TSTP Solution File: GRP617-1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% 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 : n016.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 20:21:05 EDT 2024
% Result : Unsatisfiable 13.66s 2.11s
% Output : CNFRefutation 14.26s
% 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/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(f4,axiom,
! [X] : product(X,inverse(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(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/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] :
( ~ subgroup1_member(X)
| subgroup1_member(inverse(X)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] :
( ~ subgroup2_member(X)
| subgroup2_member(inverse(X)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
! [X,A] :
( ~ subgroup1_member(X)
| subgroup1_member(multiply(A,multiply(X,inverse(A)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,hypothesis,
! [X,A] :
( ~ subgroup2_member(X)
| subgroup2_member(multiply(A,multiply(X,inverse(A)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
! [X] :
( ~ subgroup1_member(X)
| ~ subgroup2_member(X)
| X = identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
subgroup1_member(v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
subgroup2_member(u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
multiply(v,u) != multiply(u,v),
file('/export/starexec/sandbox2/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(f91,plain,
! [X0,X1] :
( ~ product(identity,X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f25,f19]) ).
fof(f93,plain,
! [X0,X1] :
( ~ product(X0,identity,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f25,f20]) ).
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(f107,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(f112,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(f130,plain,
! [X0,X1] :
( ~ subgroup1_member(X0)
| ~ subgroup1_member(X1)
| subgroup1_member(multiply(X0,X1)) ),
inference(resolution,[status(thm)],[f32,f23]) ).
fof(f132,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(resolution,[status(thm)],[f94,f21]) ).
fof(f163,plain,
! [X0,X1,X2] :
( ~ product(multiply(X0,inverse(X1)),X1,X2)
| product(X0,identity,X2) ),
inference(resolution,[status(thm)],[f107,f21]) ).
fof(f167,plain,
! [X0,X1,X2,X3] :
( ~ product(multiply(X0,X1),X2,X3)
| product(X0,multiply(X1,X2),X3) ),
inference(resolution,[status(thm)],[f107,f23]) ).
fof(f226,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,multiply(X1,X2),X3)
| product(multiply(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[f112,f23]) ).
fof(f230,plain,
! [X0,X1] : product(X0,identity,multiply(multiply(X0,inverse(X1)),X1)),
inference(resolution,[status(thm)],[f163,f23]) ).
fof(f276,plain,
! [X0,X1] :
( ~ subgroup2_member(X0)
| ~ subgroup2_member(X1)
| subgroup2_member(multiply(X0,X1)) ),
inference(resolution,[status(thm)],[f35,f23]) ).
fof(f281,plain,
! [X0] : subgroup1_member(multiply(X0,multiply(v,inverse(X0)))),
inference(resolution,[status(thm)],[f37,f41]) ).
fof(f288,plain,
! [X0] : subgroup2_member(multiply(X0,multiply(inverse(u),inverse(X0)))),
inference(resolution,[status(thm)],[f39,f54]) ).
fof(f355,plain,
! [X0] :
( ~ subgroup2_member(X0)
| subgroup2_member(multiply(u,X0)) ),
inference(resolution,[status(thm)],[f276,f42]) ).
fof(f357,plain,
! [X0,X1] :
( ~ subgroup1_member(X0)
| subgroup1_member(multiply(multiply(X1,multiply(v,inverse(X1))),X0)) ),
inference(resolution,[status(thm)],[f281,f130]) ).
fof(f694,plain,
! [X0,X1,X2] : product(X0,multiply(X1,X2),multiply(multiply(X0,X1),X2)),
inference(resolution,[status(thm)],[f167,f23]) ).
fof(f715,plain,
! [X0,X1] : X0 = multiply(multiply(X0,inverse(X1)),X1),
inference(resolution,[status(thm)],[f230,f93]) ).
fof(f753,plain,
! [X0] : inverse(inverse(X0)) = multiply(identity,X0),
inference(paramodulation,[status(thm)],[f132,f715]) ).
fof(f754,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f96,f753]) ).
fof(f788,plain,
! [X0,X1] : X0 = multiply(multiply(X0,X1),inverse(X1)),
inference(paramodulation,[status(thm)],[f754,f715]) ).
fof(f982,plain,
! [X0] : subgroup2_member(multiply(u,multiply(X0,multiply(inverse(u),inverse(X0))))),
inference(resolution,[status(thm)],[f288,f355]) ).
fof(f1022,plain,
! [X0,X1,X2] : product(multiply(X0,X1),X2,multiply(X0,multiply(X1,X2))),
inference(resolution,[status(thm)],[f226,f23]) ).
fof(f1116,plain,
! [X0] : subgroup1_member(multiply(multiply(X0,multiply(v,inverse(X0))),inverse(v))),
inference(resolution,[status(thm)],[f357,f44]) ).
fof(f1317,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(resolution,[status(thm)],[f694,f94]) ).
fof(f1340,plain,
! [X0,X1] : product(inverse(X0),multiply(X0,X1),multiply(identity,X1)),
inference(paramodulation,[status(thm)],[f132,f694]) ).
fof(f1341,plain,
! [X0,X1] : product(inverse(X0),multiply(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f96,f1340]) ).
fof(f1363,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(resolution,[status(thm)],[f1341,f94]) ).
fof(f1446,plain,
! [X0,X1] : multiply(inverse(multiply(X0,inverse(X1))),X0) = X1,
inference(paramodulation,[status(thm)],[f715,f1363]) ).
fof(f1447,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
inference(paramodulation,[status(thm)],[f788,f1363]) ).
fof(f1684,plain,
! [X0,X1] : inverse(multiply(X0,inverse(X1))) = multiply(X1,inverse(X0)),
inference(paramodulation,[status(thm)],[f1446,f788]) ).
fof(f1696,plain,
! [X0,X1] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f1363,f1447]) ).
fof(f2626,plain,
! [X0,X1,X2] : product(multiply(X0,multiply(X1,inverse(X2))),X2,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f715,f1022]) ).
fof(f5466,plain,
! [X0] : subgroup2_member(multiply(u,multiply(X0,inverse(multiply(X0,u))))),
inference(forward_demodulation,[status(thm)],[f1696,f982]) ).
fof(f5492,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)],[f5466,f40]) ).
fof(f7480,plain,
! [X0] : subgroup1_member(multiply(X0,multiply(multiply(v,inverse(X0)),inverse(v)))),
inference(forward_demodulation,[status(thm)],[f1317,f1116]) ).
fof(f7481,plain,
! [X0] : subgroup1_member(multiply(X0,multiply(v,multiply(inverse(X0),inverse(v))))),
inference(forward_demodulation,[status(thm)],[f1317,f7480]) ).
fof(f7482,plain,
! [X0] : subgroup1_member(multiply(X0,multiply(v,inverse(multiply(v,X0))))),
inference(forward_demodulation,[status(thm)],[f1696,f7481]) ).
fof(f41723,plain,
multiply(u,multiply(v,inverse(multiply(v,u)))) = identity,
inference(resolution,[status(thm)],[f5492,f7482]) ).
fof(f48180,plain,
multiply(inverse(identity),u) = inverse(multiply(v,inverse(multiply(v,u)))),
inference(paramodulation,[status(thm)],[f41723,f1447]) ).
fof(f48181,plain,
multiply(identity,u) = inverse(multiply(v,inverse(multiply(v,u)))),
inference(forward_demodulation,[status(thm)],[f95,f48180]) ).
fof(f48182,plain,
u = inverse(multiply(v,inverse(multiply(v,u)))),
inference(forward_demodulation,[status(thm)],[f96,f48181]) ).
fof(f48183,plain,
u = multiply(multiply(v,u),inverse(v)),
inference(forward_demodulation,[status(thm)],[f1684,f48182]) ).
fof(f48184,plain,
u = multiply(v,multiply(u,inverse(v))),
inference(forward_demodulation,[status(thm)],[f1317,f48183]) ).
fof(f50489,plain,
product(u,v,multiply(v,u)),
inference(paramodulation,[status(thm)],[f48184,f2626]) ).
fof(f51252,plain,
multiply(u,v) = multiply(v,u),
inference(resolution,[status(thm)],[f50489,f94]) ).
fof(f51253,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f51252,f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRP617-1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n016.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue Apr 30 00:51:40 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.14/0.32 % Drodi V3.6.0
% 13.66/2.11 % Refutation found
% 13.66/2.11 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 13.66/2.11 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 14.71/2.19 % Elapsed time: 1.862061 seconds
% 14.71/2.19 % CPU time: 14.447829 seconds
% 14.71/2.19 % Total memory used: 208.524 MB
% 14.71/2.19 % Net memory used: 188.099 MB
%------------------------------------------------------------------------------