%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP433-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 12:34:12 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 6
% Syntax : Number of formulae : 69 ( 69 unt; 4 def)
% Number of atoms : 69 ( 68 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 75 ( 75 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C,D] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),multiply(D,inverse(D)))) = C,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(X3,inverse(X3)))) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f5,definition,
sF1_fnc = inverse(a1),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f6,definition,
sF0_fnc = multiply(sF1_fnc,a1),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f7,definition,
sF3_fnc = inverse(b1),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f8,definition,
sF2_fnc = multiply(sF3_fnc,b1),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f9,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f4,f8,f7,f6,f5]) ).
fof(f10,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(X3,inverse(X3)))) = multiply(X4,inverse(X4)),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f15,plain,
! [X0,X1,X2] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(a1,sF1_fnc))) = X2,
inference(paramodulation,[status(thm)],[f5,f3]) ).
fof(f76,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
inference(paramodulation,[status(thm)],[f10,f10]) ).
fof(f225,plain,
! [X0] : multiply(b1,sF3_fnc) = multiply(X0,inverse(X0)),
inference(paramodulation,[status(thm)],[f7,f76]) ).
fof(f226,plain,
! [X0] : multiply(a1,sF1_fnc) = multiply(X0,inverse(X0)),
inference(paramodulation,[status(thm)],[f5,f76]) ).
fof(f242,plain,
! [X0] : multiply(X0,inverse(X0)) = multiply(b1,sF3_fnc),
inference(paramodulation,[status(thm)],[f7,f76]) ).
fof(f255,plain,
! [X0,X1,X2] : inverse(multiply(multiply(multiply(inverse(multiply(X0,inverse(X0))),X1),X2),multiply(a1,sF1_fnc))) = inverse(multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f76,f15]) ).
fof(f301,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(X3,inverse(X3)))) = multiply(b1,sF3_fnc),
inference(backward_demodulation,[status(thm)],[f225,f10]) ).
fof(f321,plain,
! [X0,X1,X2] : inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(b1,sF3_fnc))) = multiply(b1,sF3_fnc),
inference(forward_demodulation,[status(thm)],[f225,f301]) ).
fof(f326,plain,
multiply(a1,sF1_fnc) = multiply(b1,sF3_fnc),
inference(forward_demodulation,[status(thm)],[f225,f226]) ).
fof(f327,plain,
! [X0] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(a1,sF1_fnc),X0)),b1),sF3_fnc),multiply(a1,sF1_fnc))) = X0,
inference(paramodulation,[status(thm)],[f326,f15]) ).
fof(f328,plain,
! [X0] : multiply(X0,inverse(X0)) = multiply(a1,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f326,f242]) ).
fof(f354,plain,
! [X0,X1] : inverse(multiply(multiply(multiply(inverse(multiply(a1,sF1_fnc)),X0),X1),multiply(a1,sF1_fnc))) = inverse(multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f328,f255]) ).
fof(f404,plain,
! [X0,X1,X2] : inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(a1,sF1_fnc))) = multiply(b1,sF3_fnc),
inference(forward_demodulation,[status(thm)],[f326,f321]) ).
fof(f405,plain,
! [X0,X1,X2] : inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(a1,sF1_fnc))) = multiply(a1,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f326,f404]) ).
fof(f406,plain,
! [X0,X1] : inverse(multiply(multiply(inverse(multiply(multiply(X0,X1),inverse(multiply(a1,sF1_fnc)))),X0),X1)) = multiply(a1,sF1_fnc),
inference(paramodulation,[status(thm)],[f354,f405]) ).
fof(f555,plain,
! [X0] : inverse(multiply(multiply(inverse(multiply(multiply(a1,sF1_fnc),inverse(multiply(a1,sF1_fnc)))),X0),inverse(X0))) = multiply(a1,sF1_fnc),
inference(paramodulation,[status(thm)],[f328,f406]) ).
fof(f565,plain,
! [X0] : inverse(multiply(multiply(inverse(multiply(a1,sF1_fnc)),X0),inverse(X0))) = multiply(a1,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f328,f555]) ).
fof(f631,plain,
inverse(multiply(multiply(multiply(a1,sF1_fnc),inverse(multiply(a1,sF1_fnc))),multiply(a1,sF1_fnc))) = multiply(a1,sF1_fnc),
inference(paramodulation,[status(thm)],[f565,f406]) ).
fof(f637,plain,
! [X0] : inverse(multiply(multiply(multiply(multiply(a1,sF1_fnc),inverse(multiply(a1,sF1_fnc))),X0),multiply(a1,sF1_fnc))) = inverse(X0),
inference(paramodulation,[status(thm)],[f565,f15]) ).
fof(f640,plain,
inverse(multiply(multiply(a1,sF1_fnc),multiply(a1,sF1_fnc))) = multiply(a1,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f328,f631]) ).
fof(f646,plain,
! [X0] : inverse(multiply(multiply(multiply(a1,sF1_fnc),X0),multiply(a1,sF1_fnc))) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f328,f637]) ).
fof(f660,plain,
inverse(multiply(multiply(a1,sF1_fnc),multiply(a1,sF1_fnc))) = inverse(inverse(multiply(a1,sF1_fnc))),
inference(paramodulation,[status(thm)],[f328,f646]) ).
fof(f670,plain,
multiply(a1,sF1_fnc) = inverse(inverse(multiply(a1,sF1_fnc))),
inference(forward_demodulation,[status(thm)],[f640,f660]) ).
fof(f673,plain,
multiply(inverse(multiply(a1,sF1_fnc)),multiply(a1,sF1_fnc)) = multiply(a1,sF1_fnc),
inference(paramodulation,[status(thm)],[f670,f328]) ).
fof(f740,plain,
inverse(multiply(multiply(a1,sF1_fnc),inverse(multiply(a1,sF1_fnc)))) = multiply(a1,sF1_fnc),
inference(paramodulation,[status(thm)],[f673,f565]) ).
fof(f741,plain,
! [X0] : inverse(multiply(multiply(multiply(a1,sF1_fnc),X0),multiply(a1,sF1_fnc))) = inverse(multiply(multiply(a1,sF1_fnc),X0)),
inference(paramodulation,[status(thm)],[f673,f354]) ).
fof(f750,plain,
inverse(multiply(a1,sF1_fnc)) = multiply(a1,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f328,f740]) ).
fof(f751,plain,
! [X0] : inverse(X0) = inverse(multiply(multiply(a1,sF1_fnc),X0)),
inference(forward_demodulation,[status(thm)],[f646,f741]) ).
fof(f763,plain,
! [X0] : inverse(multiply(multiply(multiply(inverse(X0),b1),sF3_fnc),multiply(a1,sF1_fnc))) = X0,
inference(backward_demodulation,[status(thm)],[f751,f327]) ).
fof(f950,plain,
! [X0] : X0 = multiply(multiply(b1,sF3_fnc),X0),
inference(paramodulation,[status(thm)],[f15,f763]) ).
fof(f980,plain,
! [X0] : X0 = multiply(multiply(a1,sF1_fnc),X0),
inference(forward_demodulation,[status(thm)],[f326,f950]) ).
fof(f1001,plain,
! [X0] : inverse(multiply(X0,multiply(a1,sF1_fnc))) = inverse(X0),
inference(backward_demodulation,[status(thm)],[f980,f646]) ).
fof(f1023,plain,
! [X0,X1,X2] : inverse(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1)) = X2,
inference(backward_demodulation,[status(thm)],[f1001,f15]) ).
fof(f1024,plain,
! [X0] : inverse(multiply(multiply(inverse(X0),b1),sF3_fnc)) = X0,
inference(backward_demodulation,[status(thm)],[f1001,f763]) ).
fof(f1027,plain,
! [X0,X1,X2] : inverse(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2)) = multiply(a1,sF1_fnc),
inference(backward_demodulation,[status(thm)],[f1001,f405]) ).
fof(f1053,plain,
! [X0] : inverse(multiply(multiply(inverse(X0),b1),sF3_fnc)) = multiply(X0,multiply(a1,sF1_fnc)),
inference(paramodulation,[status(thm)],[f1001,f1024]) ).
fof(f1064,plain,
! [X0] : X0 = multiply(X0,multiply(a1,sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f1024,f1053]) ).
fof(f1087,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(multiply(X0,multiply(a1,sF1_fnc)),X1)),X0)) = X1,
inference(paramodulation,[status(thm)],[f1064,f1023]) ).
fof(f1104,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(X0,X1)),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f1064,f1087]) ).
fof(f1118,plain,
! [X0] : inverse(multiply(multiply(sF3_fnc,multiply(X0,inverse(X0))),b1)) = multiply(a1,sF1_fnc),
inference(paramodulation,[status(thm)],[f1024,f1027]) ).
fof(f1134,plain,
inverse(multiply(multiply(sF3_fnc,multiply(a1,sF1_fnc)),b1)) = multiply(a1,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f328,f1118]) ).
fof(f1135,plain,
inverse(multiply(sF3_fnc,b1)) = multiply(a1,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f1064,f1134]) ).
fof(f1136,plain,
inverse(sF2_fnc) = multiply(a1,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f8,f1135]) ).
fof(f1153,plain,
! [X0] : X0 = multiply(X0,inverse(sF2_fnc)),
inference(backward_demodulation,[status(thm)],[f1136,f1064]) ).
fof(f1154,plain,
! [X0] : X0 = multiply(inverse(sF2_fnc),X0),
inference(backward_demodulation,[status(thm)],[f1136,f980]) ).
fof(f1155,plain,
inverse(multiply(a1,sF1_fnc)) = inverse(sF2_fnc),
inference(backward_demodulation,[status(thm)],[f1136,f750]) ).
fof(f1156,plain,
! [X0] : multiply(X0,inverse(X0)) = inverse(sF2_fnc),
inference(backward_demodulation,[status(thm)],[f1136,f328]) ).
fof(f1159,plain,
inverse(inverse(sF2_fnc)) = inverse(sF2_fnc),
inference(forward_demodulation,[status(thm)],[f1136,f1155]) ).
fof(f1171,plain,
inverse(multiply(multiply(inverse(sF2_fnc),b1),sF3_fnc)) = inverse(sF2_fnc),
inference(paramodulation,[status(thm)],[f1159,f1024]) ).
fof(f1172,plain,
sF2_fnc = inverse(sF2_fnc),
inference(forward_demodulation,[status(thm)],[f1024,f1171]) ).
fof(f1174,plain,
! [X0] : X0 = multiply(sF2_fnc,X0),
inference(backward_demodulation,[status(thm)],[f1172,f1154]) ).
fof(f1175,plain,
! [X0] : X0 = multiply(X0,sF2_fnc),
inference(backward_demodulation,[status(thm)],[f1172,f1153]) ).
fof(f1193,plain,
! [X0] : multiply(X0,inverse(X0)) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f1172,f1156]) ).
fof(f1210,plain,
! [X0] : inverse(inverse(multiply(sF2_fnc,X0))) = X0,
inference(paramodulation,[status(thm)],[f1175,f1104]) ).
fof(f1223,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f1174,f1210]) ).
fof(f1239,plain,
inverse(sF1_fnc) = a1,
inference(paramodulation,[status(thm)],[f5,f1223]) ).
fof(f1243,plain,
multiply(sF1_fnc,a1) = sF2_fnc,
inference(paramodulation,[status(thm)],[f1239,f1193]) ).
fof(f1245,plain,
sF0_fnc = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f6,f1243]) ).
fof(f1246,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1245,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP433-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n017.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 20 20:07:57 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.11/0.40 % Refutation found
% 0.11/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.43 % Elapsed time: 0.042106 seconds
% 0.11/0.43 % CPU time: 0.095729 seconds
% 0.11/0.43 % Total memory used: 3.971 MB
% 0.11/0.43 % Net memory used: 3.828 MB
%------------------------------------------------------------------------------