%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP479-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 12:34:29 PM UTC 2026
% Result : Unsatisfiable 5.61s 1.13s
% Output : CNFRefutation 5.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 6
% Syntax : Number of formulae : 90 ( 90 unt; 3 def)
% Number of atoms : 90 ( 89 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 161 ( 161 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C,D] : divide(inverse(divide(divide(divide(A,A),B),divide(C,divide(B,D)))),D) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = divide(A,inverse(B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(divide(divide(X0,X0),X1),divide(X2,divide(X1,X3)))),X3) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f6,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f7,definition,
sF2_fnc = inverse(b2),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f8,definition,
sF1_fnc = multiply(sF2_fnc,b2),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f9,definition,
sF0_fnc = multiply(sF1_fnc,a2),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f10,plain,
sF0_fnc != a2,
inference(definition_folding,[],[f6,f9,f8,f7]) ).
fof(f11,plain,
! [X0] : multiply(X0,b2) = divide(X0,sF2_fnc),
inference(paramodulation,[status(thm)],[f7,f5]) ).
fof(f12,plain,
sF1_fnc = divide(sF2_fnc,sF2_fnc),
inference(backward_demodulation,[status(thm)],[f11,f8]) ).
fof(f15,plain,
! [X0,X1,X2] : divide(inverse(divide(divide(sF1_fnc,X0),divide(X1,divide(X0,X2)))),X2) = X1,
inference(paramodulation,[status(thm)],[f12,f4]) ).
fof(f17,plain,
! [X0,X1,X2,X3,X4,X5] : divide(inverse(divide(divide(divide(X0,X0),X1),X2)),X3) = inverse(divide(divide(divide(X4,X4),X5),divide(X2,divide(X5,divide(X1,X3))))),
inference(paramodulation,[status(thm)],[f4,f4]) ).
fof(f19,plain,
! [X0,X1] : divide(inverse(divide(divide(divide(X0,X0),sF2_fnc),divide(X1,sF1_fnc))),sF2_fnc) = X1,
inference(paramodulation,[status(thm)],[f12,f4]) ).
fof(f27,plain,
! [X0,X1,X2] : divide(inverse(divide(multiply(sF1_fnc,X0),divide(X1,divide(inverse(X0),X2)))),X2) = X1,
inference(paramodulation,[status(thm)],[f5,f15]) ).
fof(f28,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(divide(sF1_fnc,X0),X1)),X2) = inverse(divide(divide(sF1_fnc,X3),divide(X1,divide(X3,divide(X0,X2))))),
inference(paramodulation,[status(thm)],[f15,f15]) ).
fof(f29,plain,
! [X0,X1,X2,X3,X4] : divide(inverse(divide(divide(sF1_fnc,X0),X1)),X2) = inverse(divide(divide(divide(X3,X3),X4),divide(X1,divide(X4,divide(X0,X2))))),
inference(paramodulation,[status(thm)],[f4,f15]) ).
fof(f166,plain,
! [X0,X1] : divide(inverse(divide(sF0_fnc,divide(X0,divide(inverse(a2),X1)))),X1) = X0,
inference(paramodulation,[status(thm)],[f9,f27]) ).
fof(f204,plain,
! [X0,X1] : multiply(inverse(divide(sF0_fnc,divide(X0,divide(inverse(a2),inverse(X1))))),X1) = X0,
inference(paramodulation,[status(thm)],[f5,f166]) ).
fof(f228,plain,
! [X0,X1] : multiply(inverse(divide(sF0_fnc,divide(X0,multiply(inverse(a2),X1)))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f5,f204]) ).
fof(f359,plain,
! [X0,X1,X2] : X0 = inverse(divide(divide(divide(X1,X1),X2),divide(divide(X0,sF1_fnc),divide(X2,divide(sF2_fnc,sF2_fnc))))),
inference(paramodulation,[status(thm)],[f19,f17]) ).
fof(f428,plain,
! [X0,X1,X2,X3] : divide(divide(inverse(divide(divide(divide(X0,X0),X1),X2)),X3),divide(X1,X3)) = X2,
inference(paramodulation,[status(thm)],[f17,f4]) ).
fof(f436,plain,
! [X0,X1,X2] : X0 = inverse(divide(divide(divide(X1,X1),X2),divide(divide(X0,sF1_fnc),divide(X2,sF1_fnc)))),
inference(forward_demodulation,[status(thm)],[f12,f359]) ).
fof(f625,plain,
! [X0,X1,X2] : divide(divide(inverse(divide(divide(sF1_fnc,X0),X1)),X2),divide(X0,X2)) = X1,
inference(paramodulation,[status(thm)],[f28,f15]) ).
fof(f665,plain,
! [X0,X1,X2] : divide(multiply(inverse(divide(divide(sF1_fnc,X0),X1)),X2),divide(X0,inverse(X2))) = X1,
inference(paramodulation,[status(thm)],[f5,f625]) ).
fof(f667,plain,
! [X0,X1,X2] : divide(divide(inverse(multiply(divide(sF1_fnc,X0),X1)),X2),divide(X0,X2)) = inverse(X1),
inference(paramodulation,[status(thm)],[f5,f625]) ).
fof(f668,plain,
! [X0,X1,X2] : divide(divide(inverse(divide(multiply(sF1_fnc,X0),X1)),X2),divide(inverse(X0),X2)) = X1,
inference(paramodulation,[status(thm)],[f5,f625]) ).
fof(f691,plain,
! [X0,X1,X2,X3,X4,X5] : divide(inverse(divide(divide(divide(X0,X0),X1),divide(inverse(divide(divide(sF1_fnc,X2),X3)),divide(X1,X4)))),X4) = inverse(divide(divide(divide(X5,X5),X2),X3)),
inference(paramodulation,[status(thm)],[f625,f17]) ).
fof(f705,plain,
! [X0,X1,X2] : divide(multiply(inverse(divide(divide(sF1_fnc,X0),X1)),X2),multiply(X0,X2)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f665]) ).
fof(f725,plain,
! [X0,X1,X2] : inverse(divide(divide(sF1_fnc,X0),X1)) = inverse(divide(divide(divide(X2,X2),X0),X1)),
inference(forward_demodulation,[status(thm)],[f4,f691]) ).
fof(f740,plain,
! [X0] : divide(multiply(inverse(divide(divide(sF1_fnc,sF1_fnc),X0)),a2),sF0_fnc) = X0,
inference(paramodulation,[status(thm)],[f9,f705]) ).
fof(f874,plain,
! [X0,X1,X2,X3] : divide(divide(inverse(divide(X0,X1)),X2),divide(divide(X3,inverse(divide(divide(sF1_fnc,X3),X0))),X2)) = X1,
inference(paramodulation,[status(thm)],[f625,f428]) ).
fof(f919,plain,
! [X0,X1,X2,X3] : divide(divide(inverse(divide(X0,X1)),X2),divide(multiply(X3,divide(divide(sF1_fnc,X3),X0)),X2)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f874]) ).
fof(f967,plain,
! [X0,X1,X2,X3,X4] : divide(inverse(divide(divide(sF1_fnc,X0),divide(inverse(multiply(divide(sF1_fnc,X1),X2)),divide(X0,X3)))),X3) = inverse(divide(divide(divide(X4,X4),X1),inverse(X2))),
inference(paramodulation,[status(thm)],[f667,f29]) ).
fof(f1007,plain,
! [X0,X1,X2] : inverse(multiply(divide(sF1_fnc,X0),X1)) = inverse(divide(divide(divide(X2,X2),X0),inverse(X1))),
inference(forward_demodulation,[status(thm)],[f15,f967]) ).
fof(f1008,plain,
! [X0,X1,X2] : inverse(multiply(divide(sF1_fnc,X0),X1)) = inverse(multiply(divide(divide(X2,X2),X0),X1)),
inference(forward_demodulation,[status(thm)],[f5,f1007]) ).
fof(f1027,plain,
! [X0,X1] : divide(divide(inverse(divide(sF0_fnc,X0)),X1),divide(inverse(a2),X1)) = X0,
inference(paramodulation,[status(thm)],[f9,f668]) ).
fof(f1097,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(divide(sF1_fnc,X0),divide(inverse(divide(sF0_fnc,X1)),divide(X0,X2)))),X2) = inverse(divide(divide(divide(X3,X3),inverse(a2)),X1)),
inference(paramodulation,[status(thm)],[f1027,f29]) ).
fof(f1122,plain,
! [X0,X1] : inverse(divide(sF0_fnc,X0)) = inverse(divide(divide(divide(X1,X1),inverse(a2)),X0)),
inference(forward_demodulation,[status(thm)],[f15,f1097]) ).
fof(f1123,plain,
! [X0,X1] : inverse(divide(sF0_fnc,X0)) = inverse(divide(multiply(divide(X1,X1),a2),X0)),
inference(forward_demodulation,[status(thm)],[f5,f1122]) ).
fof(f1163,plain,
! [X0,X1] : inverse(divide(sF0_fnc,X0)) = inverse(divide(multiply(multiply(inverse(X1),X1),a2),X0)),
inference(paramodulation,[status(thm)],[f5,f1123]) ).
fof(f1733,plain,
! [X0,X1,X2] : multiply(X0,divide(multiply(multiply(inverse(X1),X1),a2),X2)) = divide(X0,inverse(divide(sF0_fnc,X2))),
inference(paramodulation,[status(thm)],[f1163,f5]) ).
fof(f1739,plain,
! [X0,X1,X2] : multiply(X0,divide(multiply(multiply(inverse(X1),X1),a2),X2)) = multiply(X0,divide(sF0_fnc,X2)),
inference(forward_demodulation,[status(thm)],[f5,f1733]) ).
fof(f2148,plain,
! [X0,X1] : X0 = inverse(divide(divide(sF1_fnc,X1),divide(divide(X0,sF1_fnc),divide(X1,sF1_fnc)))),
inference(forward_demodulation,[status(thm)],[f725,f436]) ).
fof(f2171,plain,
! [X0] : divide(multiply(X0,a2),sF0_fnc) = divide(divide(X0,sF1_fnc),divide(sF1_fnc,sF1_fnc)),
inference(paramodulation,[status(thm)],[f2148,f740]) ).
fof(f2174,plain,
! [X0,X1,X2] : divide(multiply(X0,X1),multiply(X2,X1)) = divide(divide(X0,sF1_fnc),divide(X2,sF1_fnc)),
inference(paramodulation,[status(thm)],[f2148,f705]) ).
fof(f2213,plain,
! [X0] : X0 = inverse(divide(divide(sF1_fnc,sF1_fnc),divide(multiply(X0,a2),sF0_fnc))),
inference(paramodulation,[status(thm)],[f2171,f2148]) ).
fof(f2263,plain,
sF1_fnc = inverse(divide(divide(sF1_fnc,sF1_fnc),divide(sF0_fnc,sF0_fnc))),
inference(paramodulation,[status(thm)],[f9,f2213]) ).
fof(f2267,plain,
! [X0,X1] : divide(divide(X0,X1),divide(sF1_fnc,X1)) = divide(multiply(X0,a2),sF0_fnc),
inference(paramodulation,[status(thm)],[f2213,f625]) ).
fof(f2282,plain,
! [X0] : divide(divide(sF1_fnc,X0),divide(sF1_fnc,X0)) = divide(sF0_fnc,sF0_fnc),
inference(paramodulation,[status(thm)],[f2263,f625]) ).
fof(f2522,plain,
! [X0,X1] : divide(divide(inverse(divide(sF0_fnc,sF0_fnc)),X0),divide(X1,X0)) = divide(sF1_fnc,X1),
inference(paramodulation,[status(thm)],[f2282,f625]) ).
fof(f9855,plain,
! [X0] : divide(sF1_fnc,multiply(X0,divide(divide(sF1_fnc,X0),sF0_fnc))) = sF0_fnc,
inference(paramodulation,[status(thm)],[f2522,f919]) ).
fof(f10051,plain,
multiply(inverse(divide(sF0_fnc,sF0_fnc)),divide(divide(sF1_fnc,inverse(a2)),sF0_fnc)) = sF1_fnc,
inference(paramodulation,[status(thm)],[f9855,f228]) ).
fof(f10084,plain,
multiply(inverse(divide(sF0_fnc,sF0_fnc)),divide(multiply(sF1_fnc,a2),sF0_fnc)) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f5,f10051]) ).
fof(f10085,plain,
multiply(inverse(divide(sF0_fnc,sF0_fnc)),divide(sF0_fnc,sF0_fnc)) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f9,f10084]) ).
fof(f10106,plain,
! [X0] : divide(sF1_fnc,multiply(X0,divide(sF0_fnc,sF0_fnc))) = divide(divide(inverse(divide(sF0_fnc,sF0_fnc)),sF1_fnc),divide(X0,sF1_fnc)),
inference(paramodulation,[status(thm)],[f10085,f2174]) ).
fof(f10111,plain,
! [X0] : divide(sF1_fnc,multiply(X0,divide(sF0_fnc,sF0_fnc))) = divide(sF1_fnc,X0),
inference(forward_demodulation,[status(thm)],[f2522,f10106]) ).
fof(f10145,plain,
! [X0,X1,X2] : divide(divide(inverse(divide(sF1_fnc,X0)),X1),divide(multiply(X2,divide(divide(sF1_fnc,X2),sF1_fnc)),X1)) = multiply(X0,divide(sF0_fnc,sF0_fnc)),
inference(paramodulation,[status(thm)],[f10111,f919]) ).
fof(f10187,plain,
! [X0] : X0 = multiply(X0,divide(sF0_fnc,sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f919,f10145]) ).
fof(f10207,plain,
inverse(divide(sF0_fnc,sF0_fnc)) = sF1_fnc,
inference(backward_demodulation,[status(thm)],[f10187,f10085]) ).
fof(f10328,plain,
! [X0] : multiply(X0,divide(sF0_fnc,sF0_fnc)) = divide(X0,sF1_fnc),
inference(paramodulation,[status(thm)],[f10207,f5]) ).
fof(f10352,plain,
! [X0] : X0 = divide(X0,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f10187,f10328]) ).
fof(f10410,plain,
! [X0] : divide(divide(X0,sF1_fnc),sF1_fnc) = divide(multiply(X0,a2),sF0_fnc),
inference(paramodulation,[status(thm)],[f10352,f2267]) ).
fof(f10435,plain,
! [X0] : divide(divide(inverse(divide(sF0_fnc,X0)),sF1_fnc),inverse(a2)) = X0,
inference(paramodulation,[status(thm)],[f10352,f1027]) ).
fof(f10521,plain,
! [X0] : divide(X0,sF1_fnc) = divide(multiply(X0,a2),sF0_fnc),
inference(forward_demodulation,[status(thm)],[f10352,f10410]) ).
fof(f10522,plain,
! [X0] : X0 = divide(multiply(X0,a2),sF0_fnc),
inference(forward_demodulation,[status(thm)],[f10352,f10521]) ).
fof(f10543,plain,
! [X0] : multiply(divide(inverse(divide(sF0_fnc,X0)),sF1_fnc),a2) = X0,
inference(forward_demodulation,[status(thm)],[f5,f10435]) ).
fof(f10544,plain,
! [X0] : multiply(inverse(divide(sF0_fnc,X0)),a2) = X0,
inference(forward_demodulation,[status(thm)],[f10352,f10543]) ).
fof(f10634,plain,
! [X0,X1] : divide(divide(X0,X1),divide(sF1_fnc,X1)) = X0,
inference(backward_demodulation,[status(thm)],[f10522,f2267]) ).
fof(f10640,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X1),X1)) = multiply(X0,divide(sF0_fnc,sF0_fnc)),
inference(paramodulation,[status(thm)],[f10522,f1739]) ).
fof(f10673,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X1),X1)) = X0,
inference(forward_demodulation,[status(thm)],[f10187,f10640]) ).
fof(f11342,plain,
multiply(inverse(sF0_fnc),a2) = sF1_fnc,
inference(paramodulation,[status(thm)],[f10352,f10544]) ).
fof(f11363,plain,
inverse(sF0_fnc) = divide(sF1_fnc,sF0_fnc),
inference(paramodulation,[status(thm)],[f11342,f10522]) ).
fof(f11875,plain,
! [X0] : inverse(X0) = inverse(multiply(divide(sF1_fnc,sF1_fnc),X0)),
inference(paramodulation,[status(thm)],[f667,f10634]) ).
fof(f11876,plain,
! [X0] : X0 = inverse(divide(divide(sF1_fnc,sF1_fnc),X0)),
inference(paramodulation,[status(thm)],[f625,f10634]) ).
fof(f11976,plain,
! [X0] : inverse(X0) = inverse(multiply(sF1_fnc,X0)),
inference(forward_demodulation,[status(thm)],[f10352,f11875]) ).
fof(f11977,plain,
! [X0] : X0 = inverse(divide(sF1_fnc,X0)),
inference(forward_demodulation,[status(thm)],[f10352,f11876]) ).
fof(f12026,plain,
sF0_fnc = inverse(inverse(sF0_fnc)),
inference(paramodulation,[status(thm)],[f11363,f11977]) ).
fof(f12079,plain,
! [X0] : multiply(X0,multiply(sF0_fnc,inverse(sF0_fnc))) = X0,
inference(paramodulation,[status(thm)],[f12026,f10673]) ).
fof(f12099,plain,
inverse(a2) = inverse(sF0_fnc),
inference(paramodulation,[status(thm)],[f9,f11976]) ).
fof(f12150,plain,
sF0_fnc = inverse(inverse(a2)),
inference(backward_demodulation,[status(thm)],[f12099,f12026]) ).
fof(f15711,plain,
! [X0] : multiply(X0,multiply(sF0_fnc,inverse(a2))) = X0,
inference(forward_demodulation,[status(thm)],[f12099,f12079]) ).
fof(f15726,plain,
! [X0,X1] : inverse(multiply(divide(sF1_fnc,X0),multiply(sF0_fnc,inverse(a2)))) = inverse(divide(divide(X1,X1),X0)),
inference(paramodulation,[status(thm)],[f15711,f1008]) ).
fof(f15791,plain,
! [X0,X1] : inverse(divide(sF1_fnc,X0)) = inverse(divide(divide(X1,X1),X0)),
inference(forward_demodulation,[status(thm)],[f15711,f15726]) ).
fof(f15792,plain,
! [X0,X1] : X0 = inverse(divide(divide(X1,X1),X0)),
inference(forward_demodulation,[status(thm)],[f11977,f15791]) ).
fof(f15868,plain,
! [X0] : divide(sF1_fnc,X0) = inverse(X0),
inference(paramodulation,[status(thm)],[f10634,f15792]) ).
fof(f16312,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(backward_demodulation,[status(thm)],[f15868,f11977]) ).
fof(f16394,plain,
sF0_fnc = a2,
inference(backward_demodulation,[status(thm)],[f16312,f12150]) ).
fof(f16422,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f16394,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP479-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:14:55 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 5.61/1.13 % Refutation found
% 5.61/1.13 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 5.61/1.13 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.61/1.19 % Elapsed time: 0.811125 seconds
% 5.61/1.19 % CPU time: 6.183913 seconds
% 5.61/1.19 % Total memory used: 141.450 MB
% 5.61/1.19 % Net memory used: 138.117 MB
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