof(f89090,plain,
r2_hidden(sk0_6521,u1_struct_0(sk0_6520)),
inference(cnf_transformation,[status(esa)],[f89077]) ).
fof(f89091,plain,
~ m1_subset_1(sk0_6521,u1_struct_0(k1_latsum_1(sk0_6519,sk0_6520))),
inference(cnf_transformation,[status(esa)],[f89077]) ).
fof(f103458,plain,
! [X0,X1,X2] :
( r2_hidden(X0,k2_xboole_0(X1,X2))
| ~ r2_hidden(X0,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f19138]) ).
fof(f107910,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)],[f89042]) ).
fof(f108184,plain,
( spl0_2346
<=> l1_orders_2(sk0_6520) ),
introduced(split_symbol_definition) ).
fof(f108186,plain,
( ~ l1_orders_2(sk0_6520)
| spl0_2346 ),
inference(component_clause,[status(thm)],[f108184]) ).
fof(f108192,plain,
( spl0_2348
<=> l1_orders_2(sk0_6519) ),
introduced(split_symbol_definition) ).
fof(f108194,plain,
( ~ l1_orders_2(sk0_6519)
| spl0_2348 ),
inference(component_clause,[status(thm)],[f108192]) ).
fof(f108200,plain,
( $false
| spl0_2348 ),
inference(forward_subsumption_resolution,[status(thm)],[f108194,f89083]) ).
fof(f108201,plain,
spl0_2348,
inference(contradiction_clause,[status(thm)],[f108200]) ).
fof(f108202,plain,
( $false
| spl0_2346 ),
inference(forward_subsumption_resolution,[status(thm)],[f108186,f89089]) ).
fof(f108203,plain,
spl0_2346,
inference(contradiction_clause,[status(thm)],[f108202]) ).
fof(f108214,plain,
! [X0] :
( ~ l1_orders_2(X0)
| l1_orders_2(k1_latsum_1(sk0_6519,X0)) ),
inference(resolution,[status(thm)],[f89023,f89083]) ).
fof(f108248,plain,
l1_orders_2(k1_latsum_1(sk0_6519,sk0_6520)),
inference(resolution,[status(thm)],[f108214,f89089]) ).
fof(f108307,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)],[f107910,f89022]) ).
fof(f108313,plain,
( spl0_2357
<=> u1_struct_0(k1_latsum_1(sk0_6519,sk0_6520)) = k2_xboole_0(u1_struct_0(sk0_6519),u1_struct_0(sk0_6520)) ),
introduced(split_symbol_definition) ).
fof(f108314,plain,
( u1_struct_0(k1_latsum_1(sk0_6519,sk0_6520)) = k2_xboole_0(u1_struct_0(sk0_6519),u1_struct_0(sk0_6520))
| ~ spl0_2357 ),
inference(component_clause,[status(thm)],[f108313]) ).
fof(f108316,plain,
( ~ l1_orders_2(sk0_6519)
| ~ l1_orders_2(sk0_6520)
| u1_struct_0(k1_latsum_1(sk0_6519,sk0_6520)) = k2_xboole_0(u1_struct_0(sk0_6519),u1_struct_0(sk0_6520)) ),
inference(resolution,[status(thm)],[f108307,f108248]) ).
fof(f108317,plain,
( ~ spl0_2348
| ~ spl0_2346
| spl0_2357 ),
inference(split_clause,[status(thm)],[f108316,f108192,f108184,f108313]) ).
fof(f112381,plain,
! [X0] : r2_hidden(sk0_6521,k2_xboole_0(X0,u1_struct_0(sk0_6520))),
inference(resolution,[status(thm)],[f103458,f89090]) ).
fof(f113025,plain,
! [X0] : m1_subset_1(sk0_6521,k2_xboole_0(X0,u1_struct_0(sk0_6520))),
inference(resolution,[status(thm)],[f112381,f20502]) ).
fof(f113035,plain,
( m1_subset_1(sk0_6521,u1_struct_0(k1_latsum_1(sk0_6519,sk0_6520)))
| ~ spl0_2357 ),
inference(paramodulation,[status(thm)],[f108314,f113025]) ).
fof(f113036,plain,
( $false
| ~ spl0_2357 ),
inference(forward_subsumption_resolution,[status(thm)],[f113035,f89091]) ).
fof(f113037,plain,
~ spl0_2357,
inference(contradiction_clause,[status(thm)],[f113036]) ).
fof(f113038,plain,
$false,
inference(sat_refutation,[status(thm)],[f108201,f108203,f108317,f113037]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : SEU408+3 : TPTP v8.1.2. Released v3.4.0.
% 0.06/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.34 % Computer : n011.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8042.1875MB
% 0.10/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Mon Apr 29 19:49:03 EDT 2024
% 0.10/0.34 % CPUTime :
% 2.63/2.88 % Drodi V3.6.0
% 26.90/6.04 % Refutation found
% 26.90/6.04 % SZS status Theorem for theBenchmark: Theorem is valid
% 26.90/6.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 30.90/6.58 % Elapsed time: 6.171194 seconds
% 30.90/6.58 % CPU time: 28.435842 seconds
% 30.90/6.58 % Total memory used: 5.210 GB
% 30.90/6.58 % Net memory used: 5.184 GB
%------------------------------------------------------------------------------