TSTP Solution File: GRP617-1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRP617-1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n014.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 12:12:13 EDT 2023
% Result : Unsatisfiable 5.24s 1.04s
% Output : CNFRefutation 5.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 18
% Syntax : Number of formulae : 94 ( 54 unt; 0 def)
% Number of atoms : 167 ( 31 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 148 ( 75 ~; 73 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 176 (; 176 !; 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(f8,axiom,
! [X,Y,U,Z,V,W] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] :
( ~ subgroup1_member(X)
| subgroup1_member(inverse(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B,C] :
( ~ subgroup1_member(A)
| ~ subgroup1_member(B)
| ~ product(A,B,C)
| subgroup1_member(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] :
( ~ subgroup2_member(X)
| subgroup2_member(inverse(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B,C] :
( ~ subgroup2_member(A)
| ~ subgroup2_member(B)
| ~ product(A,B,C)
| subgroup2_member(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
! [X,A] :
( ~ subgroup1_member(X)
| subgroup1_member(multiply(A,multiply(X,inverse(A)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,hypothesis,
! [X,A] :
( ~ subgroup2_member(X)
| subgroup2_member(multiply(A,multiply(X,inverse(A)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
! [X] :
( ~ subgroup1_member(X)
| ~ subgroup2_member(X)
| X = identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
subgroup1_member(v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
subgroup2_member(u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
multiply(v,u) != multiply(u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f20,plain,
! [X0] : product(X0,identity,X0),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f21,plain,
! [X0] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f22,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f23,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f24,plain,
! [Z,W] :
( ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) )
| Z = W ),
inference(miniscoping,[status(esa)],[f6]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f26,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(f27,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)],[f26]) ).
fof(f28,plain,
! [U,Z,W] :
( ! [X,V] :
( ! [Y] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V) )
| ~ product(X,V,W) )
| product(U,Z,W) ),
inference(miniscoping,[status(esa)],[f8]) ).
fof(f29,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X1,X3,X4)
| ~ product(X0,X4,X5)
| product(X2,X3,X5) ),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f30,plain,
! [X0] :
( ~ subgroup1_member(X0)
| subgroup1_member(inverse(X0)) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f31,plain,
! [C] :
( ! [A,B] :
( ~ subgroup1_member(A)
| ~ subgroup1_member(B)
| ~ product(A,B,C) )
| subgroup1_member(C) ),
inference(miniscoping,[status(esa)],[f10]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ~ subgroup1_member(X0)
| ~ subgroup1_member(X1)
| ~ product(X0,X1,X2)
| subgroup1_member(X2) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f33,plain,
! [X0] :
( ~ subgroup2_member(X0)
| subgroup2_member(inverse(X0)) ),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f34,plain,
! [C] :
( ! [A,B] :
( ~ subgroup2_member(A)
| ~ subgroup2_member(B)
| ~ product(A,B,C) )
| subgroup2_member(C) ),
inference(miniscoping,[status(esa)],[f12]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ~ subgroup2_member(X0)
| ~ subgroup2_member(X1)
| ~ product(X0,X1,X2)
| subgroup2_member(X2) ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f36,plain,
! [X] :
( ~ subgroup1_member(X)
| ! [A] : subgroup1_member(multiply(A,multiply(X,inverse(A)))) ),
inference(miniscoping,[status(esa)],[f13]) ).
fof(f37,plain,
! [X0,X1] :
( ~ subgroup1_member(X0)
| subgroup1_member(multiply(X1,multiply(X0,inverse(X1)))) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f38,plain,
! [X] :
( ~ subgroup2_member(X)
| ! [A] : subgroup2_member(multiply(A,multiply(X,inverse(A)))) ),
inference(miniscoping,[status(esa)],[f14]) ).
fof(f39,plain,
! [X0,X1] :
( ~ subgroup2_member(X0)
| subgroup2_member(multiply(X1,multiply(X0,inverse(X1)))) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f40,plain,
! [X0] :
( ~ subgroup1_member(X0)
| ~ subgroup2_member(X0)
| X0 = identity ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f41,plain,
subgroup1_member(v),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f42,plain,
subgroup2_member(u),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f43,plain,
multiply(v,u) != multiply(u,v),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f44,plain,
subgroup1_member(inverse(v)),
inference(resolution,[status(thm)],[f30,f41]) ).
fof(f54,plain,
subgroup2_member(inverse(u)),
inference(resolution,[status(thm)],[f33,f42]) ).
fof(f90,plain,
! [X0,X1] :
( ~ product(inverse(X0),X0,X1)
| identity = X1 ),
inference(resolution,[status(thm)],[f25,f21]) ).
fof(f91,plain,
! [X0,X1] :
( ~ product(identity,X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f25,f19]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| multiply(X0,X1) = X2 ),
inference(resolution,[status(thm)],[f25,f23]) ).
fof(f95,plain,
inverse(identity) = identity,
inference(resolution,[status(thm)],[f91,f22]) ).
fof(f96,plain,
! [X0] : X0 = multiply(identity,X0),
inference(resolution,[status(thm)],[f91,f23]) ).
fof(f104,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(resolution,[status(thm)],[f90,f23]) ).
fof(f121,plain,
! [X0,X1,X2,X3,X4] :
( ~ product(X0,X1,X2)
| ~ product(multiply(X3,X0),X1,X4)
| product(X3,X2,X4) ),
inference(resolution,[status(thm)],[f27,f23]) ).
fof(f126,plain,
! [X0,X1,X2,X3,X4] :
( ~ product(X0,X1,X2)
| ~ product(X3,X2,X4)
| product(multiply(X3,X0),X1,X4) ),
inference(resolution,[status(thm)],[f29,f23]) ).
fof(f144,plain,
! [X0,X1] :
( ~ subgroup1_member(X0)
| ~ subgroup1_member(X1)
| subgroup1_member(multiply(X0,X1)) ),
inference(resolution,[status(thm)],[f32,f23]) ).
fof(f157,plain,
! [X0,X1,X2,X3] :
( ~ product(multiply(X0,X1),X2,X3)
| product(X0,multiply(X1,X2),X3) ),
inference(resolution,[status(thm)],[f121,f23]) ).
fof(f158,plain,
! [X0,X1,X2] :
( ~ product(X0,identity,X1)
| product(multiply(X0,inverse(X2)),X2,X1) ),
inference(resolution,[status(thm)],[f126,f21]) ).
fof(f162,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,multiply(X1,X2),X3)
| product(multiply(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[f126,f23]) ).
fof(f253,plain,
! [X0,X1,X2] : product(X0,multiply(X1,X2),multiply(multiply(X0,X1),X2)),
inference(resolution,[status(thm)],[f157,f23]) ).
fof(f297,plain,
! [X0,X1] : product(multiply(X0,inverse(X1)),X1,X0),
inference(resolution,[status(thm)],[f158,f20]) ).
fof(f316,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X1)),X1) = X0,
inference(resolution,[status(thm)],[f297,f94]) ).
fof(f328,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f104,f316]) ).
fof(f329,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f96,f328]) ).
fof(f359,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X1)) = X0,
inference(paramodulation,[status(thm)],[f329,f316]) ).
fof(f438,plain,
! [X0,X1,X2] : product(multiply(X0,X1),X2,multiply(X0,multiply(X1,X2))),
inference(resolution,[status(thm)],[f162,f23]) ).
fof(f498,plain,
! [X0,X1] :
( ~ subgroup2_member(X0)
| ~ subgroup2_member(X1)
| subgroup2_member(multiply(X0,X1)) ),
inference(resolution,[status(thm)],[f35,f23]) ).
fof(f501,plain,
! [X0] :
( ~ subgroup2_member(X0)
| subgroup2_member(multiply(u,X0)) ),
inference(resolution,[status(thm)],[f498,f42]) ).
fof(f576,plain,
! [X0] : subgroup1_member(multiply(X0,multiply(v,inverse(X0)))),
inference(resolution,[status(thm)],[f37,f41]) ).
fof(f587,plain,
! [X0] : subgroup2_member(multiply(X0,multiply(inverse(u),inverse(X0)))),
inference(resolution,[status(thm)],[f39,f54]) ).
fof(f613,plain,
! [X0,X1] :
( ~ subgroup1_member(X0)
| subgroup1_member(multiply(multiply(X1,multiply(v,inverse(X1))),X0)) ),
inference(resolution,[status(thm)],[f576,f144]) ).
fof(f663,plain,
! [X0] : subgroup2_member(multiply(u,multiply(X0,multiply(inverse(u),inverse(X0))))),
inference(resolution,[status(thm)],[f587,f501]) ).
fof(f776,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(resolution,[status(thm)],[f253,f94]) ).
fof(f799,plain,
! [X0,X1] : product(inverse(X0),multiply(X0,X1),multiply(identity,X1)),
inference(paramodulation,[status(thm)],[f104,f253]) ).
fof(f800,plain,
! [X0,X1] : product(inverse(X0),multiply(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f96,f799]) ).
fof(f858,plain,
! [X0] : subgroup1_member(multiply(multiply(X0,multiply(v,inverse(X0))),inverse(v))),
inference(resolution,[status(thm)],[f613,f44]) ).
fof(f868,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(resolution,[status(thm)],[f800,f94]) ).
fof(f909,plain,
! [X0,X1] : multiply(inverse(multiply(X0,inverse(X1))),X0) = X1,
inference(paramodulation,[status(thm)],[f316,f868]) ).
fof(f910,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
inference(paramodulation,[status(thm)],[f359,f868]) ).
fof(f1132,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = inverse(multiply(X1,inverse(X0))),
inference(paramodulation,[status(thm)],[f909,f359]) ).
fof(f1144,plain,
! [X0,X1] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f868,f910]) ).
fof(f1588,plain,
! [X0,X1,X2] : product(multiply(X0,multiply(X1,inverse(X2))),X2,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f316,f438]) ).
fof(f4594,plain,
! [X0] : subgroup2_member(multiply(u,multiply(X0,inverse(multiply(X0,u))))),
inference(forward_demodulation,[status(thm)],[f1144,f663]) ).
fof(f4614,plain,
! [X0] :
( ~ subgroup1_member(multiply(u,multiply(X0,inverse(multiply(X0,u)))))
| multiply(u,multiply(X0,inverse(multiply(X0,u)))) = identity ),
inference(resolution,[status(thm)],[f4594,f40]) ).
fof(f7001,plain,
! [X0] : subgroup1_member(multiply(X0,multiply(multiply(v,inverse(X0)),inverse(v)))),
inference(forward_demodulation,[status(thm)],[f776,f858]) ).
fof(f7002,plain,
! [X0] : subgroup1_member(multiply(X0,multiply(v,multiply(inverse(X0),inverse(v))))),
inference(forward_demodulation,[status(thm)],[f776,f7001]) ).
fof(f7003,plain,
! [X0] : subgroup1_member(multiply(X0,multiply(v,inverse(multiply(v,X0))))),
inference(forward_demodulation,[status(thm)],[f1144,f7002]) ).
fof(f36854,plain,
multiply(u,multiply(v,inverse(multiply(v,u)))) = identity,
inference(resolution,[status(thm)],[f4614,f7003]) ).
fof(f51887,plain,
multiply(inverse(identity),u) = inverse(multiply(v,inverse(multiply(v,u)))),
inference(paramodulation,[status(thm)],[f36854,f910]) ).
fof(f51888,plain,
multiply(identity,u) = inverse(multiply(v,inverse(multiply(v,u)))),
inference(forward_demodulation,[status(thm)],[f95,f51887]) ).
fof(f51889,plain,
u = inverse(multiply(v,inverse(multiply(v,u)))),
inference(forward_demodulation,[status(thm)],[f96,f51888]) ).
fof(f51890,plain,
u = multiply(multiply(v,u),inverse(v)),
inference(forward_demodulation,[status(thm)],[f1132,f51889]) ).
fof(f51891,plain,
u = multiply(v,multiply(u,inverse(v))),
inference(forward_demodulation,[status(thm)],[f776,f51890]) ).
fof(f52149,plain,
product(u,v,multiply(v,u)),
inference(paramodulation,[status(thm)],[f51891,f1588]) ).
fof(f52640,plain,
multiply(u,v) = multiply(v,u),
inference(resolution,[status(thm)],[f52149,f94]) ).
fof(f52641,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f52640,f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP617-1 : TPTP v8.1.2. Released v3.1.0.
% 0.04/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n014.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue May 30 11:23:34 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 5.24/1.04 % Refutation found
% 5.24/1.04 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 5.24/1.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.50/1.10 % Elapsed time: 0.735054 seconds
% 5.50/1.10 % CPU time: 5.565068 seconds
% 5.50/1.10 % Memory used: 79.159 MB
%------------------------------------------------------------------------------