%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP064-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 12:32:26 PM UTC 2026
% Result : Unsatisfiable 0.13s 5.61s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 4
% Syntax : Number of formulae : 67 ( 62 unt; 0 def)
% Number of atoms : 75 ( 74 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 15 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 146 ( 146 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : divide(X,divide(divide(divide(divide(Y,Y),Y),Z),divide(divide(divide(Y,Y),X),Z))) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : multiply(X,Y) = divide(X,divide(divide(Z,Z),Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Z] : inverse(X) = divide(divide(Z,Z),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( 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/sandbox/benchmark/theBenchmark.p') ).
fof(f5,plain,
! [X0,X1,X2] : divide(X0,divide(divide(divide(divide(X1,X1),X1),X2),divide(divide(divide(X1,X1),X0),X2))) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f6,plain,
! [X0,X1,X2] : multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
! [X0,X1] : inverse(X0) = divide(divide(X1,X1),X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,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(cnf_transformation,[status(thm)],[f4]) ).
fof(f9,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(backward_demodulation,[status(thm)],[f7,f6]) ).
fof(f10,plain,
! [X0,X1,X2] : divide(X0,divide(divide(divide(divide(X1,X1),X1),X2),divide(inverse(X0),X2))) = X1,
inference(backward_demodulation,[status(thm)],[f7,f5]) ).
fof(f11,plain,
! [X0,X1,X2] : divide(X0,divide(divide(inverse(X1),X2),divide(inverse(X0),X2))) = X1,
inference(forward_demodulation,[status(thm)],[f7,f10]) ).
fof(f12,plain,
! [X0,X1] : inverse(X0) = divide(inverse(divide(X1,X1)),X0),
inference(paramodulation,[status(thm)],[f7,f7]) ).
fof(f13,plain,
! [X0,X1] : multiply(divide(X0,X0),X1) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f7,f9]) ).
fof(f15,plain,
! [X0,X1] : inverse(X0) = divide(multiply(inverse(X1),X1),X0),
inference(paramodulation,[status(thm)],[f9,f7]) ).
fof(f16,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(inverse(divide(X1,X1)),X0),
inference(paramodulation,[status(thm)],[f9,f12]) ).
fof(f18,plain,
! [X0,X1] : inverse(X0) = divide(inverse(inverse(divide(X1,X1))),X0),
inference(paramodulation,[status(thm)],[f7,f12]) ).
fof(f24,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f9,f13]) ).
fof(f25,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(backward_demodulation,[status(thm)],[f24,f8]) ).
fof(f26,plain,
! [X0,X1,X2] : inverse(divide(divide(inverse(X0),X1),divide(inverse(inverse(divide(X2,X2))),X1))) = X0,
inference(paramodulation,[status(thm)],[f12,f11]) ).
fof(f28,plain,
! [X0,X1] : divide(X0,inverse(divide(inverse(X0),inverse(X1)))) = X1,
inference(paramodulation,[status(thm)],[f7,f11]) ).
fof(f30,plain,
! [X0,X1,X2,X3] : divide(X0,divide(X1,divide(inverse(X0),divide(divide(inverse(X1),X2),divide(inverse(inverse(X3)),X2))))) = X3,
inference(paramodulation,[status(thm)],[f11,f11]) ).
fof(f31,plain,
! [X0,X1,X2] : divide(X0,divide(multiply(inverse(X1),X2),divide(inverse(X0),inverse(X2)))) = X1,
inference(paramodulation,[status(thm)],[f9,f11]) ).
fof(f37,plain,
! [X0,X1] : inverse(divide(divide(inverse(X0),X1),inverse(X1))) = X0,
inference(forward_demodulation,[status(thm)],[f18,f26]) ).
fof(f38,plain,
! [X0,X1] : inverse(multiply(divide(inverse(X0),X1),X1)) = X0,
inference(forward_demodulation,[status(thm)],[f9,f37]) ).
fof(f41,plain,
! [X0,X1] : multiply(X0,divide(inverse(X0),inverse(X1))) = X1,
inference(forward_demodulation,[status(thm)],[f9,f28]) ).
fof(f42,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[status(thm)],[f9,f41]) ).
fof(f43,plain,
! [X0,X1,X2] : divide(X0,divide(multiply(inverse(X1),X2),multiply(inverse(X0),X2))) = X1,
inference(forward_demodulation,[status(thm)],[f9,f31]) ).
fof(f51,plain,
! [X0,X1] : inverse(inverse(multiply(inverse(divide(X0,X0)),X1))) = X1,
inference(paramodulation,[status(thm)],[f13,f42]) ).
fof(f52,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f42,f42]) ).
fof(f54,plain,
! [X0] : inverse(inverse(inverse(inverse(X0)))) = X0,
inference(forward_demodulation,[status(thm)],[f16,f51]) ).
fof(f60,plain,
! [X0,X1] : multiply(inverse(inverse(inverse(X0))),multiply(X0,X1)) = X1,
inference(paramodulation,[status(thm)],[f54,f42]) ).
fof(f63,plain,
! [X0,X1] : multiply(X0,inverse(inverse(inverse(X1)))) = divide(X0,X1),
inference(paramodulation,[status(thm)],[f54,f9]) ).
fof(f64,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f52,f60]) ).
fof(f81,plain,
! [X0,X1] : inverse(multiply(inverse(X0),X0)) = divide(X1,X1),
inference(paramodulation,[status(thm)],[f12,f38]) ).
fof(f111,plain,
! [X0,X1] : divide(X0,X0) = divide(X1,X1),
inference(paramodulation,[status(thm)],[f81,f81]) ).
fof(f144,plain,
! [X0,X1] : multiply(inverse(X0),X0) = divide(X1,X1),
inference(paramodulation,[status(thm)],[f9,f111]) ).
fof(f221,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f9,f144]) ).
fof(f230,plain,
! [X0,X1] : multiply(X0,divide(X1,X1)) = X0,
inference(paramodulation,[status(thm)],[f144,f42]) ).
fof(f247,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2 ),
inference(backward_subsumption_resolution,[status(thm)],[f25,f221]) ).
fof(f251,plain,
! [X0,X1] : multiply(X0,divide(X1,X1)) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f52,f230]) ).
fof(f273,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(backward_demodulation,[status(thm)],[f295,f247]) ).
fof(f287,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,X1),
inference(backward_demodulation,[status(thm)],[f295,f63]) ).
fof(f292,plain,
! [X0,X1,X2,X3] : divide(X0,divide(X1,divide(inverse(X0),divide(divide(inverse(X1),X2),divide(X3,X2))))) = X3,
inference(backward_demodulation,[status(thm)],[f295,f30]) ).
fof(f295,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f230,f251]) ).
fof(f302,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(trivial_equality_resolution,[status(thm)],[f273]) ).
fof(f338,plain,
! [X0,X1,X2] : divide(X0,divide(inverse(X1),multiply(inverse(X0),divide(X2,X2)))) = X1,
inference(paramodulation,[status(thm)],[f230,f43]) ).
fof(f359,plain,
! [X0,X1] : divide(X0,divide(inverse(X1),inverse(X0))) = X1,
inference(forward_demodulation,[status(thm)],[f230,f338]) ).
fof(f360,plain,
! [X0,X1] : divide(X0,multiply(inverse(X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f9,f359]) ).
fof(f486,plain,
! [X0,X1] : divide(multiply(X0,X1),X1) = X0,
inference(paramodulation,[status(thm)],[f64,f360]) ).
fof(f492,plain,
! [X0,X1] : divide(X0,multiply(X1,X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f295,f360]) ).
fof(f518,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X1)),X1) = X0,
inference(paramodulation,[status(thm)],[f9,f486]) ).
fof(f529,plain,
! [X0,X1] : multiply(divide(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f287,f518]) ).
fof(f591,plain,
! [X0,X1] : divide(X0,X1) = inverse(divide(X1,X0)),
inference(paramodulation,[status(thm)],[f529,f492]) ).
fof(f644,plain,
! [X0,X1] : divide(inverse(X0),X1) = inverse(multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f9,f591]) ).
fof(f801,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = divide(X0,divide(inverse(X2),X1)),
inference(paramodulation,[status(thm)],[f644,f9]) ).
fof(f818,plain,
! [X0,X1,X2,X3] : divide(X0,multiply(X1,multiply(divide(divide(inverse(X1),X2),divide(X3,X2)),X0))) = X3,
inference(backward_demodulation,[status(thm)],[f801,f292]) ).
fof(f1292,plain,
! [X0,X1,X2,X3] : inverse(multiply(X0,multiply(divide(divide(inverse(X0),X1),divide(X2,X1)),multiply(inverse(X3),X3)))) = X2,
inference(paramodulation,[status(thm)],[f15,f818]) ).
fof(f1343,plain,
! [X0,X1,X2,X3] : divide(inverse(multiply(divide(divide(inverse(X0),X1),divide(X2,X1)),multiply(inverse(X3),X3))),X0) = X2,
inference(forward_demodulation,[status(thm)],[f644,f1292]) ).
fof(f1344,plain,
! [X0,X1,X2,X3] : divide(divide(inverse(multiply(inverse(X0),X0)),divide(divide(inverse(X1),X2),divide(X3,X2))),X1) = X3,
inference(forward_demodulation,[status(thm)],[f644,f1343]) ).
fof(f1345,plain,
! [X0,X1,X2,X3] : divide(divide(divide(inverse(X0),inverse(X0)),divide(divide(inverse(X1),X2),divide(X3,X2))),X1) = X3,
inference(forward_demodulation,[status(thm)],[f644,f1344]) ).
fof(f1346,plain,
! [X0,X1,X2] : divide(inverse(divide(divide(inverse(X0),X1),divide(X2,X1))),X0) = X2,
inference(forward_demodulation,[status(thm)],[f7,f1345]) ).
fof(f1347,plain,
! [X0,X1,X2] : divide(divide(divide(X0,X1),divide(inverse(X2),X1)),X2) = X0,
inference(forward_demodulation,[status(thm)],[f591,f1346]) ).
fof(f1348,plain,
! [X0,X1,X2] : divide(multiply(divide(X0,X1),multiply(X1,X2)),X2) = X0,
inference(forward_demodulation,[status(thm)],[f801,f1347]) ).
fof(f1586,plain,
! [X0,X1,X2] : divide(multiply(X0,multiply(X1,X2)),X2) = multiply(X0,X1),
inference(paramodulation,[status(thm)],[f486,f1348]) ).
fof(f1866,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f1586,f529]) ).
fof(f1959,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f1866,f302]) ).
fof(f2049,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1959]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP064-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.54 % Computer : n006.cluster.edu
% 0.09/5.54 % Model : x86_64 x86_64
% 0.09/5.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.54 % Memory : 8046.5625MB
% 0.09/5.54 % OS : Linux 6.8.0-71-generic
% 0.09/5.54 % CPULimit : 300
% 0.09/5.54 % WCLimit : 300
% 0.09/5.54 % DateTime : Sun Sep 20 19:56:03 UTC 2026
% 0.09/5.54 % CPUTime :
% 0.09/5.55 % Drodi V4.1.1
% 0.13/5.61 % Refutation found
% 0.13/5.61 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/5.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.64 % Elapsed time: 0.081259 seconds
% 0.13/5.64 % CPU time: 0.384967 seconds
% 0.13/5.64 % Total memory used: 72.958 MB
% 0.13/5.64 % Net memory used: 72.260 MB
%------------------------------------------------------------------------------