%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP094-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 12:32:30 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.44s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 86 ( 78 unt; 0 def)
% Number of atoms : 106 ( 105 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 51 ( 31 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 193 ( 193 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : divide(divide(identity,divide(X,Y)),divide(divide(Y,Z),X)) = Z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = divide(X,divide(identity,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : inverse(X) = divide(identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : identity = divide(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,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/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : divide(divide(identity,divide(X0,X1)),divide(divide(X1,X2),X0)) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,divide(identity,X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0] : inverse(X0) = divide(identity,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
! [X0] : identity = divide(X0,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f10,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)],[f5]) ).
fof(f11,plain,
! [X0,X1,X2] : divide(inverse(divide(X0,X1)),divide(divide(X1,X2),X0)) = X2,
inference(backward_demodulation,[status(thm)],[f8,f6]) ).
fof(f12,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f13,plain,
! [X0,X1,X2,X3] : divide(inverse(X0),divide(divide(divide(divide(X1,X0),X2),X3),inverse(divide(X2,X1)))) = X3,
inference(paramodulation,[status(thm)],[f11,f11]) ).
fof(f14,plain,
! [X0,X1] : divide(inverse(inverse(X0)),divide(divide(X0,X1),identity)) = X1,
inference(paramodulation,[status(thm)],[f8,f11]) ).
fof(f15,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(X0,inverse(divide(X1,X2)))),divide(X3,X0)) = divide(divide(X2,X3),X1),
inference(paramodulation,[status(thm)],[f11,f11]) ).
fof(f17,plain,
! [X0,X1,X2,X3] : divide(inverse(X0),multiply(divide(divide(divide(X1,X0),X2),X3),divide(X2,X1))) = X3,
inference(forward_demodulation,[status(thm)],[f12,f13]) ).
fof(f18,plain,
! [X0,X1,X2,X3] : divide(inverse(multiply(X0,divide(X1,X2))),divide(X3,X0)) = divide(divide(X2,X3),X1),
inference(forward_demodulation,[status(thm)],[f12,f15]) ).
fof(f19,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f12]) ).
fof(f24,plain,
! [X0,X1] : divide(multiply(identity,X0),divide(divide(X0,X1),identity)) = X1,
inference(backward_demodulation,[status(thm)],[f19,f14]) ).
fof(f26,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,multiply(identity,X1)),
inference(paramodulation,[status(thm)],[f19,f12]) ).
fof(f48,plain,
! [X0,X1,X2,X3,X4] : divide(inverse(X0),multiply(divide(divide(divide(divide(divide(X1,X2),X3),X0),inverse(divide(X3,X1))),X4),X2)) = X4,
inference(paramodulation,[status(thm)],[f11,f17]) ).
fof(f53,plain,
! [X0,X1,X2,X3,X4] : divide(inverse(divide(X0,inverse(X1))),divide(X2,X0)) = multiply(divide(divide(divide(X3,X1),X4),X2),divide(X4,X3)),
inference(paramodulation,[status(thm)],[f17,f11]) ).
fof(f63,plain,
! [X0,X1,X2,X3,X4] : divide(inverse(X0),multiply(divide(multiply(divide(divide(divide(X1,X2),X3),X0),divide(X3,X1)),X4),X2)) = X4,
inference(forward_demodulation,[status(thm)],[f12,f48]) ).
fof(f65,plain,
! [X0,X1,X2,X3,X4] : divide(inverse(multiply(X0,X1)),divide(X2,X0)) = multiply(divide(divide(divide(X3,X1),X4),X2),divide(X4,X3)),
inference(forward_demodulation,[status(thm)],[f12,f53]) ).
fof(f73,plain,
! [X0,X1,X2,X3] : divide(inverse(multiply(X0,multiply(X1,X2))),divide(X3,X0)) = divide(divide(inverse(X2),X3),X1),
inference(paramodulation,[status(thm)],[f12,f18]) ).
fof(f77,plain,
! [X0,X1,X2] : divide(inverse(multiply(X0,divide(X1,X2))),inverse(X0)) = divide(divide(X2,identity),X1),
inference(paramodulation,[status(thm)],[f8,f18]) ).
fof(f94,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,divide(X1,X2))),X0) = divide(divide(X2,identity),X1),
inference(forward_demodulation,[status(thm)],[f12,f77]) ).
fof(f102,plain,
identity = inverse(identity),
inference(paramodulation,[status(thm)],[f8,f9]) ).
fof(f104,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(paramodulation,[status(thm)],[f12,f9]) ).
fof(f105,plain,
! [X0,X1,X2] : divide(inverse(X0),multiply(identity,divide(X1,X2))) = divide(divide(X2,X0),X1),
inference(paramodulation,[status(thm)],[f9,f17]) ).
fof(f107,plain,
! [X0,X1] : divide(inverse(divide(divide(X0,X1),X0)),identity) = X1,
inference(paramodulation,[status(thm)],[f9,f11]) ).
fof(f111,plain,
! [X0,X1,X2] : divide(inverse(multiply(X0,divide(X1,X2))),identity) = divide(divide(X2,X0),X1),
inference(paramodulation,[status(thm)],[f9,f18]) ).
fof(f115,plain,
! [X0,X1] : divide(inverse(divide(X0,X1)),divide(identity,X0)) = X1,
inference(paramodulation,[status(thm)],[f9,f11]) ).
fof(f116,plain,
! [X0,X1] : divide(inverse(identity),divide(divide(X0,X1),X0)) = X1,
inference(paramodulation,[status(thm)],[f9,f11]) ).
fof(f117,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(backward_demodulation,[status(thm)],[f104,f10]) ).
fof(f118,plain,
! [X0,X1,X2] : multiply(inverse(X0),inverse(divide(X1,X2))) = divide(divide(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f26,f105]) ).
fof(f121,plain,
! [X0,X1] : divide(inverse(divide(X0,X1)),inverse(X0)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f115]) ).
fof(f122,plain,
! [X0,X1] : multiply(inverse(divide(X0,X1)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f12,f121]) ).
fof(f123,plain,
! [X0,X1] : divide(identity,divide(divide(X0,X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f102,f116]) ).
fof(f124,plain,
! [X0] : divide(X0,identity) = X0,
inference(backward_demodulation,[status(thm)],[f125,f107]) ).
fof(f125,plain,
! [X0,X1] : inverse(divide(divide(X0,X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f123]) ).
fof(f126,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| identity != multiply(inverse(b1),b1) ),
inference(forward_demodulation,[status(thm)],[f104,f117]) ).
fof(f127,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f104,f126]) ).
fof(f128,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2 ),
inference(trivial_equality_resolution,[status(thm)],[f127]) ).
fof(f132,plain,
! [X0,X1] : divide(multiply(identity,X0),divide(X0,X1)) = X1,
inference(backward_demodulation,[status(thm)],[f124,f24]) ).
fof(f133,plain,
! [X0,X1,X2] : inverse(multiply(X0,divide(X1,X2))) = divide(divide(X2,X0),X1),
inference(backward_demodulation,[status(thm)],[f124,f111]) ).
fof(f134,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,divide(X1,X2))),X0) = divide(X2,X1),
inference(backward_demodulation,[status(thm)],[f124,f94]) ).
fof(f138,plain,
! [X0,X1,X2,X3] : divide(divide(divide(X0,X1),X2),divide(X3,X1)) = divide(divide(X0,X3),X2),
inference(backward_demodulation,[status(thm)],[f133,f18]) ).
fof(f145,plain,
! [X0,X1,X2] : multiply(divide(divide(X0,X1),X2),X1) = divide(X0,X2),
inference(forward_demodulation,[status(thm)],[f133,f134]) ).
fof(f193,plain,
! [X0,X1,X2,X3] : multiply(inverse(X0),inverse(X1)) = multiply(divide(divide(divide(X2,X1),X3),X0),divide(X3,X2)),
inference(paramodulation,[status(thm)],[f17,f122]) ).
fof(f198,plain,
! [X0] : multiply(inverse(identity),X0) = X0,
inference(paramodulation,[status(thm)],[f9,f122]) ).
fof(f205,plain,
! [X0,X1,X2] : divide(inverse(multiply(X0,X1)),divide(X2,X0)) = multiply(inverse(X2),inverse(X1)),
inference(backward_demodulation,[status(thm)],[f193,f65]) ).
fof(f207,plain,
! [X0,X1,X2] : divide(inverse(X0),multiply(divide(multiply(inverse(X0),inverse(X1)),X2),X1)) = X2,
inference(backward_demodulation,[status(thm)],[f193,f63]) ).
fof(f211,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,X1),
inference(backward_demodulation,[status(thm)],[f222,f26]) ).
fof(f212,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(backward_demodulation,[status(thm)],[f222,f128]) ).
fof(f215,plain,
! [X0,X1] : divide(X0,divide(X0,X1)) = X1,
inference(backward_demodulation,[status(thm)],[f222,f132]) ).
fof(f222,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[status(thm)],[f102,f198]) ).
fof(f224,plain,
! [X0,X1,X2] : multiply(inverse(X0),inverse(multiply(X1,X2))) = divide(divide(inverse(X2),X0),X1),
inference(backward_demodulation,[status(thm)],[f205,f73]) ).
fof(f229,plain,
! [X0,X1,X2] : divide(inverse(X0),divide(X1,X2)) = divide(divide(X2,X0),X1),
inference(backward_demodulation,[status(thm)],[f211,f118]) ).
fof(f230,plain,
! [X0,X1,X2] : divide(inverse(X0),multiply(divide(divide(inverse(X0),X1),X2),X1)) = X2,
inference(backward_demodulation,[status(thm)],[f211,f207]) ).
fof(f237,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(trivial_equality_resolution,[status(thm)],[f212]) ).
fof(f255,plain,
! [X0,X1,X2] : divide(inverse(X0),multiply(X1,X2)) = divide(divide(inverse(X2),X0),X1),
inference(forward_demodulation,[status(thm)],[f211,f224]) ).
fof(f268,plain,
! [X0,X1] : divide(inverse(X0),divide(inverse(X0),X1)) = X1,
inference(forward_demodulation,[status(thm)],[f145,f230]) ).
fof(f269,plain,
! [X0,X1] : divide(divide(X0,X1),inverse(X1)) = X0,
inference(forward_demodulation,[status(thm)],[f229,f268]) ).
fof(f270,plain,
! [X0,X1] : multiply(divide(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f12,f269]) ).
fof(f297,plain,
! [X0,X1,X2] : divide(divide(X0,X1),divide(X2,X1)) = divide(divide(X0,X2),identity),
inference(paramodulation,[status(thm)],[f124,f138]) ).
fof(f299,plain,
! [X0,X1,X2] : divide(identity,divide(X0,X1)) = divide(divide(X2,X0),divide(X2,X1)),
inference(paramodulation,[status(thm)],[f9,f138]) ).
fof(f314,plain,
! [X0,X1,X2] : divide(divide(X0,X1),divide(X2,X1)) = divide(X0,X2),
inference(forward_demodulation,[status(thm)],[f124,f297]) ).
fof(f316,plain,
! [X0,X1,X2] : inverse(divide(X0,X1)) = divide(divide(X2,X0),divide(X2,X1)),
inference(forward_demodulation,[status(thm)],[f8,f299]) ).
fof(f335,plain,
! [X0,X1,X2,X3] : divide(divide(divide(X0,X1),X2),divide(divide(X0,X3),X2)) = divide(X3,X1),
inference(paramodulation,[status(thm)],[f138,f215]) ).
fof(f348,plain,
! [X0,X1] : inverse(divide(X0,X1)) = divide(X1,X0),
inference(backward_demodulation,[status(thm)],[f349,f316]) ).
fof(f349,plain,
! [X0,X1,X2] : divide(divide(X0,X1),divide(X0,X2)) = divide(X2,X1),
inference(forward_demodulation,[status(thm)],[f314,f335]) ).
fof(f389,plain,
! [X0,X1] : multiply(X0,divide(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f215,f270]) ).
fof(f391,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X1)) = X0,
inference(paramodulation,[status(thm)],[f12,f270]) ).
fof(f397,plain,
! [X0,X1] : divide(multiply(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f211,f391]) ).
fof(f417,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(paramodulation,[status(thm)],[f397,f389]) ).
fof(f424,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(backward_subsumption_resolution,[status(thm)],[f237,f417]) ).
fof(f661,plain,
! [X0,X1,X2] : multiply(X0,divide(X1,X2)) = divide(X0,divide(X2,X1)),
inference(paramodulation,[status(thm)],[f348,f211]) ).
fof(f1023,plain,
! [X0,X1,X2] : inverse(divide(inverse(X0),multiply(X1,X2))) = divide(X1,divide(inverse(X2),X0)),
inference(paramodulation,[status(thm)],[f255,f348]) ).
fof(f1096,plain,
! [X0,X1,X2] : divide(multiply(X0,X1),inverse(X2)) = divide(X0,divide(inverse(X1),X2)),
inference(forward_demodulation,[status(thm)],[f348,f1023]) ).
fof(f1097,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = divide(X0,divide(inverse(X1),X2)),
inference(forward_demodulation,[status(thm)],[f12,f1096]) ).
fof(f1098,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,divide(X2,inverse(X1))),
inference(forward_demodulation,[status(thm)],[f661,f1097]) ).
fof(f1099,plain,
multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f1108,f424]) ).
fof(f1108,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X2,X1)),
inference(forward_demodulation,[status(thm)],[f12,f1098]) ).
fof(f1174,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(paramodulation,[status(thm)],[f417,f1099]) ).
fof(f1176,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP094-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n020.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 19:57:47 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.44 % Refutation found
% 0.11/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.45 % Elapsed time: 0.079692 seconds
% 0.11/0.45 % CPU time: 0.448723 seconds
% 0.11/0.45 % Total memory used: 74.239 MB
% 0.11/0.45 % Net memory used: 73.261 MB
%------------------------------------------------------------------------------