%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP002-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 12:32:13 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.59s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 12
% Syntax : Number of formulae : 100 ( 100 unt; 0 def)
% Number of atoms : 100 ( 99 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 57 ( 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : multiply(X,identity) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : multiply(X,inverse(X)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,hypothesis,
! [X] : multiply(X,multiply(X,X)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
multiply(a,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
multiply(c,inverse(a)) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
multiply(d,inverse(b)) = h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
multiply(h,b) = j,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
multiply(j,inverse(h)) = k,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
multiply(k,inverse(b)) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f14,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f15,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f16,plain,
! [X0] : multiply(X0,identity) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f17,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f18,plain,
! [X0] : multiply(X0,multiply(X0,X0)) = identity,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f19,plain,
multiply(a,b) = c,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f20,plain,
multiply(c,inverse(a)) = d,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f21,plain,
multiply(d,inverse(b)) = h,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f22,plain,
multiply(h,b) = j,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f23,plain,
multiply(j,inverse(h)) = k,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f24,plain,
multiply(k,inverse(b)) != identity,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f36,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,inverse(multiply(X0,X1)))),
inference(paramodulation,[status(thm)],[f17,f15]) ).
fof(f39,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f14,f15]) ).
fof(f41,plain,
! [X0] : multiply(h,X0) = multiply(d,multiply(inverse(b),X0)),
inference(paramodulation,[status(thm)],[f21,f15]) ).
fof(f42,plain,
! [X0] : multiply(d,X0) = multiply(c,multiply(inverse(a),X0)),
inference(paramodulation,[status(thm)],[f20,f15]) ).
fof(f43,plain,
! [X0] : multiply(j,X0) = multiply(h,multiply(b,X0)),
inference(paramodulation,[status(thm)],[f22,f15]) ).
fof(f44,plain,
! [X0] : multiply(c,X0) = multiply(a,multiply(b,X0)),
inference(paramodulation,[status(thm)],[f19,f15]) ).
fof(f45,plain,
! [X0,X1] : multiply(identity,X0) = multiply(X1,multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f17,f15]) ).
fof(f51,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f13,f39]) ).
fof(f52,plain,
! [X0,X1] : X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(forward_demodulation,[status(thm)],[f13,f45]) ).
fof(f57,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,identity),
inference(paramodulation,[status(thm)],[f17,f52]) ).
fof(f65,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f16,f57]) ).
fof(f80,plain,
! [X0] : multiply(inverse(X0),inverse(X0)) = multiply(X0,identity),
inference(paramodulation,[status(thm)],[f18,f52]) ).
fof(f86,plain,
! [X0] : multiply(inverse(X0),inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f16,f80]) ).
fof(f89,plain,
! [X0] : multiply(k,X0) = multiply(j,multiply(inverse(h),X0)),
inference(paramodulation,[status(thm)],[f23,f15]) ).
fof(f90,plain,
! [X0] : multiply(X0,inverse(inverse(X0))) = inverse(X0),
inference(paramodulation,[status(thm)],[f65,f86]) ).
fof(f99,plain,
! [X0] : multiply(X0,X0) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f65,f90]) ).
fof(f102,plain,
! [X0,X1] : multiply(X0,multiply(X1,multiply(X0,X1))) = inverse(multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f15,f99]) ).
fof(f109,plain,
! [X0,X1] : multiply(inverse(X0),X1) = multiply(X0,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f99,f15]) ).
fof(f121,plain,
inverse(b) = multiply(inverse(d),h),
inference(paramodulation,[status(thm)],[f21,f51]) ).
fof(f122,plain,
inverse(a) = multiply(inverse(c),d),
inference(paramodulation,[status(thm)],[f20,f51]) ).
fof(f123,plain,
b = multiply(inverse(h),j),
inference(paramodulation,[status(thm)],[f22,f51]) ).
fof(f152,plain,
multiply(inverse(inverse(c)),d) = multiply(inverse(c),inverse(a)),
inference(paramodulation,[status(thm)],[f122,f109]) ).
fof(f153,plain,
multiply(inverse(inverse(d)),h) = multiply(inverse(d),inverse(b)),
inference(paramodulation,[status(thm)],[f121,f109]) ).
fof(f161,plain,
multiply(inverse(a),b) = multiply(a,c),
inference(paramodulation,[status(thm)],[f19,f109]) ).
fof(f174,plain,
multiply(c,d) = multiply(inverse(c),inverse(a)),
inference(forward_demodulation,[status(thm)],[f65,f152]) ).
fof(f175,plain,
multiply(d,h) = multiply(inverse(d),inverse(b)),
inference(forward_demodulation,[status(thm)],[f65,f153]) ).
fof(f194,plain,
! [X0] : multiply(b,X0) = multiply(inverse(h),multiply(j,X0)),
inference(paramodulation,[status(thm)],[f123,f15]) ).
fof(f275,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = multiply(inverse(X1),identity),
inference(paramodulation,[status(thm)],[f36,f51]) ).
fof(f325,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f16,f275]) ).
fof(f329,plain,
! [X0] : multiply(h,multiply(b,X0)) = multiply(d,X0),
inference(paramodulation,[status(thm)],[f51,f41]) ).
fof(f330,plain,
multiply(h,b) = multiply(d,identity),
inference(paramodulation,[status(thm)],[f14,f41]) ).
fof(f339,plain,
multiply(d,inverse(h)) = k,
inference(backward_demodulation,[status(thm)],[f349,f23]) ).
fof(f346,plain,
! [X0] : multiply(k,X0) = multiply(d,multiply(inverse(h),X0)),
inference(backward_demodulation,[status(thm)],[f349,f89]) ).
fof(f348,plain,
! [X0] : multiply(b,X0) = multiply(inverse(h),multiply(d,X0)),
inference(backward_demodulation,[status(thm)],[f349,f194]) ).
fof(f349,plain,
! [X0] : multiply(j,X0) = multiply(d,X0),
inference(forward_demodulation,[status(thm)],[f43,f329]) ).
fof(f350,plain,
j = multiply(d,identity),
inference(forward_demodulation,[status(thm)],[f22,f330]) ).
fof(f352,plain,
b = multiply(inverse(h),d),
inference(backward_demodulation,[status(thm)],[f357,f123]) ).
fof(f357,plain,
j = d,
inference(forward_demodulation,[status(thm)],[f16,f350]) ).
fof(f377,plain,
multiply(inverse(d),inverse(h)) = multiply(d,k),
inference(paramodulation,[status(thm)],[f339,f109]) ).
fof(f386,plain,
d = multiply(h,b),
inference(paramodulation,[status(thm)],[f352,f52]) ).
fof(f387,plain,
multiply(inverse(inverse(h)),d) = multiply(inverse(h),b),
inference(paramodulation,[status(thm)],[f352,f109]) ).
fof(f390,plain,
multiply(h,d) = multiply(inverse(h),b),
inference(forward_demodulation,[status(thm)],[f65,f387]) ).
fof(f395,plain,
multiply(d,b) = multiply(c,multiply(a,c)),
inference(paramodulation,[status(thm)],[f161,f42]) ).
fof(f429,plain,
multiply(b,inverse(d)) = inverse(h),
inference(paramodulation,[status(thm)],[f386,f325]) ).
fof(f450,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),inverse(inverse(X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f325,f325]) ).
fof(f460,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
inference(paramodulation,[status(thm)],[f325,f51]) ).
fof(f488,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f65,f450]) ).
fof(f493,plain,
multiply(c,d) = inverse(multiply(a,c)),
inference(backward_demodulation,[status(thm)],[f460,f174]) ).
fof(f494,plain,
inverse(multiply(h,d)) = multiply(d,k),
inference(backward_demodulation,[status(thm)],[f460,f377]) ).
fof(f495,plain,
multiply(d,h) = inverse(multiply(b,d)),
inference(backward_demodulation,[status(thm)],[f460,f175]) ).
fof(f509,plain,
multiply(inverse(b),inverse(d)) = multiply(b,inverse(h)),
inference(paramodulation,[status(thm)],[f429,f109]) ).
fof(f513,plain,
inverse(multiply(d,b)) = multiply(b,inverse(h)),
inference(forward_demodulation,[status(thm)],[f460,f509]) ).
fof(f556,plain,
multiply(k,d) = multiply(d,b),
inference(paramodulation,[status(thm)],[f352,f346]) ).
fof(f584,plain,
multiply(d,inverse(multiply(d,b))) = inverse(k),
inference(paramodulation,[status(thm)],[f556,f325]) ).
fof(f588,plain,
multiply(d,multiply(b,inverse(h))) = inverse(k),
inference(forward_demodulation,[status(thm)],[f513,f584]) ).
fof(f856,plain,
! [X0] : multiply(inverse(multiply(c,X0)),a) = inverse(multiply(b,X0)),
inference(paramodulation,[status(thm)],[f44,f488]) ).
fof(f1233,plain,
multiply(k,b) = multiply(d,multiply(h,d)),
inference(paramodulation,[status(thm)],[f390,f346]) ).
fof(f3168,plain,
multiply(h,multiply(k,b)) = inverse(multiply(h,d)),
inference(paramodulation,[status(thm)],[f1233,f102]) ).
fof(f3172,plain,
multiply(a,multiply(d,b)) = inverse(multiply(a,c)),
inference(paramodulation,[status(thm)],[f395,f102]) ).
fof(f3376,plain,
multiply(h,multiply(k,b)) = multiply(d,k),
inference(forward_demodulation,[status(thm)],[f494,f3168]) ).
fof(f3384,plain,
multiply(a,multiply(d,b)) = multiply(c,d),
inference(forward_demodulation,[status(thm)],[f493,f3172]) ).
fof(f4022,plain,
multiply(k,b) = multiply(inverse(h),multiply(d,k)),
inference(paramodulation,[status(thm)],[f3376,f51]) ).
fof(f4052,plain,
multiply(k,b) = multiply(b,k),
inference(forward_demodulation,[status(thm)],[f348,f4022]) ).
fof(f4065,plain,
b = multiply(inverse(k),multiply(b,k)),
inference(paramodulation,[status(thm)],[f4052,f51]) ).
fof(f4184,plain,
multiply(inverse(multiply(c,d)),a) = inverse(multiply(d,b)),
inference(paramodulation,[status(thm)],[f3384,f488]) ).
fof(f4204,plain,
inverse(multiply(b,d)) = inverse(multiply(d,b)),
inference(forward_demodulation,[status(thm)],[f856,f4184]) ).
fof(f4205,plain,
multiply(d,h) = inverse(multiply(d,b)),
inference(forward_demodulation,[status(thm)],[f495,f4204]) ).
fof(f4208,plain,
multiply(d,multiply(d,h)) = inverse(k),
inference(backward_demodulation,[status(thm)],[f4211,f588]) ).
fof(f4211,plain,
multiply(d,h) = multiply(b,inverse(h)),
inference(forward_demodulation,[status(thm)],[f513,f4205]) ).
fof(f4233,plain,
multiply(inverse(d),h) = inverse(k),
inference(forward_demodulation,[status(thm)],[f109,f4208]) ).
fof(f4234,plain,
b = multiply(inverse(b),multiply(b,k)),
inference(backward_demodulation,[status(thm)],[f4251,f4065]) ).
fof(f4251,plain,
inverse(b) = inverse(k),
inference(forward_demodulation,[status(thm)],[f121,f4233]) ).
fof(f4285,plain,
multiply(b,inverse(b)) != identity,
inference(backward_demodulation,[status(thm)],[f4341,f24]) ).
fof(f4341,plain,
b = k,
inference(forward_demodulation,[status(thm)],[f51,f4234]) ).
fof(f4397,plain,
identity != identity,
inference(forward_demodulation,[status(thm)],[f17,f4285]) ).
fof(f4398,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f4397]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP002-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.53 % Computer : n019.cluster.edu
% 0.09/0.53 % Model : x86_64 x86_64
% 0.09/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.53 % Memory : 8046.5625MB
% 0.09/0.53 % OS : Linux 6.8.0-71-generic
% 0.09/0.53 % CPULimit : 300
% 0.09/0.53 % WCLimit : 300
% 0.09/0.53 % DateTime : Sun Sep 20 19:53:05 UTC 2026
% 0.09/0.53 % CPUTime :
% 0.09/0.54 % Drodi V4.1.1
% 0.13/0.59 % Refutation found
% 0.13/0.59 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.61/1.82 % Elapsed time: 1.065434 seconds
% 1.61/1.82 % CPU time: 0.333988 seconds
% 1.61/1.82 % Total memory used: 11.825 MB
% 1.61/1.82 % Net memory used: 11.542 MB
%------------------------------------------------------------------------------