TSTP Solution File: GRP039-4 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GRP039-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n022.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 20:18:53 EDT 2024
% Result : Unsatisfiable 0.20s 0.44s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 24
% Syntax : Number of formulae : 102 ( 34 unt; 0 def)
% Number of atoms : 207 ( 12 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 189 ( 84 ~; 97 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 9 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 104 ( 104 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : product(identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : product(X,identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : product(inverse(X),X,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : product(X,inverse(X),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z,W] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| Z = W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,U,Z,V,W] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W)
| product(X,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] :
( ~ subgroup_member(X)
| subgroup_member(inverse(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B,C] :
( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(A,B,C)
| subgroup_member(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
subgroup_member(identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( subgroup_member(element_in_O2(A,B))
| subgroup_member(B)
| subgroup_member(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B] :
( product(A,element_in_O2(A,B),B)
| subgroup_member(B)
| subgroup_member(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
product(b,inverse(a),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
product(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f19,plain,
! [X0] : product(X0,identity,X0),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f20,plain,
! [X0] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f21,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f22,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f23,plain,
! [Z,W] :
( ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) )
| Z = W ),
inference(miniscoping,[status(esa)],[f6]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f25,plain,
! [X,V,W] :
( ! [U,Z] :
( ! [Y] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V) )
| ~ product(U,Z,W) )
| product(X,V,W) ),
inference(miniscoping,[status(esa)],[f7]) ).
fof(f26,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X1,X3,X4)
| ~ product(X2,X3,X5)
| product(X0,X4,X5) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f29,plain,
! [X0] :
( ~ subgroup_member(X0)
| subgroup_member(inverse(X0)) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f30,plain,
! [C] :
( ! [A,B] :
( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(A,B,C) )
| subgroup_member(C) ),
inference(miniscoping,[status(esa)],[f10]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ~ subgroup_member(X0)
| ~ subgroup_member(X1)
| ~ product(X0,X1,X2)
| subgroup_member(X2) ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f32,plain,
subgroup_member(identity),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f33,plain,
! [A] :
( ! [B] :
( subgroup_member(element_in_O2(A,B))
| subgroup_member(B) )
| subgroup_member(A) ),
inference(miniscoping,[status(esa)],[f12]) ).
fof(f34,plain,
! [X0,X1] :
( subgroup_member(element_in_O2(X0,X1))
| subgroup_member(X1)
| subgroup_member(X0) ),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f35,plain,
! [A] :
( ! [B] :
( product(A,element_in_O2(A,B),B)
| subgroup_member(B) )
| subgroup_member(A) ),
inference(miniscoping,[status(esa)],[f13]) ).
fof(f36,plain,
! [X0,X1] :
( product(X0,element_in_O2(X0,X1),X1)
| subgroup_member(X1)
| subgroup_member(X0) ),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f37,plain,
subgroup_member(b),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f38,plain,
product(b,inverse(a),c),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f39,plain,
product(a,c,d),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f40,plain,
~ subgroup_member(d),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f45,plain,
! [X0,X1] :
( ~ subgroup_member(X0)
| ~ subgroup_member(X1)
| ~ product(X0,X1,d) ),
inference(resolution,[status(thm)],[f31,f40]) ).
fof(f46,plain,
( spl0_0
<=> subgroup_member(a) ),
introduced(split_symbol_definition) ).
fof(f48,plain,
( ~ subgroup_member(a)
| spl0_0 ),
inference(component_clause,[status(thm)],[f46]) ).
fof(f49,plain,
( spl0_1
<=> subgroup_member(c) ),
introduced(split_symbol_definition) ).
fof(f51,plain,
( ~ subgroup_member(c)
| spl0_1 ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( ~ subgroup_member(a)
| ~ subgroup_member(c) ),
inference(resolution,[status(thm)],[f45,f39]) ).
fof(f53,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f52,f46,f49]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,inverse(X1),X2)
| ~ product(X2,X1,X3)
| product(X0,identity,X3) ),
inference(resolution,[status(thm)],[f26,f20]) ).
fof(f61,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X2,inverse(X1),X3)
| product(X0,identity,X3) ),
inference(resolution,[status(thm)],[f26,f21]) ).
fof(f79,plain,
( spl0_2
<=> subgroup_member(identity) ),
introduced(split_symbol_definition) ).
fof(f81,plain,
( ~ subgroup_member(identity)
| spl0_2 ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( spl0_3
<=> subgroup_member(d) ),
introduced(split_symbol_definition) ).
fof(f85,plain,
( ~ subgroup_member(identity)
| ~ subgroup_member(d) ),
inference(resolution,[status(thm)],[f18,f45]) ).
fof(f86,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f85,f79,f82]) ).
fof(f93,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,identity)
| ~ product(X1,X2,X3)
| product(X0,X3,X2) ),
inference(resolution,[status(thm)],[f18,f26]) ).
fof(f97,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f81,f32]) ).
fof(f98,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f97]) ).
fof(f109,plain,
! [X0,X1] :
( ~ product(X0,identity,X1)
| X1 = X0 ),
inference(resolution,[status(thm)],[f19,f24]) ).
fof(f126,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| X2 = multiply(X0,X1) ),
inference(resolution,[status(thm)],[f22,f24]) ).
fof(f142,plain,
! [X0] :
( product(X0,element_in_O2(X0,d),d)
| subgroup_member(X0) ),
inference(resolution,[status(thm)],[f36,f40]) ).
fof(f145,plain,
! [X0] :
( ~ product(c,a,X0)
| product(b,identity,X0) ),
inference(resolution,[status(thm)],[f55,f38]) ).
fof(f150,plain,
! [X0,X1] :
( ~ subgroup_member(X0)
| ~ subgroup_member(X1)
| ~ product(X0,X1,a)
| spl0_0 ),
inference(resolution,[status(thm)],[f48,f31]) ).
fof(f180,plain,
! [X0,X1] :
( ~ subgroup_member(X0)
| ~ subgroup_member(X1)
| ~ product(X0,X1,c)
| spl0_1 ),
inference(resolution,[status(thm)],[f51,f31]) ).
fof(f183,plain,
( spl0_6
<=> subgroup_member(b) ),
introduced(split_symbol_definition) ).
fof(f185,plain,
( ~ subgroup_member(b)
| spl0_6 ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,plain,
( spl0_7
<=> subgroup_member(inverse(a)) ),
introduced(split_symbol_definition) ).
fof(f188,plain,
( ~ subgroup_member(inverse(a))
| spl0_7 ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,plain,
( ~ subgroup_member(b)
| ~ subgroup_member(inverse(a))
| spl0_1 ),
inference(resolution,[status(thm)],[f180,f38]) ).
fof(f190,plain,
( ~ spl0_6
| ~ spl0_7
| spl0_1 ),
inference(split_clause,[status(thm)],[f189,f183,f186,f49]) ).
fof(f273,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f185,f37]) ).
fof(f274,plain,
spl0_6,
inference(contradiction_clause,[status(thm)],[f273]) ).
fof(f288,plain,
( product(a,element_in_O2(a,d),d)
| spl0_0 ),
inference(resolution,[status(thm)],[f142,f48]) ).
fof(f337,plain,
! [X0,X1] :
( ~ product(X0,X1,identity)
| product(X0,identity,inverse(X1)) ),
inference(resolution,[status(thm)],[f61,f18]) ).
fof(f343,plain,
product(b,identity,multiply(c,a)),
inference(resolution,[status(thm)],[f145,f22]) ).
fof(f344,plain,
multiply(c,a) = b,
inference(resolution,[status(thm)],[f343,f109]) ).
fof(f355,plain,
product(c,a,b),
inference(paramodulation,[status(thm)],[f344,f22]) ).
fof(f378,plain,
! [X0] : product(X0,identity,inverse(inverse(X0))),
inference(resolution,[status(thm)],[f337,f21]) ).
fof(f394,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(resolution,[status(thm)],[f378,f109]) ).
fof(f415,plain,
! [X0] :
( ~ subgroup_member(inverse(X0))
| subgroup_member(X0) ),
inference(paramodulation,[status(thm)],[f394,f29]) ).
fof(f418,plain,
( ~ subgroup_member(inverse(inverse(a)))
| spl0_7 ),
inference(resolution,[status(thm)],[f415,f188]) ).
fof(f419,plain,
~ subgroup_member(inverse(d)),
inference(resolution,[status(thm)],[f415,f40]) ).
fof(f426,plain,
! [X0,X1] :
( ~ subgroup_member(X0)
| ~ subgroup_member(X1)
| ~ product(X0,X1,inverse(d)) ),
inference(resolution,[status(thm)],[f419,f31]) ).
fof(f444,plain,
( d = multiply(a,element_in_O2(a,d))
| spl0_0 ),
inference(resolution,[status(thm)],[f288,f126]) ).
fof(f505,plain,
( spl0_14
<=> subgroup_member(inverse(d)) ),
introduced(split_symbol_definition) ).
fof(f587,plain,
( ~ subgroup_member(identity)
| ~ subgroup_member(inverse(d)) ),
inference(resolution,[status(thm)],[f426,f18]) ).
fof(f588,plain,
( ~ spl0_2
| ~ spl0_14 ),
inference(split_clause,[status(thm)],[f587,f79,f505]) ).
fof(f648,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| product(inverse(X0),X2,X1) ),
inference(resolution,[status(thm)],[f93,f20]) ).
fof(f658,plain,
product(inverse(c),b,a),
inference(resolution,[status(thm)],[f648,f355]) ).
fof(f676,plain,
product(inverse(a),d,c),
inference(resolution,[status(thm)],[f648,f39]) ).
fof(f679,plain,
! [X0,X1] : product(inverse(X0),multiply(X0,X1),X1),
inference(resolution,[status(thm)],[f648,f22]) ).
fof(f683,plain,
( spl0_16
<=> subgroup_member(inverse(c)) ),
introduced(split_symbol_definition) ).
fof(f685,plain,
( ~ subgroup_member(inverse(c))
| spl0_16 ),
inference(component_clause,[status(thm)],[f683]) ).
fof(f686,plain,
( ~ subgroup_member(inverse(c))
| ~ subgroup_member(b)
| spl0_0 ),
inference(resolution,[status(thm)],[f658,f150]) ).
fof(f687,plain,
( ~ spl0_16
| ~ spl0_6
| spl0_0 ),
inference(split_clause,[status(thm)],[f686,f683,f183,f46]) ).
fof(f702,plain,
c = multiply(inverse(a),d),
inference(resolution,[status(thm)],[f676,f126]) ).
fof(f725,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(resolution,[status(thm)],[f679,f126]) ).
fof(f788,plain,
( element_in_O2(a,d) = multiply(inverse(a),d)
| spl0_0 ),
inference(paramodulation,[status(thm)],[f444,f725]) ).
fof(f789,plain,
( element_in_O2(a,d) = c
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f702,f788]) ).
fof(f812,plain,
( ~ subgroup_member(c)
| spl0_16 ),
inference(resolution,[status(thm)],[f685,f29]) ).
fof(f833,plain,
( subgroup_member(c)
| subgroup_member(d)
| subgroup_member(a)
| spl0_0 ),
inference(paramodulation,[status(thm)],[f789,f34]) ).
fof(f834,plain,
( spl0_1
| spl0_3
| spl0_0 ),
inference(split_clause,[status(thm)],[f833,f49,f82,f46]) ).
fof(f835,plain,
( ~ subgroup_member(a)
| spl0_7 ),
inference(forward_demodulation,[status(thm)],[f394,f418]) ).
fof(f836,plain,
( ~ spl0_0
| spl0_7 ),
inference(split_clause,[status(thm)],[f835,f46,f186]) ).
fof(f841,plain,
( ~ spl0_1
| spl0_16 ),
inference(split_clause,[status(thm)],[f812,f49,f683]) ).
fof(f843,plain,
$false,
inference(sat_refutation,[status(thm)],[f53,f86,f98,f190,f274,f588,f687,f834,f836,f841]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP039-4 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 30 00:21:28 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 0.20/0.44 % Refutation found
% 0.20/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.45 % Elapsed time: 0.101212 seconds
% 0.20/0.45 % CPU time: 0.685711 seconds
% 0.20/0.45 % Total memory used: 57.424 MB
% 0.20/0.45 % Net memory used: 56.687 MB
%------------------------------------------------------------------------------