%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP062-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 12:32:25 PM UTC 2026
% Result : Unsatisfiable 135.59s 27.63s
% Output : CNFRefutation 132.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 5
% Syntax : Number of formulae : 80 ( 67 unt; 3 def)
% Number of atoms : 96 ( 76 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 13 ~; 13 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 231 ( 231 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z,U] : inverse(multiply(X,multiply(Y,multiply(multiply(Z,inverse(Z)),inverse(multiply(U,multiply(X,Y))))))) = U,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,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(f3,plain,
! [X0,X1,X2,X3] : inverse(multiply(X0,multiply(X1,multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,multiply(X0,X1))))))) = X3,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,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)],[f2]) ).
fof(f5,definition,
( sQ0_spl
<=> multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f7,plain,
( sQ0_spl
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(component_clause,[status(thm)],[f5]) ).
fof(f8,definition,
( sQ1_spl
<=> multiply(multiply(inverse(b2),b2),a2) = a2 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f10,plain,
( sQ1_spl
| multiply(multiply(inverse(b2),b2),a2) != a2 ),
inference(component_clause,[status(thm)],[f8]) ).
fof(f11,definition,
( sQ2_spl
<=> multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f13,plain,
( sQ2_spl
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(component_clause,[status(thm)],[f11]) ).
fof(f14,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f4,f5,f8,f11]) ).
fof(f15,plain,
! [X0,X1,X2,X3,X4,X5,X6] : inverse(multiply(X0,multiply(X1,multiply(multiply(multiply(X2,multiply(X3,multiply(multiply(X4,inverse(X4)),inverse(multiply(X5,multiply(X2,X3)))))),X5),inverse(multiply(X6,multiply(X0,X1))))))) = X6,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f16,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(X0,multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(X3,X0)))),multiply(multiply(X4,inverse(X4)),X2)))) = X3,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f19,plain,
! [X0,X1,X2,X3,X4,X5,X6] : inverse(multiply(multiply(multiply(X0,inverse(X0)),X1),multiply(multiply(multiply(X2,inverse(X2)),X3),multiply(multiply(X4,inverse(X4)),X5)))) = multiply(multiply(X6,inverse(X6)),inverse(multiply(X1,multiply(X3,X5)))),
inference(paramodulation,[status(thm)],[f16,f16]) ).
fof(f20,plain,
! [X0,X1,X2,X3,X4,X5] : inverse(multiply(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,multiply(X2,X3)))),multiply(multiply(multiply(X4,inverse(X4)),X1),multiply(multiply(X5,inverse(X5)),X2)))) = X3,
inference(paramodulation,[status(thm)],[f3,f16]) ).
fof(f100,plain,
! [X0,X1,X2,X3] : X0 = multiply(multiply(X1,inverse(X1)),inverse(multiply(inverse(multiply(X2,multiply(X3,X0))),multiply(X2,X3)))),
inference(paramodulation,[status(thm)],[f20,f19]) ).
fof(f183,plain,
! [X0,X1,X2,X3,X4,X5,X6] : multiply(multiply(X0,inverse(X0)),X1) = multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X5,multiply(X1,X3)))),multiply(multiply(X6,inverse(X6)),X5))))),
inference(paramodulation,[status(thm)],[f20,f100]) ).
fof(f215,plain,
! [X0,X1,X2] : multiply(multiply(X0,inverse(X0)),X1) = multiply(multiply(X2,inverse(X2)),X1),
inference(forward_demodulation,[status(thm)],[f16,f183]) ).
fof(f290,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] : inverse(multiply(X0,multiply(X1,multiply(multiply(multiply(X2,multiply(X3,multiply(multiply(X4,inverse(X4)),inverse(multiply(X5,multiply(X2,X3)))))),X5),inverse(multiply(multiply(X6,inverse(X6)),multiply(X0,X1))))))) = multiply(X7,inverse(X7)),
inference(paramodulation,[status(thm)],[f215,f15]) ).
fof(f367,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f15,f290]) ).
fof(f384,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(X0,multiply(X1,multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,multiply(X0,X1)))))),X3) = multiply(X4,inverse(X4)),
inference(paramodulation,[status(thm)],[f3,f367]) ).
fof(f424,plain,
! [X0,X1,X2,X3] : X0 = multiply(multiply(X1,inverse(X1)),inverse(multiply(inverse(multiply(X2,multiply(inverse(X2),X0))),multiply(X3,inverse(X3))))),
inference(paramodulation,[status(thm)],[f367,f100]) ).
fof(f425,plain,
! [X0,X1,X2,X3] : inverse(X0) = multiply(multiply(X1,inverse(X1)),inverse(multiply(inverse(multiply(X2,multiply(X3,inverse(X3)))),multiply(X2,X0)))),
inference(paramodulation,[status(thm)],[f367,f100]) ).
fof(f1193,plain,
! [X0,X1,X2,X3] : inverse(multiply(inverse(X0),multiply(X1,multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,multiply(inverse(X3),X1))))))) = X0,
inference(paramodulation,[status(thm)],[f424,f16]) ).
fof(f1194,plain,
! [X0,X1,X2] : inverse(multiply(X0,multiply(inverse(X0),X1))) = inverse(multiply(X2,multiply(inverse(X2),X1))),
inference(paramodulation,[status(thm)],[f424,f3]) ).
fof(f1232,plain,
! [X0,X1,X2] : inverse(multiply(X0,multiply(X1,inverse(X1)))) = inverse(multiply(X2,multiply(inverse(X2),inverse(inverse(X0))))),
inference(paramodulation,[status(thm)],[f367,f1194]) ).
fof(f4196,plain,
! [X0,X1,X2,X3,X4,X5] : inverse(multiply(inverse(multiply(X0,multiply(X1,inverse(X1)))),multiply(X2,multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,multiply(inverse(X4),X2))))))) = multiply(X5,multiply(inverse(X5),inverse(inverse(X0)))),
inference(paramodulation,[status(thm)],[f1232,f1193]) ).
fof(f4197,plain,
! [X0,X1,X2,X3,X4,X5] : inverse(multiply(inverse(multiply(X0,multiply(inverse(X0),X1))),multiply(X2,multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,multiply(inverse(X4),X2))))))) = multiply(X5,multiply(inverse(X5),X1)),
inference(paramodulation,[status(thm)],[f1194,f1193]) ).
fof(f4219,plain,
! [X0,X1,X2] : inverse(multiply(inverse(X0),multiply(inverse(inverse(inverse(multiply(X1,multiply(inverse(X1),X2))))),X2))) = X0,
inference(paramodulation,[status(thm)],[f424,f1193]) ).
fof(f4403,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,inverse(X1))) = multiply(X2,multiply(inverse(X2),inverse(inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f1193,f4196]) ).
fof(f4404,plain,
! [X0,X1,X2] : multiply(X0,multiply(inverse(X0),X1)) = multiply(X2,multiply(inverse(X2),X1)),
inference(forward_demodulation,[status(thm)],[f1193,f4197]) ).
fof(f4415,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,multiply(inverse(X1),X2))) = multiply(X3,multiply(inverse(X3),multiply(inverse(inverse(X0)),X2))),
inference(paramodulation,[status(thm)],[f4404,f4404]) ).
fof(f6634,plain,
! [X0,X1,X2,X3] : X0 = multiply(multiply(X1,inverse(X1)),multiply(inverse(inverse(inverse(multiply(X2,multiply(inverse(X2),X3))))),multiply(X3,X0))),
inference(paramodulation,[status(thm)],[f4219,f100]) ).
fof(f8538,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,multiply(inverse(X1),X2))) = multiply(X0,multiply(X3,multiply(inverse(X3),X2))),
inference(paramodulation,[status(thm)],[f4415,f4415]) ).
fof(f19763,plain,
! [X0,X1,X2,X3,X4,X5,X6] : multiply(X0,multiply(inverse(X0),multiply(inverse(inverse(multiply(X1,multiply(X2,multiply(multiply(X3,inverse(X3)),inverse(multiply(multiply(X4,multiply(inverse(X4),X5)),multiply(X1,X2)))))))),X5))) = multiply(X6,inverse(X6)),
inference(paramodulation,[status(thm)],[f4415,f384]) ).
fof(f19768,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(X0,multiply(inverse(X0),inverse(inverse(multiply(X1,multiply(X2,multiply(multiply(X3,inverse(X3)),inverse(multiply(multiply(X4,inverse(X4)),multiply(X1,X2)))))))))) = multiply(X5,inverse(X5)),
inference(paramodulation,[status(thm)],[f4403,f384]) ).
fof(f20451,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(inverse(X0),multiply(inverse(multiply(X1,multiply(inverse(X1),X2))),X2))) = multiply(X3,inverse(X3)),
inference(forward_demodulation,[status(thm)],[f3,f19763]) ).
fof(f20452,plain,
! [X0,X1,X2] : multiply(X0,multiply(inverse(X0),inverse(multiply(X1,inverse(X1))))) = multiply(X2,inverse(X2)),
inference(forward_demodulation,[status(thm)],[f3,f19768]) ).
fof(f20813,plain,
! [X0,X1,X2,X3,X4] : multiply(inverse(X0),inverse(multiply(X1,inverse(X1)))) = multiply(multiply(X2,inverse(X2)),inverse(multiply(inverse(multiply(X3,multiply(X4,inverse(X4)))),multiply(X3,X0)))),
inference(paramodulation,[status(thm)],[f20452,f100]) ).
fof(f21099,plain,
! [X0,X1] : multiply(inverse(X0),inverse(multiply(X1,inverse(X1)))) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f425,f20813]) ).
fof(f21101,plain,
! [X0,X1,X2,X3] : multiply(X0,inverse(multiply(X1,inverse(X1)))) = inverse(multiply(inverse(X0),multiply(inverse(inverse(inverse(multiply(X2,multiply(inverse(X2),X3))))),X3))),
inference(paramodulation,[status(thm)],[f4219,f21099]) ).
fof(f21200,plain,
! [X0,X1,X2] : inverse(multiply(inverse(X0),inverse(inverse(inverse(multiply(X1,multiply(inverse(X1),inverse(multiply(X2,inverse(X2)))))))))) = X0,
inference(paramodulation,[status(thm)],[f21099,f4219]) ).
fof(f21276,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,inverse(X1)))) = X0,
inference(forward_demodulation,[status(thm)],[f4219,f21101]) ).
fof(f21313,plain,
! [X0,X1] : inverse(multiply(inverse(X0),inverse(inverse(inverse(multiply(X1,inverse(X1))))))) = X0,
inference(forward_demodulation,[status(thm)],[f21099,f21200]) ).
fof(f21405,plain,
! [X0,X1,X2,X3] : inverse(multiply(inverse(X0),multiply(inverse(multiply(X1,inverse(X1))),multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,inverse(X3))))))) = X0,
inference(paramodulation,[status(thm)],[f21276,f1193]) ).
fof(f21675,plain,
! [X0,X1,X2] : inverse(multiply(inverse(X0),multiply(inverse(multiply(X1,inverse(X1))),multiply(X2,inverse(X2))))) = X0,
inference(forward_demodulation,[status(thm)],[f21276,f21405]) ).
fof(f24407,plain,
! [X0,X1,X2] : inverse(multiply(inverse(X0),multiply(X1,multiply(inverse(X1),inverse(inverse(inverse(multiply(X2,inverse(X2))))))))) = X0,
inference(paramodulation,[status(thm)],[f8538,f21675]) ).
fof(f29964,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(inverse(X0),multiply(inverse(multiply(X1,multiply(inverse(X1),X2))),X2)) = multiply(multiply(X3,inverse(X3)),inverse(multiply(inverse(multiply(X4,multiply(X5,inverse(X5)))),multiply(X4,X0)))),
inference(paramodulation,[status(thm)],[f20451,f100]) ).
fof(f30385,plain,
! [X0,X1,X2] : multiply(inverse(X0),multiply(inverse(multiply(X1,multiply(inverse(X1),X2))),X2)) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f425,f29964]) ).
fof(f30397,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(inverse(multiply(X1,multiply(inverse(X1),X2))),X2)) = inverse(multiply(inverse(X0),inverse(inverse(inverse(multiply(X3,inverse(X3))))))),
inference(paramodulation,[status(thm)],[f21313,f30385]) ).
fof(f30739,plain,
! [X0,X1,X2] : multiply(X0,multiply(inverse(multiply(X1,multiply(inverse(X1),X2))),X2)) = X0,
inference(forward_demodulation,[status(thm)],[f21313,f30397]) ).
fof(f48955,plain,
! [X0,X1,X2,X3] : inverse(multiply(inverse(X0),inverse(inverse(inverse(multiply(X1,inverse(X1))))))) = multiply(multiply(X2,inverse(X2)),multiply(X0,multiply(X3,inverse(X3)))),
inference(paramodulation,[status(thm)],[f24407,f425]) ).
fof(f49316,plain,
! [X0,X1,X2] : X0 = multiply(multiply(X1,inverse(X1)),multiply(X0,multiply(X2,inverse(X2)))),
inference(forward_demodulation,[status(thm)],[f21313,f48955]) ).
fof(f49317,plain,
! [X0,X1] : inverse(inverse(inverse(multiply(X0,multiply(inverse(X0),X1))))) = inverse(X1),
inference(paramodulation,[status(thm)],[f6634,f49316]) ).
fof(f49942,plain,
! [X0,X1] : inverse(multiply(inverse(X0),multiply(inverse(X1),X1))) = X0,
inference(backward_demodulation,[status(thm)],[f49317,f4219]) ).
fof(f50496,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X1))) = X0,
inference(paramodulation,[status(thm)],[f49942,f30739]) ).
fof(f50850,plain,
! [X0,X1] : inverse(multiply(inverse(X0),inverse(multiply(X1,inverse(X1))))) = X0,
inference(backward_demodulation,[status(thm)],[f50496,f21675]) ).
fof(f50854,plain,
! [X0,X1] : X0 = multiply(multiply(X1,inverse(X1)),X0),
inference(backward_demodulation,[status(thm)],[f50496,f49316]) ).
fof(f51426,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f21276,f50850]) ).
fof(f51615,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X1),X1)) = X0,
inference(paramodulation,[status(thm)],[f51426,f50496]) ).
fof(f54101,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(inverse(multiply(X0,multiply(X1,X2))),multiply(multiply(multiply(X3,inverse(X3)),X0),multiply(multiply(X4,inverse(X4)),X1)))) = X2,
inference(backward_demodulation,[status(thm)],[f50854,f20]) ).
fof(f54103,plain,
! [X0,X1,X2] : inverse(multiply(X0,multiply(X1,inverse(multiply(X2,multiply(X0,X1)))))) = X2,
inference(backward_demodulation,[status(thm)],[f50854,f3]) ).
fof(f54117,plain,
! [X0,X1] : X0 = multiply(inverse(multiply(X1,inverse(X1))),X0),
inference(paramodulation,[status(thm)],[f50854,f50854]) ).
fof(f54123,plain,
! [X0,X1] : X0 = multiply(multiply(inverse(X1),X1),X0),
inference(paramodulation,[status(thm)],[f51426,f50854]) ).
fof(f54259,plain,
! [X0,X1,X2,X3] : inverse(multiply(inverse(multiply(X0,multiply(X1,X2))),multiply(X0,multiply(multiply(X3,inverse(X3)),X1)))) = X2,
inference(forward_demodulation,[status(thm)],[f50854,f54101]) ).
fof(f54260,plain,
! [X0,X1,X2] : inverse(multiply(inverse(multiply(X0,multiply(X1,X2))),multiply(X0,X1))) = X2,
inference(forward_demodulation,[status(thm)],[f50854,f54259]) ).
fof(f54335,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f51615,f54123]) ).
fof(f54591,plain,
! [X0,X1,X2] : inverse(multiply(X0,inverse(multiply(X1,multiply(inverse(multiply(X2,inverse(X2))),X0))))) = X1,
inference(paramodulation,[status(thm)],[f54117,f54103]) ).
fof(f54638,plain,
! [X0,X1] : inverse(multiply(X0,inverse(multiply(X1,X0)))) = X1,
inference(forward_demodulation,[status(thm)],[f54117,f54591]) ).
fof(f55756,plain,
! [X0,X1] : inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f54638,f51426]) ).
fof(f59979,plain,
! [X0,X1,X2] : inverse(inverse(multiply(X0,multiply(X1,X2)))) = multiply(multiply(X0,X1),X2),
inference(paramodulation,[status(thm)],[f54260,f55756]) ).
fof(f60103,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f51426,f59979]) ).
fof(f63729,plain,
( sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f13,f60103]) ).
fof(f64165,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f63729]) ).
fof(f64281,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7,f54335]) ).
fof(f64282,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f64281]) ).
fof(f64283,plain,
( sQ1_spl
| a2 != a2 ),
inference(forward_demodulation,[status(thm)],[f54123,f10]) ).
fof(f64284,plain,
( sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f64283]) ).
fof(f64285,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f64284]) ).
fof(f64286,plain,
$false,
inference(sat_refutation,[status(thm)],[f14,f64165,f64282,f64285]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP062-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/10.47 % Computer : n013.cluster.edu
% 0.20/10.47 % Model : x86_64 x86_64
% 0.20/10.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/10.47 % Memory : 8046.5625MB
% 0.20/10.47 % OS : Linux 6.8.0-71-generic
% 0.20/10.47 % CPULimit : 300
% 0.20/10.47 % WCLimit : 300
% 0.20/10.47 % DateTime : Sun Sep 20 19:55:47 UTC 2026
% 0.20/10.47 % CPUTime :
% 0.20/10.48 % Drodi V4.1.1
% 135.59/27.63 % Refutation found
% 135.59/27.63 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 135.59/27.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 132.56/27.74 % Elapsed time: 17.246028 seconds
% 132.56/27.74 % CPU time: 136.294353 seconds
% 132.56/27.74 % Total memory used: 646.067 MB
% 132.56/27.74 % Net memory used: 640.714 MB
%------------------------------------------------------------------------------