%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP201-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 12:33:05 PM UTC 2026
% Result : Unsatisfiable 151.85s 19.60s
% Output : CNFRefutation 9.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 15
% Syntax : Number of formulae : 78 ( 78 unt; 6 def)
% Number of atoms : 78 ( 77 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 94 ( 94 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(X,identity) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : multiply(X,left_division(X,Y)) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : left_division(X,multiply(X,Y)) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : multiply(right_division(X,Y),Y) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : right_division(multiply(X,Y),Y) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : multiply(X,right_inverse(X)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] : multiply(multiply(multiply(X,Y),Z),Y) = multiply(X,multiply(Y,multiply(Z,Y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
multiply(multiply(multiply(a,b),a),c) != multiply(a,multiply(b,multiply(a,c))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
! [X0] : multiply(X0,identity) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f13,plain,
! [X0,X1] : multiply(X0,left_division(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f14,plain,
! [X0,X1] : left_division(X0,multiply(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f15,plain,
! [X0,X1] : multiply(right_division(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f16,plain,
! [X0,X1] : right_division(multiply(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f17,plain,
! [X0] : multiply(X0,right_inverse(X0)) = identity,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f19,plain,
! [X0,X1,X2] : multiply(multiply(multiply(X0,X1),X2),X1) = multiply(X0,multiply(X1,multiply(X2,X1))),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f20,plain,
multiply(multiply(multiply(a,b),a),c) != multiply(a,multiply(b,multiply(a,c))),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f21,definition,
sF2_fnc = multiply(a,b),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f22,definition,
sF1_fnc = multiply(sF2_fnc,a),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f23,definition,
sF0_fnc = multiply(sF1_fnc,c),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f24,definition,
sF5_fnc = multiply(a,c),
introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition]) ).
fof(f25,definition,
sF4_fnc = multiply(b,sF5_fnc),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f26,definition,
sF3_fnc = multiply(a,sF4_fnc),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f27,plain,
sF0_fnc != sF3_fnc,
inference(definition_folding,[],[f20,f26,f25,f24,f23,f22,f21]) ).
fof(f177,plain,
! [X0,X1] : multiply(multiply(X0,X1),X0) = multiply(identity,multiply(X0,multiply(X1,X0))),
inference(paramodulation,[status(thm)],[f11,f19]) ).
fof(f183,plain,
! [X0,X1] : multiply(multiply(X0,X1),X0) = multiply(X0,multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f11,f177]) ).
fof(f243,plain,
! [X0,X1,X2] : left_division(multiply(multiply(X0,X1),X2),multiply(X0,multiply(X1,multiply(X2,X1)))) = X1,
inference(paramodulation,[status(thm)],[f19,f14]) ).
fof(f253,plain,
left_division(a,sF3_fnc) = sF4_fnc,
inference(paramodulation,[status(thm)],[f26,f14]) ).
fof(f257,plain,
! [X0] : left_division(X0,X0) = identity,
inference(paramodulation,[status(thm)],[f12,f14]) ).
fof(f275,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(right_division(X0,X2),multiply(X2,multiply(X1,X2))),
inference(paramodulation,[status(thm)],[f15,f19]) ).
fof(f300,plain,
! [X0,X1] : right_division(X0,left_division(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f13,f16]) ).
fof(f315,plain,
! [X0,X1] : multiply(multiply(identity,X0),right_inverse(X1)) = multiply(X1,multiply(right_inverse(X1),multiply(X0,right_inverse(X1)))),
inference(paramodulation,[status(thm)],[f17,f19]) ).
fof(f321,plain,
! [X0,X1] : multiply(X0,right_inverse(X1)) = multiply(X1,multiply(right_inverse(X1),multiply(X0,right_inverse(X1)))),
inference(forward_demodulation,[status(thm)],[f11,f315]) ).
fof(f400,plain,
multiply(sF2_fnc,a) = multiply(a,multiply(b,a)),
inference(paramodulation,[status(thm)],[f21,f183]) ).
fof(f401,plain,
! [X0] : multiply(identity,X0) = multiply(X0,multiply(right_inverse(X0),X0)),
inference(paramodulation,[status(thm)],[f17,f183]) ).
fof(f426,plain,
sF1_fnc = multiply(a,multiply(b,a)),
inference(forward_demodulation,[status(thm)],[f22,f400]) ).
fof(f427,plain,
! [X0] : X0 = multiply(X0,multiply(right_inverse(X0),X0)),
inference(forward_demodulation,[status(thm)],[f11,f401]) ).
fof(f522,plain,
! [X0] : left_division(X0,X0) = multiply(right_inverse(X0),X0),
inference(paramodulation,[status(thm)],[f427,f14]) ).
fof(f541,plain,
! [X0] : identity = multiply(right_inverse(X0),X0),
inference(forward_demodulation,[status(thm)],[f257,f522]) ).
fof(f928,plain,
left_division(a,sF1_fnc) = multiply(b,a),
inference(paramodulation,[status(thm)],[f426,f14]) ).
fof(f1034,plain,
! [X0] : left_division(multiply(multiply(X0,a),b),multiply(X0,multiply(a,left_division(a,sF1_fnc)))) = a,
inference(paramodulation,[status(thm)],[f928,f243]) ).
fof(f1089,plain,
! [X0] : left_division(multiply(multiply(X0,a),b),multiply(X0,sF1_fnc)) = a,
inference(forward_demodulation,[status(thm)],[f13,f1034]) ).
fof(f1112,plain,
! [X0,X1] : multiply(multiply(X0,right_inverse(X1)),X1) = multiply(right_division(X0,X1),multiply(X1,identity)),
inference(paramodulation,[status(thm)],[f541,f275]) ).
fof(f1142,plain,
! [X0,X1] : multiply(multiply(X0,X1),right_inverse(X1)) = multiply(right_division(X0,right_inverse(X1)),multiply(right_inverse(X1),identity)),
inference(paramodulation,[status(thm)],[f17,f275]) ).
fof(f1167,plain,
! [X0,X1] : multiply(multiply(X0,right_inverse(X1)),X1) = multiply(right_division(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f12,f1112]) ).
fof(f1168,plain,
! [X0,X1] : multiply(multiply(X0,right_inverse(X1)),X1) = X0,
inference(forward_demodulation,[status(thm)],[f15,f1167]) ).
fof(f1171,plain,
! [X0,X1] : multiply(multiply(X0,X1),right_inverse(X1)) = multiply(right_division(X0,right_inverse(X1)),right_inverse(X1)),
inference(forward_demodulation,[status(thm)],[f12,f1142]) ).
fof(f1172,plain,
! [X0,X1] : multiply(multiply(X0,X1),right_inverse(X1)) = X0,
inference(forward_demodulation,[status(thm)],[f15,f1171]) ).
fof(f1361,plain,
! [X0,X1] : multiply(X0,X1) = right_division(X0,right_inverse(X1)),
inference(paramodulation,[status(thm)],[f15,f1168]) ).
fof(f1398,plain,
! [X0,X1] : right_division(X0,X1) = multiply(X0,right_inverse(X1)),
inference(paramodulation,[status(thm)],[f1168,f16]) ).
fof(f1477,plain,
! [X0,X1] : left_division(multiply(X0,X1),X0) = right_inverse(X1),
inference(paramodulation,[status(thm)],[f1172,f14]) ).
fof(f1558,plain,
! [X0,X1] : left_division(X0,right_division(X0,X1)) = right_inverse(X1),
inference(paramodulation,[status(thm)],[f1398,f14]) ).
fof(f1800,plain,
! [X0,X1] : right_division(X0,X1) = multiply(X1,multiply(right_inverse(X1),multiply(X0,right_inverse(X1)))),
inference(forward_demodulation,[status(thm)],[f1398,f321]) ).
fof(f1801,plain,
! [X0,X1] : right_division(X0,X1) = multiply(X1,multiply(right_inverse(X1),right_division(X0,X1))),
inference(forward_demodulation,[status(thm)],[f1398,f1800]) ).
fof(f1814,plain,
! [X0,X1] : right_division(multiply(X0,X1),X1) = multiply(X1,multiply(right_inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f16,f1801]) ).
fof(f1855,plain,
! [X0,X1] : X0 = multiply(X1,multiply(right_inverse(X1),X0)),
inference(forward_demodulation,[status(thm)],[f16,f1814]) ).
fof(f1901,plain,
left_division(sF4_fnc,b) = right_inverse(sF5_fnc),
inference(paramodulation,[status(thm)],[f25,f1477]) ).
fof(f1910,plain,
left_division(sF5_fnc,a) = right_inverse(c),
inference(paramodulation,[status(thm)],[f24,f1477]) ).
fof(f1917,plain,
! [X0,X1] : left_division(X0,X1) = right_inverse(left_division(X1,X0)),
inference(paramodulation,[status(thm)],[f13,f1477]) ).
fof(f1981,plain,
! [X0,X1] : left_division(right_inverse(X0),X1) = multiply(X0,X1),
inference(paramodulation,[status(thm)],[f13,f1855]) ).
fof(f2019,plain,
! [X0,X1] : left_division(X0,X1) = multiply(right_inverse(X0),X1),
inference(paramodulation,[status(thm)],[f1855,f14]) ).
fof(f2185,plain,
! [X0,X1,X2] : right_division(X0,left_division(X1,X2)) = multiply(X0,left_division(X2,X1)),
inference(paramodulation,[status(thm)],[f1917,f1398]) ).
fof(f2745,plain,
! [X0,X1,X2] : left_division(left_division(X0,X1),X2) = multiply(left_division(X1,X0),X2),
inference(paramodulation,[status(thm)],[f1917,f1981]) ).
fof(f126105,plain,
! [X0] : left_division(multiply(left_division(X0,a),b),multiply(right_inverse(X0),sF1_fnc)) = a,
inference(paramodulation,[status(thm)],[f2019,f1089]) ).
fof(f126221,plain,
! [X0] : left_division(left_division(left_division(a,X0),b),multiply(right_inverse(X0),sF1_fnc)) = a,
inference(forward_demodulation,[status(thm)],[f2745,f126105]) ).
fof(f126222,plain,
! [X0] : left_division(left_division(left_division(a,X0),b),left_division(X0,sF1_fnc)) = a,
inference(forward_demodulation,[status(thm)],[f2019,f126221]) ).
fof(f353100,plain,
left_division(left_division(sF4_fnc,b),left_division(sF3_fnc,sF1_fnc)) = a,
inference(paramodulation,[status(thm)],[f253,f126222]) ).
fof(f353237,plain,
left_division(right_inverse(sF5_fnc),left_division(sF3_fnc,sF1_fnc)) = a,
inference(forward_demodulation,[status(thm)],[f1901,f353100]) ).
fof(f353238,plain,
multiply(sF5_fnc,left_division(sF3_fnc,sF1_fnc)) = a,
inference(forward_demodulation,[status(thm)],[f1981,f353237]) ).
fof(f353239,plain,
right_division(sF5_fnc,left_division(sF1_fnc,sF3_fnc)) = a,
inference(forward_demodulation,[status(thm)],[f2185,f353238]) ).
fof(f353948,plain,
left_division(sF5_fnc,a) = right_inverse(left_division(sF1_fnc,sF3_fnc)),
inference(paramodulation,[status(thm)],[f353239,f1558]) ).
fof(f354001,plain,
right_inverse(c) = right_inverse(left_division(sF1_fnc,sF3_fnc)),
inference(forward_demodulation,[status(thm)],[f1910,f353948]) ).
fof(f354002,plain,
right_inverse(c) = left_division(sF3_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f1917,f354001]) ).
fof(f354320,plain,
right_division(sF1_fnc,right_inverse(c)) = sF3_fnc,
inference(paramodulation,[status(thm)],[f354002,f300]) ).
fof(f355011,plain,
multiply(sF1_fnc,c) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f1361,f354320]) ).
fof(f355012,plain,
sF0_fnc = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f23,f355011]) ).
fof(f355013,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f355012,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP201-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n003.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 20:07:31 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 151.85/19.60 % Refutation found
% 151.85/19.60 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 151.85/19.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.92/19.94 % Elapsed time: 19.527896 seconds
% 4.92/19.94 % CPU time: 153.899694 seconds
% 4.92/19.94 % Total memory used: 1.337 GB
% 4.92/19.94 % Net memory used: 1.312 GB
%------------------------------------------------------------------------------