%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP202-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 187.42s 24.38s
% Output : CNFRefutation 29.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 15
% Syntax : Number of formulae : 80 ( 80 unt; 6 def)
% Number of atoms : 80 ( 79 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 : 103 ( 103 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(X,identity) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : multiply(X,left_division(X,Y)) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : left_division(X,multiply(X,Y)) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : multiply(right_division(X,Y),Y) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : right_division(multiply(X,Y),Y) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : multiply(X,right_inverse(X)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] : multiply(multiply(multiply(X,Y),X),Z) = multiply(X,multiply(Y,multiply(X,Z))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)),
file('/export/starexec/sandbox/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),X0),X2) = multiply(X0,multiply(X1,multiply(X0,X2))),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f20,plain,
multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f21,definition,
sF2_fnc = multiply(b,c),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f22,definition,
sF1_fnc = multiply(a,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f23,definition,
sF0_fnc = multiply(sF1_fnc,a),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f24,definition,
sF4_fnc = multiply(a,b),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f25,definition,
sF5_fnc = multiply(c,a),
introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition]) ).
fof(f26,definition,
sF3_fnc = multiply(sF4_fnc,sF5_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(f34,plain,
! [X0] : multiply(multiply(sF1_fnc,a),X0) = multiply(a,multiply(sF2_fnc,multiply(a,X0))),
inference(paramodulation,[status(thm)],[f22,f19]) ).
fof(f38,plain,
! [X0] : multiply(sF0_fnc,X0) = multiply(a,multiply(sF2_fnc,multiply(a,X0))),
inference(forward_demodulation,[status(thm)],[f23,f34]) ).
fof(f340,plain,
! [X0,X1] : multiply(X0,multiply(X1,multiply(X0,identity))) = multiply(multiply(X0,X1),X0),
inference(paramodulation,[status(thm)],[f19,f12]) ).
fof(f359,plain,
! [X0,X1,X2] : multiply(multiply(X0,multiply(X1,X0)),X2) = multiply(X0,multiply(X1,multiply(X0,X2))),
inference(backward_demodulation,[status(thm)],[f375,f19]) ).
fof(f375,plain,
! [X0,X1] : multiply(X0,multiply(X1,X0)) = multiply(multiply(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f12,f340]) ).
fof(f438,plain,
! [X0] : multiply(sF0_fnc,left_division(a,X0)) = multiply(a,multiply(sF2_fnc,X0)),
inference(paramodulation,[status(thm)],[f13,f38]) ).
fof(f463,plain,
left_division(c,sF5_fnc) = a,
inference(paramodulation,[status(thm)],[f25,f14]) ).
fof(f470,plain,
! [X0] : left_division(X0,identity) = right_inverse(X0),
inference(paramodulation,[status(thm)],[f17,f14]) ).
fof(f472,plain,
! [X0] : left_division(X0,X0) = identity,
inference(paramodulation,[status(thm)],[f12,f14]) ).
fof(f489,plain,
right_division(sF2_fnc,c) = b,
inference(paramodulation,[status(thm)],[f21,f16]) ).
fof(f491,plain,
! [X0,X1] : right_division(X0,left_division(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f13,f16]) ).
fof(f503,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(right_division(X1,X0),multiply(X0,X2))),
inference(paramodulation,[status(thm)],[f15,f359]) ).
fof(f515,plain,
! [X0,X1] : multiply(multiply(right_inverse(X0),identity),X1) = multiply(right_inverse(X0),multiply(X0,multiply(right_inverse(X0),X1))),
inference(paramodulation,[status(thm)],[f17,f359]) ).
fof(f538,plain,
! [X0,X1] : multiply(right_inverse(X0),X1) = multiply(right_inverse(X0),multiply(X0,multiply(right_inverse(X0),X1))),
inference(forward_demodulation,[status(thm)],[f12,f515]) ).
fof(f708,plain,
! [X0] : multiply(X0,multiply(right_inverse(X0),X0)) = multiply(identity,X0),
inference(paramodulation,[status(thm)],[f17,f375]) ).
fof(f715,plain,
! [X0,X1] : right_division(multiply(X0,multiply(X1,X0)),X0) = multiply(X0,X1),
inference(paramodulation,[status(thm)],[f375,f16]) ).
fof(f730,plain,
! [X0] : multiply(X0,multiply(right_inverse(X0),X0)) = X0,
inference(forward_demodulation,[status(thm)],[f11,f708]) ).
fof(f787,plain,
! [X0] : left_division(X0,X0) = multiply(right_inverse(X0),X0),
inference(paramodulation,[status(thm)],[f730,f14]) ).
fof(f813,plain,
! [X0] : identity = multiply(right_inverse(X0),X0),
inference(forward_demodulation,[status(thm)],[f472,f787]) ).
fof(f832,plain,
! [X0] : left_division(right_inverse(X0),identity) = X0,
inference(paramodulation,[status(thm)],[f813,f14]) ).
fof(f847,plain,
! [X0] : right_inverse(right_inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f470,f832]) ).
fof(f1850,plain,
! [X0,X1] : multiply(multiply(right_inverse(X0),X1),X0) = multiply(right_inverse(X0),multiply(right_division(X1,right_inverse(X0)),identity)),
inference(paramodulation,[status(thm)],[f813,f503]) ).
fof(f1915,plain,
! [X0,X1] : multiply(multiply(right_inverse(X0),X1),X0) = multiply(right_inverse(X0),right_division(X1,right_inverse(X0))),
inference(forward_demodulation,[status(thm)],[f12,f1850]) ).
fof(f3037,plain,
! [X0,X1] : left_division(right_inverse(X0),multiply(right_inverse(X0),X1)) = multiply(X0,multiply(right_inverse(X0),X1)),
inference(paramodulation,[status(thm)],[f538,f14]) ).
fof(f3102,plain,
! [X0,X1] : X0 = multiply(X1,multiply(right_inverse(X1),X0)),
inference(forward_demodulation,[status(thm)],[f14,f3037]) ).
fof(f3248,plain,
! [X0,X1] : left_division(right_inverse(X0),X1) = multiply(X0,X1),
inference(paramodulation,[status(thm)],[f13,f3102]) ).
fof(f3284,plain,
! [X0,X1] : left_division(X0,X1) = multiply(right_inverse(X0),X1),
inference(paramodulation,[status(thm)],[f3102,f14]) ).
fof(f3359,plain,
! [X0,X1] : multiply(multiply(right_inverse(X0),X1),X0) = left_division(X0,right_division(X1,right_inverse(X0))),
inference(backward_demodulation,[status(thm)],[f3284,f1915]) ).
fof(f3413,plain,
! [X0,X1] : multiply(left_division(X0,X1),X0) = left_division(X0,right_division(X1,right_inverse(X0))),
inference(forward_demodulation,[status(thm)],[f3284,f3359]) ).
fof(f3452,plain,
! [X0,X1] : right_division(X0,multiply(X1,X0)) = right_inverse(X1),
inference(paramodulation,[status(thm)],[f3248,f491]) ).
fof(f3523,plain,
! [X0,X1] : right_division(left_division(X0,X1),X1) = right_inverse(X0),
inference(paramodulation,[status(thm)],[f3284,f16]) ).
fof(f4904,plain,
! [X0,X1] : right_division(multiply(X0,X1),X0) = multiply(X0,right_division(X1,X0)),
inference(paramodulation,[status(thm)],[f15,f715]) ).
fof(f5250,plain,
! [X0,X1] : right_division(X0,X1) = multiply(X1,right_division(left_division(X1,X0),X1)),
inference(paramodulation,[status(thm)],[f13,f4904]) ).
fof(f9488,plain,
! [X0,X1] : right_division(X0,right_inverse(X1)) = left_division(X1,right_division(left_division(right_inverse(X1),X0),right_inverse(X1))),
inference(paramodulation,[status(thm)],[f3284,f5250]) ).
fof(f9557,plain,
! [X0,X1] : right_division(X0,right_inverse(X1)) = multiply(left_division(X1,left_division(right_inverse(X1),X0)),X1),
inference(forward_demodulation,[status(thm)],[f3413,f9488]) ).
fof(f9558,plain,
! [X0,X1] : right_division(X0,right_inverse(X1)) = multiply(left_division(X1,multiply(X1,X0)),X1),
inference(forward_demodulation,[status(thm)],[f3248,f9557]) ).
fof(f9585,plain,
! [X0,X1] : right_division(X0,right_inverse(X1)) = multiply(X0,X1),
inference(forward_demodulation,[status(thm)],[f14,f9558]) ).
fof(f9748,plain,
! [X0,X1] : right_inverse(X0) = multiply(left_division(X0,right_inverse(X1)),X1),
inference(paramodulation,[status(thm)],[f3523,f9585]) ).
fof(f9759,plain,
! [X0,X1] : right_division(X0,X1) = multiply(X0,right_inverse(X1)),
inference(paramodulation,[status(thm)],[f847,f9585]) ).
fof(f9982,plain,
! [X0,X1] : right_division(X0,right_inverse(X1)) = right_inverse(left_division(X1,right_inverse(X0))),
inference(paramodulation,[status(thm)],[f9748,f3452]) ).
fof(f9989,plain,
! [X0,X1] : right_division(right_inverse(X0),X1) = left_division(X0,right_inverse(X1)),
inference(paramodulation,[status(thm)],[f9748,f16]) ).
fof(f10082,plain,
! [X0,X1] : multiply(X0,X1) = right_inverse(left_division(X1,right_inverse(X0))),
inference(forward_demodulation,[status(thm)],[f9585,f9982]) ).
fof(f10206,plain,
! [X0,X1] : multiply(right_inverse(X0),X1) = right_inverse(left_division(X1,X0)),
inference(paramodulation,[status(thm)],[f847,f10082]) ).
fof(f10226,plain,
! [X0,X1] : left_division(X0,X1) = right_inverse(left_division(X1,X0)),
inference(forward_demodulation,[status(thm)],[f3284,f10206]) ).
fof(f10276,plain,
left_division(sF5_fnc,c) = right_inverse(a),
inference(paramodulation,[status(thm)],[f463,f10226]) ).
fof(f16239,plain,
right_division(right_inverse(a),c) = right_inverse(sF5_fnc),
inference(paramodulation,[status(thm)],[f10276,f3523]) ).
fof(f16244,plain,
left_division(a,right_inverse(c)) = right_inverse(sF5_fnc),
inference(forward_demodulation,[status(thm)],[f9989,f16239]) ).
fof(f20341,plain,
multiply(sF0_fnc,right_inverse(sF5_fnc)) = multiply(a,multiply(sF2_fnc,right_inverse(c))),
inference(paramodulation,[status(thm)],[f16244,f438]) ).
fof(f20374,plain,
right_division(sF0_fnc,sF5_fnc) = multiply(a,multiply(sF2_fnc,right_inverse(c))),
inference(forward_demodulation,[status(thm)],[f9759,f20341]) ).
fof(f20375,plain,
right_division(sF0_fnc,sF5_fnc) = multiply(a,right_division(sF2_fnc,c)),
inference(forward_demodulation,[status(thm)],[f9759,f20374]) ).
fof(f20376,plain,
right_division(sF0_fnc,sF5_fnc) = multiply(a,b),
inference(forward_demodulation,[status(thm)],[f489,f20375]) ).
fof(f20377,plain,
right_division(sF0_fnc,sF5_fnc) = sF4_fnc,
inference(forward_demodulation,[status(thm)],[f24,f20376]) ).
fof(f20427,plain,
multiply(sF4_fnc,sF5_fnc) = sF0_fnc,
inference(paramodulation,[status(thm)],[f20377,f15]) ).
fof(f20471,plain,
sF3_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f26,f20427]) ).
fof(f20472,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f20471,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP202-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.56 % Computer : n001.cluster.edu
% 0.10/0.56 % Model : x86_64 x86_64
% 0.10/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.56 % Memory : 8046.5625MB
% 0.10/0.56 % OS : Linux 6.8.0-71-generic
% 0.10/0.56 % CPULimit : 300
% 0.10/0.56 % WCLimit : 300
% 0.10/0.56 % DateTime : Sun Sep 20 20:11:28 UTC 2026
% 0.10/0.56 % CPUTime :
% 0.10/0.57 % Drodi V4.1.1
% 187.42/24.38 % Refutation found
% 187.42/24.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 187.42/24.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 29.00/24.69 % Elapsed time: 24.086337 seconds
% 29.00/24.69 % CPU time: 189.214091 seconds
% 29.00/24.69 % Total memory used: 1.593 GB
% 29.00/24.69 % Net memory used: 1.564 GB
%------------------------------------------------------------------------------