%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP085-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 12:32:28 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 2
% Syntax : Number of formulae : 81 ( 75 unt; 0 def)
% Number of atoms : 93 ( 92 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 31 ( 19 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 218 ( 218 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : multiply(multiply(multiply(X,Y),Z),inverse(multiply(X,Z))) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2] : multiply(multiply(multiply(X0,X1),X2),inverse(multiply(X0,X2))) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f5,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(multiply(X1,X0),inverse(multiply(X1,X2))))) = X2,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f6,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),inverse(multiply(multiply(multiply(X2,X0),X3),X1))) = inverse(multiply(X2,X3)),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f7,plain,
! [X0,X1,X2,X3] : multiply(multiply(multiply(multiply(multiply(X0,X1),X2),X3),inverse(multiply(X0,X2))),inverse(X1)) = X3,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f11,plain,
! [X0,X1,X2,X3] : multiply(X0,inverse(multiply(multiply(X1,X0),inverse(X2)))) = inverse(multiply(multiply(X3,X1),inverse(multiply(X3,X2)))),
inference(paramodulation,[status(thm)],[f5,f5]) ).
fof(f12,plain,
! [X0,X1,X2,X3] : multiply(X0,inverse(multiply(X1,inverse(multiply(multiply(X2,multiply(X1,X3)),inverse(multiply(X2,X0))))))) = X3,
inference(paramodulation,[status(thm)],[f5,f3]) ).
fof(f14,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),inverse(multiply(X2,X1))) = inverse(multiply(multiply(X3,X2),inverse(multiply(X3,X0)))),
inference(paramodulation,[status(thm)],[f5,f3]) ).
fof(f15,plain,
! [X0,X1,X2] : X0 = inverse(multiply(X1,multiply(X2,inverse(multiply(multiply(X1,X2),X0))))),
inference(paramodulation,[status(thm)],[f5,f6]) ).
fof(f19,plain,
! [X0,X1,X2] : multiply(multiply(X0,inverse(multiply(X1,X2))),inverse(X0)) = inverse(multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f3,f6]) ).
fof(f36,plain,
! [X0,X1,X2] : X0 = inverse(multiply(multiply(X1,X2),inverse(multiply(X1,multiply(X2,X0))))),
inference(paramodulation,[status(thm)],[f6,f15]) ).
fof(f38,plain,
! [X0,X1,X2,X3] : multiply(X0,inverse(multiply(multiply(multiply(X1,X2),X0),X3))) = inverse(multiply(X1,multiply(X2,X3))),
inference(paramodulation,[status(thm)],[f15,f15]) ).
fof(f41,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(X0,multiply(X1,X2)),inverse(multiply(X0,X3)))) = inverse(multiply(X1,multiply(X2,inverse(X3)))),
inference(paramodulation,[status(thm)],[f5,f15]) ).
fof(f47,plain,
! [X0,X1,X2,X3] : multiply(multiply(multiply(X0,X1),multiply(X2,inverse(multiply(multiply(X0,X2),X3)))),X3) = X1,
inference(paramodulation,[status(thm)],[f15,f3]) ).
fof(f52,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(X1,inverse(multiply(X1,multiply(X2,inverse(X0))))))) = X2,
inference(backward_demodulation,[status(thm)],[f41,f12]) ).
fof(f60,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(X0,X1),inverse(multiply(X0,X2)))) = inverse(multiply(multiply(X3,X1),inverse(multiply(X3,X2)))),
inference(paramodulation,[status(thm)],[f5,f36]) ).
fof(f69,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(multiply(X1,X0),X2))) = inverse(multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f3,f19]) ).
fof(f72,plain,
! [X0,X1,X2] : multiply(X0,inverse(X1)) = inverse(multiply(multiply(X2,X1),inverse(multiply(X2,X0)))),
inference(paramodulation,[status(thm)],[f5,f19]) ).
fof(f73,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),inverse(X0)) = inverse(multiply(multiply(X2,X3),inverse(multiply(X2,multiply(X3,X1))))),
inference(paramodulation,[status(thm)],[f36,f19]) ).
fof(f74,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),inverse(X0)) = inverse(multiply(X2,multiply(X3,inverse(multiply(multiply(X2,X3),X1))))),
inference(paramodulation,[status(thm)],[f15,f19]) ).
fof(f97,plain,
! [X0,X1,X2] : inverse(multiply(multiply(X0,X1),X2)) = inverse(multiply(X0,multiply(X1,X2))),
inference(backward_demodulation,[status(thm)],[f69,f38]) ).
fof(f99,plain,
! [X0,X1,X2] : inverse(multiply(X0,inverse(X1))) = inverse(multiply(multiply(X2,X0),inverse(multiply(X2,X1)))),
inference(backward_demodulation,[status(thm)],[f69,f11]) ).
fof(f100,plain,
! [X0,X1,X2] : multiply(multiply(multiply(X0,X1),inverse(multiply(X0,X2))),X2) = X1,
inference(backward_demodulation,[status(thm)],[f69,f47]) ).
fof(f112,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(X1,X2))) = inverse(multiply(X1,multiply(X2,inverse(X0)))),
inference(backward_demodulation,[status(thm)],[f72,f41]) ).
fof(f113,plain,
! [X0,X1,X2] : inverse(multiply(multiply(X0,X1),inverse(multiply(X0,X2)))) = multiply(X2,inverse(X1)),
inference(backward_demodulation,[status(thm)],[f72,f60]) ).
fof(f116,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),inverse(multiply(X2,X1))) = multiply(X0,inverse(X2)),
inference(backward_demodulation,[status(thm)],[f72,f14]) ).
fof(f119,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X0)) = X1,
inference(forward_demodulation,[status(thm)],[f36,f73]) ).
fof(f120,plain,
! [X0,X1,X2] : X0 = inverse(multiply(X1,multiply(X2,inverse(multiply(multiply(X1,X2),X0))))),
inference(forward_demodulation,[status(thm)],[f119,f74]) ).
fof(f121,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X0))) = X1,
inference(backward_demodulation,[status(thm)],[f123,f52]) ).
fof(f123,plain,
! [X0,X1] : X0 = inverse(multiply(X1,inverse(multiply(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f69,f120]) ).
fof(f139,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),inverse(multiply(multiply(X2,X0),multiply(X3,X1)))) = inverse(multiply(X2,X3)),
inference(backward_demodulation,[status(thm)],[f97,f6]) ).
fof(f160,plain,
! [X0,X1] : inverse(multiply(X0,inverse(X1))) = multiply(X1,inverse(X0)),
inference(forward_demodulation,[status(thm)],[f72,f99]) ).
fof(f195,plain,
! [X0,X1,X2] : inverse(multiply(X0,multiply(X1,inverse(multiply(X0,X2))))) = multiply(X2,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f97,f113]) ).
fof(f197,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X1)),X1) = X0,
inference(backward_demodulation,[status(thm)],[f198,f100]) ).
fof(f198,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),inverse(multiply(X0,X2))) = multiply(X1,inverse(X2)),
inference(forward_demodulation,[status(thm)],[f112,f195]) ).
fof(f205,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),inverse(multiply(X2,multiply(X0,multiply(X3,X1))))) = inverse(multiply(X2,X3)),
inference(forward_demodulation,[status(thm)],[f97,f139]) ).
fof(f226,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,inverse(multiply(multiply(multiply(X1,X2),X3),inverse(multiply(X1,X3))))),inverse(X0)) = inverse(X2),
inference(paramodulation,[status(thm)],[f7,f7]) ).
fof(f230,plain,
! [X0,X1,X2] : inverse(multiply(multiply(multiply(X0,X1),X2),inverse(multiply(X0,X2)))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f119,f226]) ).
fof(f231,plain,
! [X0,X1,X2] : inverse(multiply(multiply(X0,X1),multiply(X2,inverse(multiply(X0,X2))))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f97,f230]) ).
fof(f233,plain,
! [X0,X1,X2] : inverse(multiply(X0,multiply(X1,multiply(X2,inverse(multiply(X0,X2)))))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f97,f231]) ).
fof(f257,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f119,f119]) ).
fof(f259,plain,
! [X0,X1,X2] : multiply(multiply(multiply(X0,X1),inverse(multiply(X2,inverse(X2)))),inverse(X0)) = X1,
inference(paramodulation,[status(thm)],[f119,f7]) ).
fof(f268,plain,
! [X0,X1] : inverse(multiply(X0,multiply(X1,inverse(X0)))) = inverse(X1),
inference(backward_demodulation,[status(thm)],[f257,f233]) ).
fof(f276,plain,
! [X0,X1,X2] : multiply(multiply(multiply(X0,X1),multiply(X2,inverse(X2))),inverse(X0)) = X1,
inference(forward_demodulation,[status(thm)],[f160,f259]) ).
fof(f280,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X0,X1))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f112,f268]) ).
fof(f317,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(paramodulation,[status(thm)],[f119,f197]) ).
fof(f320,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(paramodulation,[status(thm)],[f119,f197]) ).
fof(f326,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),inverse(multiply(X2,multiply(X0,X3)))) = inverse(multiply(X2,multiply(X3,inverse(X1)))),
inference(paramodulation,[status(thm)],[f197,f205]) ).
fof(f333,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(backward_subsumption_resolution,[status(thm)],[f4,f320]) ).
fof(f337,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(X1,multiply(X2,X0)))) = inverse(multiply(X1,X2)),
inference(backward_demodulation,[status(thm)],[f340,f205]) ).
fof(f340,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),inverse(multiply(X2,multiply(X0,X3)))) = multiply(X1,inverse(multiply(X2,X3))),
inference(forward_demodulation,[status(thm)],[f112,f326]) ).
fof(f344,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f317,f121]) ).
fof(f345,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X1),X0) = X1,
inference(paramodulation,[status(thm)],[f317,f119]) ).
fof(f384,plain,
( multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(paramodulation,[status(thm)],[f320,f333]) ).
fof(f420,plain,
! [X0,X1,X2] : inverse(multiply(X0,multiply(X1,inverse(X2)))) = multiply(multiply(X2,inverse(X1)),inverse(X0)),
inference(paramodulation,[status(thm)],[f160,f160]) ).
fof(f435,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(X1,X2))) = multiply(multiply(X0,inverse(X2)),inverse(X1)),
inference(forward_demodulation,[status(thm)],[f112,f420]) ).
fof(f439,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
inference(paramodulation,[status(thm)],[f344,f344]) ).
fof(f464,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,inverse(X1)),inverse(multiply(X2,inverse(multiply(X1,X3))))) = multiply(multiply(X0,X3),inverse(X2)),
inference(paramodulation,[status(thm)],[f116,f116]) ).
fof(f466,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(X1,inverse(X2)))) = multiply(multiply(X2,X0),inverse(X1)),
inference(paramodulation,[status(thm)],[f119,f116]) ).
fof(f481,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X0)) = X1,
inference(paramodulation,[status(thm)],[f116,f119]) ).
fof(f484,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),multiply(X2,inverse(X0))) = multiply(X2,X1),
inference(paramodulation,[status(thm)],[f116,f121]) ).
fof(f492,plain,
! [X0,X1,X2,X3] : multiply(X0,inverse(multiply(multiply(X1,inverse(multiply(X2,X3))),X2))) = multiply(multiply(X0,X3),inverse(X1)),
inference(forward_demodulation,[status(thm)],[f435,f464]) ).
fof(f493,plain,
! [X0,X1,X2,X3] : multiply(X0,inverse(multiply(X1,multiply(inverse(multiply(X2,X3)),X2)))) = multiply(multiply(X0,X3),inverse(X1)),
inference(forward_demodulation,[status(thm)],[f97,f492]) ).
fof(f494,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(X1,inverse(X2)))) = multiply(multiply(X0,X2),inverse(X1)),
inference(forward_demodulation,[status(thm)],[f439,f493]) ).
fof(f507,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),multiply(multiply(X2,inverse(X2)),inverse(X0))) = X1,
inference(backward_demodulation,[status(thm)],[f527,f276]) ).
fof(f527,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,inverse(X2))) = multiply(multiply(X0,X1),inverse(X2)),
inference(forward_demodulation,[status(thm)],[f160,f494]) ).
fof(f529,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,inverse(X2))) = multiply(multiply(X1,X0),inverse(X2)),
inference(forward_demodulation,[status(thm)],[f160,f466]) ).
fof(f547,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X1))) = X0,
inference(forward_demodulation,[status(thm)],[f529,f481]) ).
fof(f572,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X0)),X1) = X1,
inference(forward_demodulation,[status(thm)],[f484,f507]) ).
fof(f696,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X1),X1)) = X0,
inference(paramodulation,[status(thm)],[f317,f547]) ).
fof(f866,plain,
! [X0,X1,X2] : multiply(X0,inverse(inverse(multiply(X1,X2)))) = inverse(inverse(multiply(X1,multiply(X2,X0)))),
inference(paramodulation,[status(thm)],[f337,f280]) ).
fof(f885,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = inverse(inverse(multiply(X1,multiply(X2,X0)))),
inference(forward_demodulation,[status(thm)],[f317,f866]) ).
fof(f886,plain,
( multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(backward_subsumption_resolution,[status(thm)],[f384,f887]) ).
fof(f887,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X2,X0)),
inference(forward_demodulation,[status(thm)],[f317,f885]) ).
fof(f910,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(paramodulation,[status(thm)],[f317,f572]) ).
fof(f935,plain,
( a2 != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(backward_demodulation,[status(thm)],[f910,f886]) ).
fof(f950,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(trivial_equality_resolution,[status(thm)],[f935]) ).
fof(f970,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f696,f345]) ).
fof(f989,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f950,f970]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP085-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 19:59:51 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.072664 seconds
% 0.13/0.44 % CPU time: 0.343076 seconds
% 0.13/0.44 % Total memory used: 47.540 MB
% 0.13/0.44 % Net memory used: 47.199 MB
%------------------------------------------------------------------------------