%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP543-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 12:34:38 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 5
% Syntax : Number of formulae : 72 ( 72 unt; 0 def)
% Number of atoms : 72 ( 71 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 134 ( 134 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = divide(A,divide(identity,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : inverse(A) = divide(identity,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : identity = divide(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : divide(divide(identity,divide(divide(divide(X0,X1),X2),X0)),X2) = X1,
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(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f16,plain,
! [X0,X1,X2] : divide(inverse(divide(divide(divide(X0,X1),X2),X0)),X2) = X1,
inference(backward_demodulation,[status(thm)],[f8,f6]) ).
fof(f17,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f18,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f9,f8]) ).
fof(f20,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f17]) ).
fof(f22,plain,
! [X0] : multiply(X0,identity) = divide(X0,identity),
inference(paramodulation,[status(thm)],[f18,f17]) ).
fof(f25,plain,
! [X0,X1,X2] : multiply(inverse(divide(divide(divide(X0,X1),inverse(X2)),X0)),X2) = X1,
inference(paramodulation,[status(thm)],[f17,f16]) ).
fof(f26,plain,
! [X0,X1,X2] : divide(inverse(multiply(divide(divide(inverse(X0),X1),X2),X0)),X2) = X1,
inference(paramodulation,[status(thm)],[f17,f16]) ).
fof(f28,plain,
! [X0,X1] : divide(inverse(divide(identity,X0)),divide(X0,X1)) = X1,
inference(paramodulation,[status(thm)],[f9,f16]) ).
fof(f34,plain,
! [X0,X1,X2] : multiply(inverse(divide(multiply(divide(X0,X1),X2),X0)),X2) = X1,
inference(forward_demodulation,[status(thm)],[f17,f25]) ).
fof(f36,plain,
! [X0,X1] : divide(inverse(inverse(X0)),divide(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f28]) ).
fof(f37,plain,
! [X0,X1] : divide(multiply(identity,X0),divide(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f20,f36]) ).
fof(f53,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,multiply(identity,X1)),
inference(paramodulation,[status(thm)],[f20,f17]) ).
fof(f68,plain,
! [X0] : divide(divide(identity,identity),divide(identity,X0)) = X0,
inference(paramodulation,[status(thm)],[f22,f37]) ).
fof(f72,plain,
! [X0,X1] : divide(multiply(identity,X0),multiply(X0,X1)) = inverse(X1),
inference(paramodulation,[status(thm)],[f17,f37]) ).
fof(f73,plain,
! [X0] : divide(multiply(identity,X0),identity) = X0,
inference(paramodulation,[status(thm)],[f9,f37]) ).
fof(f75,plain,
! [X0] : divide(inverse(identity),divide(identity,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f68]) ).
fof(f76,plain,
! [X0] : divide(identity,divide(identity,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f18,f75]) ).
fof(f77,plain,
! [X0] : inverse(divide(identity,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f76]) ).
fof(f78,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f77]) ).
fof(f79,plain,
! [X0,X1] : divide(X0,divide(X0,X1)) = X1,
inference(backward_demodulation,[status(thm)],[f85,f37]) ).
fof(f84,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,X1),
inference(backward_demodulation,[status(thm)],[f85,f53]) ).
fof(f85,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[status(thm)],[f20,f78]) ).
fof(f92,plain,
! [X0,X1] : divide(X0,multiply(X0,X1)) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f85,f72]) ).
fof(f95,plain,
! [X0] : divide(X0,identity) = X0,
inference(forward_demodulation,[status(thm)],[f85,f73]) ).
fof(f109,plain,
! [X0] : inverse(divide(identity,X0)) = X0,
inference(paramodulation,[status(thm)],[f8,f79]) ).
fof(f116,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f109]) ).
fof(f129,plain,
! [X0,X1] : multiply(inverse(multiply(divide(identity,X0),X1)),X1) = X0,
inference(paramodulation,[status(thm)],[f95,f34]) ).
fof(f133,plain,
! [X0,X1,X2] : multiply(inverse(divide(multiply(X0,X1),X2)),X1) = divide(X2,X0),
inference(paramodulation,[status(thm)],[f79,f34]) ).
fof(f138,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(X0),X1)),X1) = X0,
inference(forward_demodulation,[status(thm)],[f8,f129]) ).
fof(f145,plain,
! [X0,X1] : inverse(multiply(divide(divide(inverse(X0),X1),identity),X0)) = X1,
inference(paramodulation,[status(thm)],[f95,f26]) ).
fof(f163,plain,
! [X0,X1] : inverse(multiply(divide(inverse(X0),X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f95,f145]) ).
fof(f206,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),X1) = inverse(X0),
inference(paramodulation,[status(thm)],[f116,f138]) ).
fof(f221,plain,
! [X0,X1] : divide(inverse(multiply(X0,inverse(X1))),X1) = inverse(X0),
inference(paramodulation,[status(thm)],[f84,f206]) ).
fof(f231,plain,
! [X0,X1] : divide(inverse(divide(X0,X1)),X1) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f84,f221]) ).
fof(f243,plain,
! [X0,X1] : divide(inverse(inverse(X0)),multiply(X1,X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f92,f231]) ).
fof(f244,plain,
! [X0,X1] : divide(inverse(X0),divide(X1,X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f79,f231]) ).
fof(f255,plain,
! [X0,X1] : divide(X0,multiply(X1,X0)) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f116,f243]) ).
fof(f263,plain,
! [X0,X1] : divide(X0,inverse(X1)) = inverse(inverse(multiply(X1,X0))),
inference(paramodulation,[status(thm)],[f206,f255]) ).
fof(f272,plain,
! [X0,X1] : multiply(X0,X1) = inverse(inverse(multiply(X1,X0))),
inference(forward_demodulation,[status(thm)],[f17,f263]) ).
fof(f275,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f282,f10]) ).
fof(f277,plain,
! [X0,X1,X2] : multiply(X0,inverse(divide(multiply(X1,X0),X2))) = divide(X2,X1),
inference(backward_demodulation,[status(thm)],[f282,f133]) ).
fof(f281,plain,
! [X0,X1] : inverse(multiply(X0,divide(inverse(X0),X1))) = X1,
inference(backward_demodulation,[status(thm)],[f282,f163]) ).
fof(f282,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f116,f272]) ).
fof(f290,plain,
! [X0,X1,X2] : divide(X0,divide(multiply(X1,X0),X2)) = divide(X2,X1),
inference(forward_demodulation,[status(thm)],[f84,f277]) ).
fof(f295,plain,
! [X0,X1] : divide(X0,X1) = multiply(inverse(X1),X0),
inference(paramodulation,[status(thm)],[f84,f282]) ).
fof(f368,plain,
! [X0,X1] : inverse(multiply(X0,inverse(X1))) = divide(X1,X0),
inference(paramodulation,[status(thm)],[f244,f281]) ).
fof(f371,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = divide(inverse(X0),X1),
inference(paramodulation,[status(thm)],[f79,f281]) ).
fof(f388,plain,
! [X0,X1] : inverse(divide(X0,X1)) = divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f84,f368]) ).
fof(f422,plain,
! [X0,X1,X2] : divide(X0,divide(X1,X2)) = multiply(divide(X2,X1),X0),
inference(paramodulation,[status(thm)],[f388,f295]) ).
fof(f423,plain,
! [X0,X1,X2] : multiply(X0,divide(X1,X2)) = divide(X0,divide(X2,X1)),
inference(paramodulation,[status(thm)],[f388,f84]) ).
fof(f538,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = divide(X0,divide(inverse(X1),X2)),
inference(paramodulation,[status(thm)],[f371,f17]) ).
fof(f574,plain,
! [X0,X1,X2] : divide(X0,divide(X1,X2)) = divide(multiply(X2,X0),X1),
inference(paramodulation,[status(thm)],[f290,f79]) ).
fof(f801,plain,
! [X0,X1,X2] : divide(X0,divide(inverse(X1),X2)) = multiply(multiply(X2,X1),X0),
inference(paramodulation,[status(thm)],[f17,f422]) ).
fof(f830,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X2,X1),X0),
inference(forward_demodulation,[status(thm)],[f538,f801]) ).
fof(f856,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = divide(X0,divide(inverse(X2),X1)),
inference(paramodulation,[status(thm)],[f17,f423]) ).
fof(f888,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X0,multiply(X2,X1)),
inference(forward_demodulation,[status(thm)],[f538,f856]) ).
fof(f910,plain,
! [X0,X1,X2] : divide(X0,divide(inverse(X1),X2)) = multiply(multiply(X2,X0),X1),
inference(paramodulation,[status(thm)],[f17,f574]) ).
fof(f943,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X0,X2)),
inference(backward_demodulation,[status(thm)],[f945,f830]) ).
fof(f945,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f538,f910]) ).
fof(f982,plain,
multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f943,f275]) ).
fof(f984,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(forward_demodulation,[status(thm)],[f888,f982]) ).
fof(f985,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f984]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP543-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.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 20:16:28 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.44/1.63 % Elapsed time: 1.044269 seconds
% 1.44/1.63 % CPU time: 0.165933 seconds
% 1.44/1.63 % Total memory used: 6.218 MB
% 1.44/1.63 % Net memory used: 6.046 MB
%------------------------------------------------------------------------------