%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP617-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:34:48 PM UTC 2026
% Result : Unsatisfiable 16.53s 2.61s
% Output : CNFRefutation 7.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 18
% Syntax : Number of formulae : 95 ( 53 unt; 0 def)
% Number of atoms : 171 ( 31 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 154 ( 78 ~; 76 |; 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 : 181 ( 181 !; 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] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,U,Z,V,W] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y,U,Z,V,W] :
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] :
( subgroup1_member(inverse(X))
| ~ subgroup1_member(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B,C] :
( subgroup1_member(C)
| ~ product(A,B,C)
| ~ subgroup1_member(B)
| ~ subgroup1_member(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] :
( subgroup2_member(inverse(X))
| ~ subgroup2_member(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B,C] :
( subgroup2_member(C)
| ~ product(A,B,C)
| ~ subgroup2_member(B)
| ~ subgroup2_member(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
! [X,A] :
( subgroup1_member(multiply(A,multiply(X,inverse(A))))
| ~ subgroup1_member(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,hypothesis,
! [X,A] :
( subgroup2_member(multiply(A,multiply(X,inverse(A))))
| ~ subgroup2_member(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
! [X] :
( X = identity
| ~ subgroup2_member(X)
| ~ subgroup1_member(X) ),
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(thm)],[f1]) ).
fof(f20,plain,
! [X0] : product(X0,identity,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f21,plain,
! [X0] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f22,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f23,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [X,V,W] :
( product(X,V,W)
| ! [U,Z] :
( ~ product(U,Z,W)
| ! [Y] :
( ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f27,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [U,Z,W] :
( product(U,Z,W)
| ! [X,V] :
( ~ product(X,V,W)
| ! [Y] :
( ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f29,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0] :
( subgroup1_member(inverse(X0))
| ~ subgroup1_member(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f31,plain,
! [C] :
( subgroup1_member(C)
| ! [A,B] :
( ~ product(A,B,C)
| ~ subgroup1_member(B)
| ~ subgroup1_member(A) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f32,plain,
! [X0,X1,X2] :
( subgroup1_member(X2)
| ~ product(X0,X1,X2)
| ~ subgroup1_member(X1)
| ~ subgroup1_member(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0] :
( subgroup2_member(inverse(X0))
| ~ subgroup2_member(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f34,plain,
! [C] :
( subgroup2_member(C)
| ! [A,B] :
( ~ product(A,B,C)
| ~ subgroup2_member(B)
| ~ subgroup2_member(A) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f35,plain,
! [X0,X1,X2] :
( subgroup2_member(X2)
| ~ product(X0,X1,X2)
| ~ subgroup2_member(X1)
| ~ subgroup2_member(X0) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [X] :
( ! [A] : subgroup1_member(multiply(A,multiply(X,inverse(A))))
| ~ subgroup1_member(X) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f37,plain,
! [X0,X1] :
( subgroup1_member(multiply(X1,multiply(X0,inverse(X1))))
| ~ subgroup1_member(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
! [X] :
( ! [A] : subgroup2_member(multiply(A,multiply(X,inverse(A))))
| ~ subgroup2_member(X) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f39,plain,
! [X0,X1] :
( subgroup2_member(multiply(X1,multiply(X0,inverse(X1))))
| ~ subgroup2_member(X0) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [X0] :
( X0 = identity
| ~ subgroup2_member(X0)
| ~ subgroup1_member(X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f41,plain,
subgroup1_member(v),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f42,plain,
subgroup2_member(u),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f43,plain,
multiply(v,u) != multiply(u,v),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f44,plain,
subgroup1_member(inverse(v)),
inference(resolution,[status(thm)],[f30,f41]) ).
fof(f51,plain,
subgroup2_member(inverse(u)),
inference(resolution,[status(thm)],[f33,f42]) ).
fof(f60,plain,
! [X0,X1] :
( X0 = X1
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[f25,f19]) ).
fof(f62,plain,
! [X0,X1] :
( X0 = X1
| ~ product(X0,identity,X1) ),
inference(resolution,[status(thm)],[f25,f20]) ).
fof(f63,plain,
! [X0,X1,X2] :
( multiply(X0,X1) = X2
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f25,f23]) ).
fof(f65,plain,
inverse(identity) = identity,
inference(resolution,[status(thm)],[f60,f22]) ).
fof(f67,plain,
! [X0] : X0 = multiply(identity,X0),
inference(resolution,[status(thm)],[f60,f23]) ).
fof(f78,plain,
! [X0,X1,X2,X3] :
( product(inverse(X0),X2,X3)
| ~ product(identity,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f27,f21]) ).
fof(f82,plain,
! [X0,X1,X2,X3,X4] :
( product(X3,X2,X4)
| ~ product(multiply(X3,X0),X1,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f27,f23]) ).
fof(f87,plain,
! [X0,X1,X2,X3,X4] :
( product(multiply(X3,X0),X1,X4)
| ~ product(X3,X2,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f29,f23]) ).
fof(f92,plain,
! [X0,X1] :
( subgroup1_member(multiply(X0,X1))
| ~ subgroup1_member(X1)
| ~ subgroup1_member(X0) ),
inference(resolution,[status(thm)],[f32,f23]) ).
fof(f95,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(resolution,[status(thm)],[f63,f21]) ).
fof(f108,plain,
! [X0,X1,X2] :
( product(X0,identity,X2)
| ~ product(multiply(X0,inverse(X1)),X1,X2) ),
inference(resolution,[status(thm)],[f82,f21]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( product(X0,multiply(X1,X2),X3)
| ~ product(multiply(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[f82,f23]) ).
fof(f162,plain,
! [X0,X1,X2,X3] :
( product(multiply(X0,X1),X2,X3)
| ~ product(X0,multiply(X1,X2),X3) ),
inference(resolution,[status(thm)],[f87,f23]) ).
fof(f164,plain,
! [X0,X1] : product(X0,identity,multiply(multiply(X0,inverse(X1)),X1)),
inference(resolution,[status(thm)],[f108,f23]) ).
fof(f201,plain,
! [X0,X1] :
( subgroup2_member(multiply(X0,X1))
| ~ subgroup2_member(X1)
| ~ subgroup2_member(X0) ),
inference(resolution,[status(thm)],[f35,f23]) ).
fof(f225,plain,
! [X0] : subgroup1_member(multiply(X0,multiply(v,inverse(X0)))),
inference(resolution,[status(thm)],[f37,f41]) ).
fof(f232,plain,
! [X0] : subgroup2_member(multiply(X0,multiply(inverse(u),inverse(X0)))),
inference(resolution,[status(thm)],[f39,f51]) ).
fof(f240,plain,
! [X0,X1,X2] :
( product(inverse(X2),multiply(X2,X0),X1)
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[f78,f23]) ).
fof(f246,plain,
! [X0] :
( subgroup2_member(multiply(u,X0))
| ~ subgroup2_member(X0) ),
inference(resolution,[status(thm)],[f201,f42]) ).
fof(f250,plain,
! [X0,X1] :
( subgroup1_member(multiply(multiply(X1,multiply(v,inverse(X1))),X0))
| ~ subgroup1_member(X0) ),
inference(resolution,[status(thm)],[f225,f92]) ).
fof(f460,plain,
! [X0,X1] : X0 = multiply(multiply(X0,inverse(X1)),X1),
inference(resolution,[status(thm)],[f164,f62]) ).
fof(f499,plain,
! [X0] : inverse(inverse(X0)) = multiply(identity,X0),
inference(paramodulation,[status(thm)],[f95,f460]) ).
fof(f509,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f67,f499]) ).
fof(f531,plain,
! [X0,X1] : X0 = multiply(multiply(X0,X1),inverse(X1)),
inference(paramodulation,[status(thm)],[f509,f460]) ).
fof(f552,plain,
! [X0,X1,X2] : product(X0,multiply(X1,X2),multiply(multiply(X0,X1),X2)),
inference(resolution,[status(thm)],[f112,f23]) ).
fof(f757,plain,
! [X0] : subgroup2_member(multiply(u,multiply(X0,multiply(inverse(u),inverse(X0))))),
inference(resolution,[status(thm)],[f232,f246]) ).
fof(f839,plain,
! [X0,X1,X2] : product(multiply(X0,X1),X2,multiply(X0,multiply(X1,X2))),
inference(resolution,[status(thm)],[f162,f23]) ).
fof(f889,plain,
! [X0,X1] : product(inverse(X0),multiply(X0,X1),X1),
inference(resolution,[status(thm)],[f240,f19]) ).
fof(f934,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(resolution,[status(thm)],[f889,f63]) ).
fof(f955,plain,
! [X0,X1] : multiply(inverse(multiply(X0,inverse(X1))),X0) = X1,
inference(paramodulation,[status(thm)],[f460,f934]) ).
fof(f956,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
inference(paramodulation,[status(thm)],[f531,f934]) ).
fof(f1183,plain,
! [X0,X1] : inverse(multiply(X0,inverse(X1))) = multiply(X1,inverse(X0)),
inference(paramodulation,[status(thm)],[f955,f531]) ).
fof(f1204,plain,
! [X0,X1] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f934,f956]) ).
fof(f1304,plain,
! [X0] : subgroup1_member(multiply(multiply(X0,multiply(v,inverse(X0))),inverse(v))),
inference(resolution,[status(thm)],[f250,f44]) ).
fof(f1686,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(resolution,[status(thm)],[f552,f63]) ).
fof(f2240,plain,
! [X0,X1,X2] : product(multiply(X0,multiply(X1,inverse(X2))),X2,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f460,f839]) ).
fof(f4344,plain,
! [X0] : subgroup2_member(multiply(u,multiply(X0,inverse(multiply(X0,u))))),
inference(forward_demodulation,[status(thm)],[f1204,f757]) ).
fof(f4355,plain,
! [X0] :
( multiply(u,multiply(X0,inverse(multiply(X0,u)))) = identity
| ~ subgroup1_member(multiply(u,multiply(X0,inverse(multiply(X0,u))))) ),
inference(resolution,[status(thm)],[f4344,f40]) ).
fof(f6698,plain,
! [X0] : subgroup1_member(multiply(X0,multiply(multiply(v,inverse(X0)),inverse(v)))),
inference(forward_demodulation,[status(thm)],[f1686,f1304]) ).
fof(f6699,plain,
! [X0] : subgroup1_member(multiply(X0,multiply(v,multiply(inverse(X0),inverse(v))))),
inference(forward_demodulation,[status(thm)],[f1686,f6698]) ).
fof(f6700,plain,
! [X0] : subgroup1_member(multiply(X0,multiply(v,inverse(multiply(v,X0))))),
inference(forward_demodulation,[status(thm)],[f1204,f6699]) ).
fof(f33426,plain,
multiply(u,multiply(v,inverse(multiply(v,u)))) = identity,
inference(resolution,[status(thm)],[f4355,f6700]) ).
fof(f55448,plain,
multiply(inverse(identity),u) = inverse(multiply(v,inverse(multiply(v,u)))),
inference(paramodulation,[status(thm)],[f33426,f956]) ).
fof(f55819,plain,
multiply(identity,u) = inverse(multiply(v,inverse(multiply(v,u)))),
inference(forward_demodulation,[status(thm)],[f65,f55448]) ).
fof(f55820,plain,
u = inverse(multiply(v,inverse(multiply(v,u)))),
inference(forward_demodulation,[status(thm)],[f67,f55819]) ).
fof(f55821,plain,
u = multiply(multiply(v,u),inverse(v)),
inference(forward_demodulation,[status(thm)],[f1183,f55820]) ).
fof(f55822,plain,
u = multiply(v,multiply(u,inverse(v))),
inference(forward_demodulation,[status(thm)],[f1686,f55821]) ).
fof(f56473,plain,
product(u,v,multiply(v,u)),
inference(paramodulation,[status(thm)],[f55822,f2240]) ).
fof(f56924,plain,
multiply(u,v) = multiply(v,u),
inference(resolution,[status(thm)],[f56473,f63]) ).
fof(f56929,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f56924,f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP617-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:18:05 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 16.53/2.61 % Refutation found
% 16.53/2.61 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 16.53/2.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.54/2.65 % Elapsed time: 2.270247 seconds
% 7.54/2.65 % CPU time: 17.503561 seconds
% 7.54/2.65 % Total memory used: 175.551 MB
% 7.54/2.65 % Net memory used: 149.309 MB
%------------------------------------------------------------------------------