TSTP Solution File: GRP039-1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GRP039-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n017.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 20:18:52 EDT 2024
% Result : Unsatisfiable 0.19s 0.46s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 26
% Syntax : Number of formulae : 122 ( 28 unt; 0 def)
% Number of atoms : 266 ( 18 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 249 ( 105 ~; 132 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 13 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 114 ( 114 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : product(identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : product(X,identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : product(inverse(X),X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z,W] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| Z = W ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] :
( ~ subgroup_member(X)
| subgroup_member(inverse(X)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] :
( subgroup_member(element_in_O2(A,B))
| subgroup_member(B)
| subgroup_member(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( product(A,element_in_O2(A,B),B)
| subgroup_member(B)
| subgroup_member(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
product(b,inverse(a),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
product(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f18,plain,
! [X0] : product(X0,identity,X0),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f19,plain,
! [X0] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f21,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f22,plain,
! [Z,W] :
( ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) )
| Z = W ),
inference(miniscoping,[status(esa)],[f6]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f24,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(f25,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)],[f24]) ).
fof(f28,plain,
! [X0] :
( ~ subgroup_member(X0)
| subgroup_member(inverse(X0)) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f29,plain,
! [C] :
( ! [A,B] :
( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(A,B,C) )
| subgroup_member(C) ),
inference(miniscoping,[status(esa)],[f10]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ~ subgroup_member(X0)
| ~ subgroup_member(X1)
| ~ product(X0,X1,X2)
| subgroup_member(X2) ),
inference(cnf_transformation,[status(esa)],[f29]) ).
fof(f31,plain,
! [A] :
( ! [B] :
( subgroup_member(element_in_O2(A,B))
| subgroup_member(B) )
| subgroup_member(A) ),
inference(miniscoping,[status(esa)],[f11]) ).
fof(f32,plain,
! [X0,X1] :
( subgroup_member(element_in_O2(X0,X1))
| subgroup_member(X1)
| subgroup_member(X0) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f33,plain,
! [A] :
( ! [B] :
( product(A,element_in_O2(A,B),B)
| subgroup_member(B) )
| subgroup_member(A) ),
inference(miniscoping,[status(esa)],[f12]) ).
fof(f34,plain,
! [X0,X1] :
( product(X0,element_in_O2(X0,X1),X1)
| subgroup_member(X1)
| subgroup_member(X0) ),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f35,plain,
subgroup_member(b),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f36,plain,
product(b,inverse(a),c),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f37,plain,
product(a,c,d),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f38,plain,
~ subgroup_member(d),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f39,plain,
! [X0,X1] :
( ~ product(inverse(X0),X0,X1)
| X1 = identity ),
inference(resolution,[status(thm)],[f23,f19]) ).
fof(f43,plain,
! [X0,X1] :
( ~ subgroup_member(X0)
| ~ subgroup_member(X1)
| ~ product(X0,X1,d) ),
inference(resolution,[status(thm)],[f30,f38]) ).
fof(f44,plain,
( spl0_0
<=> subgroup_member(a) ),
introduced(split_symbol_definition) ).
fof(f45,plain,
( subgroup_member(a)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f46,plain,
( ~ subgroup_member(a)
| spl0_0 ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,plain,
( spl0_1
<=> subgroup_member(c) ),
introduced(split_symbol_definition) ).
fof(f49,plain,
( ~ subgroup_member(c)
| spl0_1 ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,plain,
( ~ subgroup_member(a)
| ~ subgroup_member(c) ),
inference(resolution,[status(thm)],[f43,f37]) ).
fof(f51,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f50,f44,f47]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,inverse(X1),X2)
| ~ product(X2,X1,X3)
| product(X0,identity,X3) ),
inference(resolution,[status(thm)],[f25,f19]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ~ product(X0,a,X1)
| ~ product(X1,c,X2)
| product(X0,d,X2) ),
inference(resolution,[status(thm)],[f25,f37]) ).
fof(f77,plain,
( spl0_2
<=> subgroup_member(identity) ),
introduced(split_symbol_definition) ).
fof(f78,plain,
( subgroup_member(identity)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f79,plain,
( ~ subgroup_member(identity)
| spl0_2 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( spl0_3
<=> subgroup_member(d) ),
introduced(split_symbol_definition) ).
fof(f82,plain,
( ~ subgroup_member(d)
| spl0_3 ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f83,plain,
( ~ subgroup_member(identity)
| ~ subgroup_member(d) ),
inference(resolution,[status(thm)],[f17,f43]) ).
fof(f84,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f83,f77,f80]) ).
fof(f91,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,identity)
| ~ product(X1,X2,X3)
| product(X0,X3,X2) ),
inference(resolution,[status(thm)],[f17,f25]) ).
fof(f94,plain,
! [X0,X1] :
( ~ product(identity,X0,X1)
| X1 = X0 ),
inference(resolution,[status(thm)],[f17,f23]) ).
fof(f105,plain,
! [X0,X1] :
( ~ product(X0,identity,X1)
| X1 = X0 ),
inference(resolution,[status(thm)],[f18,f23]) ).
fof(f114,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(resolution,[status(thm)],[f21,f39]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| X2 = multiply(X0,X1) ),
inference(resolution,[status(thm)],[f21,f23]) ).
fof(f124,plain,
! [X0] : multiply(identity,X0) = X0,
inference(resolution,[status(thm)],[f94,f21]) ).
fof(f139,plain,
! [X0] :
( product(X0,element_in_O2(X0,d),d)
| subgroup_member(X0) ),
inference(resolution,[status(thm)],[f34,f38]) ).
fof(f142,plain,
! [X0] :
( ~ product(c,a,X0)
| product(b,identity,X0) ),
inference(resolution,[status(thm)],[f53,f36]) ).
fof(f147,plain,
! [X0,X1] :
( ~ subgroup_member(X0)
| ~ subgroup_member(X1)
| ~ product(X0,X1,a)
| spl0_0 ),
inference(resolution,[status(thm)],[f46,f30]) ).
fof(f149,plain,
! [X0,X1] :
( ~ subgroup_member(X0)
| ~ subgroup_member(X1)
| ~ product(X0,X1,identity)
| spl0_2 ),
inference(resolution,[status(thm)],[f79,f30]) ).
fof(f156,plain,
! [X0] :
( ~ subgroup_member(inverse(X0))
| ~ subgroup_member(X0)
| spl0_2 ),
inference(resolution,[status(thm)],[f149,f19]) ).
fof(f157,plain,
! [X0] :
( ~ subgroup_member(X0)
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f156,f28]) ).
fof(f169,plain,
( $false
| spl0_2 ),
inference(backward_subsumption_resolution,[status(thm)],[f35,f157]) ).
fof(f170,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f169]) ).
fof(f171,plain,
! [X0] :
( ~ subgroup_member(X0)
| ~ product(X0,identity,a)
| spl0_0
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f147,f78]) ).
fof(f249,plain,
( product(a,element_in_O2(a,d),d)
| spl0_0 ),
inference(resolution,[status(thm)],[f139,f46]) ).
fof(f250,plain,
( product(d,element_in_O2(d,d),d)
| spl0_3 ),
inference(resolution,[status(thm)],[f139,f82]) ).
fof(f300,plain,
! [X0,X1] :
( ~ subgroup_member(X0)
| ~ product(X0,b,X1)
| subgroup_member(X1) ),
inference(resolution,[status(thm)],[f30,f35]) ).
fof(f317,plain,
! [X0,X1] :
( subgroup_member(X0)
| subgroup_member(X1)
| subgroup_member(inverse(element_in_O2(X1,X0))) ),
inference(resolution,[status(thm)],[f32,f28]) ).
fof(f330,plain,
( spl0_5
<=> subgroup_member(b) ),
introduced(split_symbol_definition) ).
fof(f333,plain,
( ~ subgroup_member(identity)
| subgroup_member(b) ),
inference(resolution,[status(thm)],[f300,f17]) ).
fof(f334,plain,
( ~ spl0_2
| spl0_5 ),
inference(split_clause,[status(thm)],[f333,f77,f330]) ).
fof(f335,plain,
( spl0_6
<=> subgroup_member(inverse(b)) ),
introduced(split_symbol_definition) ).
fof(f340,plain,
! [X0] :
( ~ subgroup_member(X0)
| subgroup_member(multiply(X0,b)) ),
inference(resolution,[status(thm)],[f300,f21]) ).
fof(f342,plain,
! [X0] :
( ~ subgroup_member(X0)
| subgroup_member(inverse(multiply(X0,b))) ),
inference(resolution,[status(thm)],[f340,f28]) ).
fof(f345,plain,
! [X0] :
( ~ subgroup_member(X0)
| ~ product(multiply(X0,b),identity,a)
| spl0_0
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f340,f171]) ).
fof(f352,plain,
! [X0] :
( ~ subgroup_member(X0)
| subgroup_member(inverse(inverse(multiply(X0,b)))) ),
inference(resolution,[status(thm)],[f342,f28]) ).
fof(f357,plain,
( spl0_7
<=> subgroup_member(inverse(identity)) ),
introduced(split_symbol_definition) ).
fof(f362,plain,
( ~ subgroup_member(identity)
| subgroup_member(inverse(b)) ),
inference(paramodulation,[status(thm)],[f124,f342]) ).
fof(f363,plain,
( ~ spl0_2
| spl0_6 ),
inference(split_clause,[status(thm)],[f362,f77,f335]) ).
fof(f370,plain,
product(b,identity,multiply(c,a)),
inference(resolution,[status(thm)],[f142,f21]) ).
fof(f371,plain,
multiply(c,a) = b,
inference(resolution,[status(thm)],[f370,f105]) ).
fof(f382,plain,
product(c,a,b),
inference(paramodulation,[status(thm)],[f371,f21]) ).
fof(f401,plain,
! [X0] :
( ~ product(X0,a,identity)
| product(X0,d,c) ),
inference(resolution,[status(thm)],[f57,f17]) ).
fof(f411,plain,
( d = multiply(a,element_in_O2(a,d))
| spl0_0 ),
inference(resolution,[status(thm)],[f249,f122]) ).
fof(f419,plain,
( d = multiply(d,element_in_O2(d,d))
| spl0_3 ),
inference(resolution,[status(thm)],[f250,f122]) ).
fof(f471,plain,
! [X0,X1] :
( ~ subgroup_member(X0)
| ~ subgroup_member(X1)
| ~ product(X0,X1,c)
| spl0_1 ),
inference(resolution,[status(thm)],[f49,f30]) ).
fof(f483,plain,
( spl0_13
<=> subgroup_member(inverse(a)) ),
introduced(split_symbol_definition) ).
fof(f485,plain,
( ~ subgroup_member(inverse(a))
| spl0_13 ),
inference(component_clause,[status(thm)],[f483]) ).
fof(f486,plain,
( ~ subgroup_member(b)
| ~ subgroup_member(inverse(a))
| spl0_1 ),
inference(resolution,[status(thm)],[f471,f36]) ).
fof(f487,plain,
( ~ spl0_5
| ~ spl0_13
| spl0_1 ),
inference(split_clause,[status(thm)],[f486,f330,f483,f47]) ).
fof(f510,plain,
( subgroup_member(inverse(a))
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f45,f28]) ).
fof(f511,plain,
( $false
| spl0_13
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f510,f485]) ).
fof(f512,plain,
( spl0_13
| ~ spl0_0 ),
inference(contradiction_clause,[status(thm)],[f511]) ).
fof(f533,plain,
( spl0_15
<=> subgroup_member(inverse(inverse(b))) ),
introduced(split_symbol_definition) ).
fof(f562,plain,
( spl0_16
<=> subgroup_member(inverse(inverse(identity))) ),
introduced(split_symbol_definition) ).
fof(f565,plain,
( ~ subgroup_member(inverse(b))
| subgroup_member(inverse(inverse(identity))) ),
inference(paramodulation,[status(thm)],[f114,f352]) ).
fof(f566,plain,
( ~ spl0_6
| spl0_16 ),
inference(split_clause,[status(thm)],[f565,f335,f562]) ).
fof(f567,plain,
( ~ subgroup_member(identity)
| subgroup_member(inverse(inverse(b))) ),
inference(paramodulation,[status(thm)],[f124,f352]) ).
fof(f568,plain,
( ~ spl0_2
| spl0_15 ),
inference(split_clause,[status(thm)],[f567,f77,f533]) ).
fof(f572,plain,
product(inverse(a),d,c),
inference(resolution,[status(thm)],[f401,f19]) ).
fof(f573,plain,
c = multiply(inverse(a),d),
inference(resolution,[status(thm)],[f572,f122]) ).
fof(f748,plain,
( spl0_17
<=> product(identity,identity,a) ),
introduced(split_symbol_definition) ).
fof(f751,plain,
( ~ subgroup_member(inverse(b))
| ~ product(identity,identity,a)
| spl0_0
| ~ spl0_2 ),
inference(paramodulation,[status(thm)],[f114,f345]) ).
fof(f752,plain,
( ~ spl0_6
| ~ spl0_17
| spl0_0
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f751,f335,f748,f44,f77]) ).
fof(f807,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| product(inverse(X0),X2,X1) ),
inference(resolution,[status(thm)],[f91,f19]) ).
fof(f816,plain,
product(inverse(c),b,a),
inference(resolution,[status(thm)],[f807,f382]) ).
fof(f830,plain,
! [X0,X1] : product(inverse(X0),multiply(X0,X1),X1),
inference(resolution,[status(thm)],[f807,f21]) ).
fof(f834,plain,
( spl0_20
<=> subgroup_member(inverse(c)) ),
introduced(split_symbol_definition) ).
fof(f837,plain,
( ~ subgroup_member(inverse(c))
| subgroup_member(a) ),
inference(resolution,[status(thm)],[f816,f300]) ).
fof(f838,plain,
( ~ spl0_20
| spl0_0 ),
inference(split_clause,[status(thm)],[f837,f834,f44]) ).
fof(f865,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(resolution,[status(thm)],[f830,f122]) ).
fof(f917,plain,
( element_in_O2(d,d) = multiply(inverse(d),d)
| spl0_3 ),
inference(paramodulation,[status(thm)],[f419,f865]) ).
fof(f918,plain,
( element_in_O2(d,d) = identity
| spl0_3 ),
inference(forward_demodulation,[status(thm)],[f114,f917]) ).
fof(f927,plain,
( element_in_O2(a,d) = multiply(inverse(a),d)
| spl0_0 ),
inference(paramodulation,[status(thm)],[f411,f865]) ).
fof(f928,plain,
( element_in_O2(a,d) = c
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f573,f927]) ).
fof(f1186,plain,
( subgroup_member(d)
| subgroup_member(d)
| subgroup_member(inverse(identity))
| spl0_3 ),
inference(paramodulation,[status(thm)],[f918,f317]) ).
fof(f1187,plain,
( spl0_3
| spl0_7 ),
inference(split_clause,[status(thm)],[f1186,f80,f357]) ).
fof(f1193,plain,
( subgroup_member(d)
| subgroup_member(a)
| subgroup_member(inverse(c))
| spl0_0 ),
inference(paramodulation,[status(thm)],[f928,f317]) ).
fof(f1194,plain,
( spl0_3
| spl0_0
| spl0_20 ),
inference(split_clause,[status(thm)],[f1193,f80,f44,f834]) ).
fof(f1197,plain,
$false,
inference(sat_refutation,[status(thm)],[f51,f84,f170,f334,f363,f487,f512,f566,f568,f752,f838,f1187,f1194]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP039-1 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 29 23:51:03 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.6.0
% 0.19/0.46 % Refutation found
% 0.19/0.46 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.47 % Elapsed time: 0.121330 seconds
% 0.19/0.47 % CPU time: 0.862688 seconds
% 0.19/0.47 % Total memory used: 61.316 MB
% 0.19/0.47 % Net memory used: 59.938 MB
%------------------------------------------------------------------------------