%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP511-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 12:34:34 PM UTC 2026
% Result : Unsatisfiable 0.05s 1.38s
% Output : CNFRefutation 0.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 46 unt; 4 def)
% Number of atoms : 46 ( 45 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 50 ( 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2] : multiply(multiply(multiply(X0,X1),X2),inverse(multiply(X0,X2))) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f5,definition,
sF1_fnc = multiply(a3,b3),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f6,definition,
sF0_fnc = multiply(sF1_fnc,c3),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f7,definition,
sF3_fnc = multiply(b3,c3),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f8,definition,
sF2_fnc = multiply(a3,sF3_fnc),
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] : multiply(X0,inverse(multiply(multiply(X1,X0),inverse(multiply(X1,X2))))) = X2,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f11,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),inverse(multiply(multiply(multiply(X2,X0),X3),X1))) = inverse(multiply(X2,X3)),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f12,plain,
! [X0] : multiply(multiply(sF3_fnc,X0),inverse(multiply(b3,X0))) = c3,
inference(paramodulation,[status(thm)],[f7,f3]) ).
fof(f13,plain,
! [X0] : multiply(multiply(sF0_fnc,X0),inverse(multiply(sF1_fnc,X0))) = c3,
inference(paramodulation,[status(thm)],[f6,f3]) ).
fof(f15,plain,
! [X0] : multiply(multiply(sF1_fnc,X0),inverse(multiply(a3,X0))) = b3,
inference(paramodulation,[status(thm)],[f5,f3]) ).
fof(f16,plain,
! [X0,X1,X2,X3] : multiply(multiply(multiply(multiply(multiply(X0,X1),X2),X3),inverse(multiply(X0,X2))),inverse(X1)) = X3,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f17,plain,
! [X0] : multiply(multiply(multiply(b3,X0),c3),inverse(sF3_fnc)) = X0,
inference(paramodulation,[status(thm)],[f7,f3]) ).
fof(f18,plain,
! [X0] : multiply(multiply(multiply(sF1_fnc,X0),c3),inverse(sF0_fnc)) = X0,
inference(paramodulation,[status(thm)],[f6,f3]) ).
fof(f21,plain,
multiply(multiply(sF3_fnc,c3),inverse(sF3_fnc)) = c3,
inference(paramodulation,[status(thm)],[f7,f12]) ).
fof(f47,plain,
multiply(multiply(sF1_fnc,sF3_fnc),inverse(sF2_fnc)) = b3,
inference(paramodulation,[status(thm)],[f8,f15]) ).
fof(f55,plain,
multiply(b3,inverse(multiply(sF1_fnc,inverse(sF2_fnc)))) = sF3_fnc,
inference(paramodulation,[status(thm)],[f47,f3]) ).
fof(f89,plain,
multiply(multiply(sF3_fnc,c3),inverse(sF3_fnc)) = inverse(multiply(sF1_fnc,inverse(sF2_fnc))),
inference(paramodulation,[status(thm)],[f55,f17]) ).
fof(f93,plain,
c3 = inverse(multiply(sF1_fnc,inverse(sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f21,f89]) ).
fof(f96,plain,
multiply(multiply(sF0_fnc,inverse(sF2_fnc)),c3) = c3,
inference(paramodulation,[status(thm)],[f93,f13]) ).
fof(f97,plain,
! [X0] : multiply(multiply(multiply(sF1_fnc,X0),inverse(sF2_fnc)),c3) = X0,
inference(paramodulation,[status(thm)],[f93,f3]) ).
fof(f98,plain,
multiply(c3,inverse(multiply(sF0_fnc,c3))) = inverse(sF2_fnc),
inference(paramodulation,[status(thm)],[f96,f3]) ).
fof(f221,plain,
! [X0] : multiply(multiply(X0,c3),inverse(X0)) = inverse(multiply(sF1_fnc,inverse(sF2_fnc))),
inference(paramodulation,[status(thm)],[f97,f11]) ).
fof(f222,plain,
! [X0] : multiply(multiply(X0,inverse(sF0_fnc)),inverse(X0)) = inverse(multiply(sF1_fnc,c3)),
inference(paramodulation,[status(thm)],[f18,f11]) ).
fof(f284,plain,
! [X0] : multiply(multiply(X0,c3),inverse(X0)) = c3,
inference(forward_demodulation,[status(thm)],[f93,f221]) ).
fof(f285,plain,
! [X0] : multiply(multiply(X0,inverse(sF0_fnc)),inverse(X0)) = inverse(sF0_fnc),
inference(forward_demodulation,[status(thm)],[f6,f222]) ).
fof(f288,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,inverse(multiply(multiply(multiply(X1,X2),X3),inverse(multiply(X1,X3))))),inverse(X0)) = inverse(X2),
inference(paramodulation,[status(thm)],[f16,f16]) ).
fof(f390,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X1)),inverse(X0)) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f3,f288]) ).
fof(f423,plain,
! [X0] : multiply(c3,inverse(multiply(X0,inverse(X0)))) = c3,
inference(paramodulation,[status(thm)],[f284,f3]) ).
fof(f574,plain,
multiply(c3,inverse(multiply(sF0_fnc,c3))) = inverse(sF0_fnc),
inference(paramodulation,[status(thm)],[f284,f285]) ).
fof(f594,plain,
inverse(sF2_fnc) = inverse(sF0_fnc),
inference(forward_demodulation,[status(thm)],[f98,f574]) ).
fof(f688,plain,
! [X0] : multiply(c3,inverse(c3)) = inverse(multiply(X0,inverse(X0))),
inference(paramodulation,[status(thm)],[f423,f390]) ).
fof(f1117,plain,
! [X0] : multiply(X0,multiply(c3,inverse(c3))) = X0,
inference(paramodulation,[status(thm)],[f688,f10]) ).
fof(f1162,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(multiply(X0,multiply(c3,inverse(c3))))) = X1,
inference(paramodulation,[status(thm)],[f1117,f3]) ).
fof(f1207,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X0)) = X1,
inference(forward_demodulation,[status(thm)],[f1117,f1162]) ).
fof(f1299,plain,
! [X0,X1] : multiply(multiply(multiply(X0,inverse(X0)),X1),multiply(c3,inverse(c3))) = X1,
inference(paramodulation,[status(thm)],[f688,f1207]) ).
fof(f1324,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X0)),X1) = X1,
inference(forward_demodulation,[status(thm)],[f1117,f1299]) ).
fof(f1517,plain,
! [X0,X1,X2] : multiply(multiply(multiply(multiply(X0,inverse(X0)),X1),X2),inverse(X2)) = X1,
inference(paramodulation,[status(thm)],[f1324,f3]) ).
fof(f1534,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X1)) = X0,
inference(forward_demodulation,[status(thm)],[f1324,f1517]) ).
fof(f1537,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(paramodulation,[status(thm)],[f1324,f1534]) ).
fof(f1727,plain,
inverse(inverse(sF0_fnc)) = sF2_fnc,
inference(paramodulation,[status(thm)],[f594,f1537]) ).
fof(f1734,plain,
sF0_fnc = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f1537,f1727]) ).
fof(f1735,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1734,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP511-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/1.30 % Computer : n016.cluster.edu
% 0.19/1.30 % Model : x86_64 x86_64
% 0.19/1.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/1.30 % Memory : 8046.5625MB
% 0.19/1.30 % OS : Linux 6.8.0-71-generic
% 0.05/1.30 % CPULimit : 300
% 0.05/1.30 % WCLimit : 300
% 0.05/1.30 % DateTime : Sun Sep 20 20:19:54 UTC 2026
% 0.05/1.30 % CPUTime :
% 0.05/1.31 % Drodi V4.1.1
% 0.05/1.38 % Refutation found
% 0.05/1.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.05/1.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/1.42 % Elapsed time: 0.112726 seconds
% 0.23/1.42 % CPU time: 0.355789 seconds
% 0.23/1.42 % Total memory used: 11.664 MB
% 0.23/1.42 % Net memory used: 11.419 MB
%------------------------------------------------------------------------------