%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP205-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 12:33:06 PM UTC 2026
% Result : Unsatisfiable 127.79s 16.54s
% Output : CNFRefutation 104.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 15
% Syntax : Number of formulae : 66 ( 66 unt; 6 def)
% Number of atoms : 66 ( 65 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 : 82 ( 82 !; 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),X),Z) = multiply(X,multiply(Y,multiply(X,Z))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
multiply(x,multiply(multiply(y,z),x)) != multiply(multiply(x,y),multiply(z,x)),
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),X0),X2) = multiply(X0,multiply(X1,multiply(X0,X2))),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f20,plain,
multiply(x,multiply(multiply(y,z),x)) != multiply(multiply(x,y),multiply(z,x)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f21,definition,
sF2_fnc = multiply(y,z),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f22,definition,
sF1_fnc = multiply(sF2_fnc,x),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f23,definition,
sF0_fnc = multiply(x,sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f24,definition,
sF4_fnc = multiply(x,y),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f25,definition,
sF5_fnc = multiply(z,x),
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(f30,plain,
right_division(sF5_fnc,x) = z,
inference(paramodulation,[status(thm)],[f25,f16]) ).
fof(f45,plain,
! [X0] : left_division(X0,X0) = identity,
inference(paramodulation,[status(thm)],[f12,f14]) ).
fof(f71,plain,
! [X0,X1] : right_division(X0,left_division(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f13,f16]) ).
fof(f94,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X1,multiply(left_division(X1,X0),multiply(X1,X2))),
inference(paramodulation,[status(thm)],[f13,f19]) ).
fof(f98,plain,
! [X0,X1] : multiply(X0,multiply(X1,multiply(X0,identity))) = multiply(multiply(X0,X1),X0),
inference(paramodulation,[status(thm)],[f19,f12]) ).
fof(f99,plain,
! [X0,X1,X2] : left_division(multiply(multiply(X0,X1),X0),multiply(X0,multiply(X1,multiply(X0,X2)))) = X2,
inference(paramodulation,[status(thm)],[f19,f14]) ).
fof(f102,plain,
! [X0,X1,X2] : multiply(multiply(X0,multiply(X1,X0)),X2) = multiply(X0,multiply(X1,multiply(X0,X2))),
inference(backward_demodulation,[status(thm)],[f103,f19]) ).
fof(f103,plain,
! [X0,X1] : multiply(X0,multiply(X1,X0)) = multiply(multiply(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f12,f98]) ).
fof(f110,plain,
! [X0,X1,X2] : left_division(multiply(X0,multiply(X1,X0)),multiply(X0,multiply(X1,multiply(X0,X2)))) = X2,
inference(forward_demodulation,[status(thm)],[f103,f99]) ).
fof(f132,plain,
! [X0] : multiply(X0,multiply(right_inverse(X0),X0)) = multiply(identity,X0),
inference(paramodulation,[status(thm)],[f17,f103]) ).
fof(f141,plain,
! [X0] : multiply(X0,multiply(right_inverse(X0),X0)) = X0,
inference(forward_demodulation,[status(thm)],[f11,f132]) ).
fof(f172,plain,
! [X0] : left_division(X0,X0) = multiply(right_inverse(X0),X0),
inference(paramodulation,[status(thm)],[f141,f14]) ).
fof(f178,plain,
! [X0] : identity = multiply(right_inverse(X0),X0),
inference(forward_demodulation,[status(thm)],[f45,f172]) ).
fof(f227,plain,
! [X0] : multiply(multiply(x,sF1_fnc),X0) = multiply(x,multiply(sF2_fnc,multiply(x,X0))),
inference(paramodulation,[status(thm)],[f22,f102]) ).
fof(f241,plain,
! [X0] : multiply(sF0_fnc,X0) = multiply(x,multiply(sF2_fnc,multiply(x,X0))),
inference(forward_demodulation,[status(thm)],[f23,f227]) ).
fof(f1473,plain,
! [X0,X1] : multiply(multiply(X0,right_inverse(X1)),X1) = multiply(right_inverse(X1),multiply(left_division(right_inverse(X1),X0),identity)),
inference(paramodulation,[status(thm)],[f178,f94]) ).
fof(f1526,plain,
! [X0,X1] : multiply(multiply(X0,right_inverse(X1)),X1) = multiply(right_inverse(X1),left_division(right_inverse(X1),X0)),
inference(forward_demodulation,[status(thm)],[f12,f1473]) ).
fof(f1527,plain,
! [X0,X1] : multiply(multiply(X0,right_inverse(X1)),X1) = X0,
inference(forward_demodulation,[status(thm)],[f13,f1526]) ).
fof(f1654,plain,
! [X0,X1] : left_division(multiply(X0,identity),multiply(X0,multiply(right_inverse(X0),multiply(X0,X1)))) = X1,
inference(paramodulation,[status(thm)],[f178,f110]) ).
fof(f1760,plain,
! [X0,X1] : left_division(X0,multiply(X0,multiply(right_inverse(X0),multiply(X0,X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f12,f1654]) ).
fof(f1764,plain,
! [X0,X1] : multiply(right_inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f14,f1760]) ).
fof(f1856,plain,
! [X0,X1] : multiply(X0,X1) = right_division(X0,right_inverse(X1)),
inference(paramodulation,[status(thm)],[f15,f1527]) ).
fof(f1878,plain,
! [X0,X1] : right_division(X0,X1) = multiply(X0,right_inverse(X1)),
inference(paramodulation,[status(thm)],[f1527,f16]) ).
fof(f1999,plain,
! [X0,X1] : right_division(X0,multiply(X1,X0)) = right_inverse(X1),
inference(paramodulation,[status(thm)],[f1764,f16]) ).
fof(f2140,plain,
! [X0,X1] : left_division(X0,right_division(X0,X1)) = right_inverse(X1),
inference(paramodulation,[status(thm)],[f1878,f14]) ).
fof(f2367,plain,
! [X0,X1] : right_division(X0,X1) = right_inverse(right_division(X1,X0)),
inference(paramodulation,[status(thm)],[f15,f1999]) ).
fof(f2381,plain,
right_division(z,sF2_fnc) = right_inverse(y),
inference(paramodulation,[status(thm)],[f21,f1999]) ).
fof(f2557,plain,
! [X0,X1,X2] : right_division(X0,right_division(X1,X2)) = multiply(X0,right_division(X2,X1)),
inference(paramodulation,[status(thm)],[f2367,f1878]) ).
fof(f3262,plain,
! [X0] : multiply(sF0_fnc,right_inverse(X0)) = multiply(x,multiply(sF2_fnc,right_division(x,X0))),
inference(paramodulation,[status(thm)],[f1878,f241]) ).
fof(f3302,plain,
! [X0] : right_division(sF0_fnc,X0) = multiply(x,multiply(sF2_fnc,right_division(x,X0))),
inference(forward_demodulation,[status(thm)],[f1878,f3262]) ).
fof(f3303,plain,
! [X0] : right_division(sF0_fnc,X0) = multiply(x,right_division(sF2_fnc,right_division(X0,x))),
inference(forward_demodulation,[status(thm)],[f2557,f3302]) ).
fof(f3304,plain,
! [X0] : right_division(sF0_fnc,X0) = right_division(x,right_division(right_division(X0,x),sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f2557,f3303]) ).
fof(f42835,plain,
right_division(sF0_fnc,sF5_fnc) = right_division(x,right_division(z,sF2_fnc)),
inference(paramodulation,[status(thm)],[f30,f3304]) ).
fof(f42882,plain,
right_division(sF0_fnc,sF5_fnc) = right_division(x,right_inverse(y)),
inference(forward_demodulation,[status(thm)],[f2381,f42835]) ).
fof(f42883,plain,
right_division(sF0_fnc,sF5_fnc) = multiply(x,y),
inference(forward_demodulation,[status(thm)],[f1856,f42882]) ).
fof(f42884,plain,
right_division(sF0_fnc,sF5_fnc) = sF4_fnc,
inference(forward_demodulation,[status(thm)],[f24,f42883]) ).
fof(f43699,plain,
left_division(sF0_fnc,sF4_fnc) = right_inverse(sF5_fnc),
inference(paramodulation,[status(thm)],[f42884,f2140]) ).
fof(f43783,plain,
right_division(sF4_fnc,right_inverse(sF5_fnc)) = sF0_fnc,
inference(paramodulation,[status(thm)],[f43699,f71]) ).
fof(f43786,plain,
multiply(sF4_fnc,sF5_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f1856,f43783]) ).
fof(f43787,plain,
sF3_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f26,f43786]) ).
fof(f43788,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f43787,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP205-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.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 20:06:05 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 127.79/16.54 % Refutation found
% 127.79/16.54 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 127.79/16.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 20.55/16.75 % Elapsed time: 16.374414 seconds
% 20.55/16.75 % CPU time: 129.262508 seconds
% 20.55/16.75 % Total memory used: 1.852 GB
% 20.55/16.75 % Net memory used: 1.824 GB
%------------------------------------------------------------------------------