%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP167-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 12:32:55 PM UTC 2026
% Result : Unsatisfiable 177.76s 22.86s
% Output : CNFRefutation 72.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 21
% Syntax : Number of formulae : 180 ( 180 unt; 0 def)
% Number of atoms : 180 ( 179 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 313 ( 313 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] : greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,Z] : least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] : least_upper_bound(X,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] : least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] : greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y,Z] : multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,Z] : multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [Y,Z,X] : multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [Y,Z,X] : multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X] : inverse(inverse(X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y] : inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X] : positive_part(X) = least_upper_bound(X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X] : negative_part(X) = greatest_lower_bound(X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X,Y,Z] : least_upper_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(X,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y,Z] : greatest_lower_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f25,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f26,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f27,plain,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f28,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f29,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f30,plain,
! [X0,X1,X2] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f31,plain,
! [X0] : least_upper_bound(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f33,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f34,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f35,plain,
! [X0,X1,X2] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f36,plain,
! [X0,X1,X2] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f37,plain,
! [X0,X1,X2] : multiply(least_upper_bound(X0,X1),X2) = least_upper_bound(multiply(X0,X2),multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f38,plain,
! [X0,X1,X2] : multiply(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f40,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f41,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f42,plain,
! [X0] : positive_part(X0) = least_upper_bound(X0,identity),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f43,plain,
! [X0] : negative_part(X0) = greatest_lower_bound(X0,identity),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f44,plain,
! [X0,X1,X2] : least_upper_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(least_upper_bound(X0,X1),least_upper_bound(X0,X2)),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f45,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(greatest_lower_bound(X0,X1),greatest_lower_bound(X0,X2)),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f46,plain,
a != multiply(positive_part(a),negative_part(a)),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f61,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(paramodulation,[status(thm)],[f40,f25]) ).
fof(f63,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f25,f26]) ).
fof(f64,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f24,f63]) ).
fof(f65,plain,
! [X0,X1] : X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f40,f64]) ).
fof(f68,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f25,f64]) ).
fof(f70,plain,
! [X0,X1,X2] : X0 = multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X0))),
inference(paramodulation,[status(thm)],[f26,f64]) ).
fof(f73,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f40,f68]) ).
fof(f109,plain,
! [X0,X1] : X0 = multiply(inverse(multiply(inverse(multiply(X1,X0)),X1)),identity),
inference(paramodulation,[status(thm)],[f25,f70]) ).
fof(f138,plain,
! [X0,X1] : X0 = inverse(multiply(inverse(multiply(X1,X0)),X1)),
inference(forward_demodulation,[status(thm)],[f73,f109]) ).
fof(f155,plain,
! [X0,X1] : X0 = inverse(multiply(X1,inverse(multiply(X0,X1)))),
inference(paramodulation,[status(thm)],[f138,f138]) ).
fof(f165,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(multiply(X1,X0)),X1),
inference(paramodulation,[status(thm)],[f138,f40]) ).
fof(f191,plain,
! [X0,X1] : inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f155,f40]) ).
fof(f349,plain,
! [X0] : negative_part(X0) = greatest_lower_bound(identity,X0),
inference(paramodulation,[status(thm)],[f43,f27]) ).
fof(f357,plain,
! [X0] : positive_part(X0) = least_upper_bound(identity,X0),
inference(paramodulation,[status(thm)],[f42,f28]) ).
fof(f365,plain,
! [X0] : least_upper_bound(X0,negative_part(X0)) = X0,
inference(paramodulation,[status(thm)],[f43,f33]) ).
fof(f366,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f27,f33]) ).
fof(f373,plain,
! [X0] : greatest_lower_bound(X0,positive_part(X0)) = X0,
inference(paramodulation,[status(thm)],[f42,f34]) ).
fof(f374,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f28,f34]) ).
fof(f403,plain,
! [X0] : negative_part(least_upper_bound(identity,X0)) = identity,
inference(paramodulation,[status(thm)],[f34,f349]) ).
fof(f411,plain,
! [X0] : least_upper_bound(identity,negative_part(X0)) = identity,
inference(paramodulation,[status(thm)],[f349,f33]) ).
fof(f416,plain,
! [X0] : negative_part(positive_part(X0)) = identity,
inference(forward_demodulation,[status(thm)],[f357,f403]) ).
fof(f418,plain,
! [X0] : positive_part(negative_part(X0)) = identity,
inference(forward_demodulation,[status(thm)],[f357,f411]) ).
fof(f420,plain,
! [X0] : least_upper_bound(positive_part(X0),identity) = positive_part(X0),
inference(paramodulation,[status(thm)],[f416,f365]) ).
fof(f421,plain,
! [X0] : positive_part(positive_part(X0)) = positive_part(X0),
inference(forward_demodulation,[status(thm)],[f42,f420]) ).
fof(f425,plain,
! [X0] : greatest_lower_bound(negative_part(X0),identity) = negative_part(X0),
inference(paramodulation,[status(thm)],[f418,f373]) ).
fof(f426,plain,
! [X0] : negative_part(negative_part(X0)) = negative_part(X0),
inference(forward_demodulation,[status(thm)],[f43,f425]) ).
fof(f447,plain,
! [X0,X1] : least_upper_bound(least_upper_bound(X0,X1),X0) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f34,f366]) ).
fof(f456,plain,
! [X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X0)) = least_upper_bound(X0,X1),
inference(forward_demodulation,[status(thm)],[f30,f447]) ).
fof(f526,plain,
! [X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,identity)) = negative_part(greatest_lower_bound(X0,X1)),
inference(paramodulation,[status(thm)],[f43,f29]) ).
fof(f532,plain,
! [X0,X1] : greatest_lower_bound(identity,greatest_lower_bound(X0,X1)) = greatest_lower_bound(negative_part(X0),X1),
inference(paramodulation,[status(thm)],[f349,f29]) ).
fof(f549,plain,
! [X0,X1] : greatest_lower_bound(X0,negative_part(X1)) = negative_part(greatest_lower_bound(X0,X1)),
inference(forward_demodulation,[status(thm)],[f43,f526]) ).
fof(f553,plain,
! [X0,X1] : negative_part(greatest_lower_bound(X0,X1)) = greatest_lower_bound(negative_part(X0),X1),
inference(forward_demodulation,[status(thm)],[f349,f532]) ).
fof(f556,plain,
! [X0,X1] : greatest_lower_bound(X0,negative_part(X1)) = greatest_lower_bound(negative_part(X0),X1),
inference(forward_demodulation,[status(thm)],[f549,f553]) ).
fof(f567,plain,
! [X0,X1] : least_upper_bound(X0,least_upper_bound(X1,identity)) = positive_part(least_upper_bound(X0,X1)),
inference(paramodulation,[status(thm)],[f42,f30]) ).
fof(f568,plain,
! [X0,X1,X2] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X2,least_upper_bound(X0,X1)),
inference(paramodulation,[status(thm)],[f28,f30]) ).
fof(f573,plain,
! [X0,X1] : least_upper_bound(identity,least_upper_bound(X0,X1)) = least_upper_bound(positive_part(X0),X1),
inference(paramodulation,[status(thm)],[f357,f30]) ).
fof(f581,plain,
! [X0,X1] : least_upper_bound(X0,least_upper_bound(X0,X1)) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f31,f30]) ).
fof(f593,plain,
! [X0,X1] : least_upper_bound(X0,positive_part(X1)) = positive_part(least_upper_bound(X0,X1)),
inference(forward_demodulation,[status(thm)],[f42,f567]) ).
fof(f597,plain,
! [X0,X1] : positive_part(least_upper_bound(X0,X1)) = least_upper_bound(positive_part(X0),X1),
inference(forward_demodulation,[status(thm)],[f357,f573]) ).
fof(f600,plain,
! [X0,X1] : least_upper_bound(X0,positive_part(X1)) = least_upper_bound(positive_part(X0),X1),
inference(forward_demodulation,[status(thm)],[f593,f597]) ).
fof(f624,plain,
! [X0,X1] : multiply(X0,least_upper_bound(identity,X1)) = least_upper_bound(X0,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f73,f35]) ).
fof(f628,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X1,X0)) = least_upper_bound(multiply(inverse(X0),X1),identity),
inference(paramodulation,[status(thm)],[f25,f35]) ).
fof(f633,plain,
! [X0,X1] : multiply(X0,least_upper_bound(X1,identity)) = least_upper_bound(multiply(X0,X1),X0),
inference(paramodulation,[status(thm)],[f73,f35]) ).
fof(f646,plain,
! [X0,X1] : multiply(X0,positive_part(X1)) = least_upper_bound(X0,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f357,f624]) ).
fof(f647,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X1,X0)) = positive_part(multiply(inverse(X0),X1)),
inference(forward_demodulation,[status(thm)],[f42,f628]) ).
fof(f653,plain,
! [X0,X1] : multiply(X0,positive_part(X1)) = least_upper_bound(multiply(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f42,f633]) ).
fof(f736,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,negative_part(X0))) = X0,
inference(paramodulation,[status(thm)],[f556,f366]) ).
fof(f851,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,positive_part(X0))) = X0,
inference(paramodulation,[status(thm)],[f600,f374]) ).
fof(f1157,plain,
! [X0] : multiply(inverse(X0),positive_part(X0)) = least_upper_bound(inverse(X0),identity),
inference(paramodulation,[status(thm)],[f25,f646]) ).
fof(f1162,plain,
! [X0,X1] : multiply(X0,positive_part(multiply(inverse(X0),X1))) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f65,f646]) ).
fof(f1170,plain,
! [X0,X1] : greatest_lower_bound(X0,multiply(X0,positive_part(X1))) = X0,
inference(paramodulation,[status(thm)],[f646,f34]) ).
fof(f1172,plain,
! [X0] : multiply(inverse(X0),positive_part(X0)) = positive_part(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f42,f1157]) ).
fof(f1185,plain,
! [X0] : greatest_lower_bound(inverse(positive_part(X0)),identity) = inverse(positive_part(X0)),
inference(paramodulation,[status(thm)],[f25,f1170]) ).
fof(f1201,plain,
! [X0] : negative_part(inverse(positive_part(X0))) = inverse(positive_part(X0)),
inference(forward_demodulation,[status(thm)],[f43,f1185]) ).
fof(f1250,plain,
! [X0] : positive_part(inverse(positive_part(X0))) = identity,
inference(paramodulation,[status(thm)],[f1201,f418]) ).
fof(f2410,plain,
! [X0] : multiply(inverse(negative_part(X0)),identity) = positive_part(inverse(negative_part(X0))),
inference(paramodulation,[status(thm)],[f418,f1172]) ).
fof(f2416,plain,
! [X0] : inverse(inverse(X0)) = multiply(positive_part(X0),inverse(positive_part(inverse(X0)))),
inference(paramodulation,[status(thm)],[f1172,f191]) ).
fof(f2443,plain,
! [X0] : inverse(negative_part(X0)) = positive_part(inverse(negative_part(X0))),
inference(forward_demodulation,[status(thm)],[f73,f2410]) ).
fof(f2451,plain,
! [X0] : X0 = multiply(positive_part(X0),inverse(positive_part(inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f40,f2416]) ).
fof(f2488,plain,
! [X0] : negative_part(inverse(negative_part(X0))) = identity,
inference(paramodulation,[status(thm)],[f2443,f416]) ).
fof(f2697,plain,
! [X0,X1] : multiply(X0,greatest_lower_bound(identity,X1)) = greatest_lower_bound(X0,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f73,f36]) ).
fof(f2710,plain,
! [X0,X1] : multiply(X0,greatest_lower_bound(X1,identity)) = greatest_lower_bound(multiply(X0,X1),X0),
inference(paramodulation,[status(thm)],[f73,f36]) ).
fof(f2731,plain,
! [X0,X1] : multiply(X0,negative_part(X1)) = greatest_lower_bound(X0,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f349,f2697]) ).
fof(f2740,plain,
! [X0,X1] : multiply(X0,negative_part(X1)) = greatest_lower_bound(multiply(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f43,f2710]) ).
fof(f2763,plain,
! [X0,X1] : multiply(least_upper_bound(identity,X0),X1) = least_upper_bound(X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f24,f37]) ).
fof(f2767,plain,
! [X0,X1] : multiply(least_upper_bound(X0,X1),inverse(X0)) = least_upper_bound(identity,multiply(X1,inverse(X0))),
inference(paramodulation,[status(thm)],[f61,f37]) ).
fof(f2806,plain,
! [X0,X1] : multiply(positive_part(X0),X1) = least_upper_bound(X1,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f357,f2763]) ).
fof(f2808,plain,
! [X0,X1] : multiply(least_upper_bound(X0,X1),inverse(X0)) = positive_part(multiply(X1,inverse(X0))),
inference(forward_demodulation,[status(thm)],[f357,f2767]) ).
fof(f2840,plain,
! [X0,X1] : multiply(greatest_lower_bound(identity,X0),X1) = greatest_lower_bound(X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f24,f38]) ).
fof(f2873,plain,
! [X0,X1] : multiply(negative_part(X0),X1) = greatest_lower_bound(X1,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f349,f2840]) ).
fof(f3314,plain,
! [X0] : multiply(X0,negative_part(inverse(X0))) = greatest_lower_bound(X0,identity),
inference(paramodulation,[status(thm)],[f61,f2731]) ).
fof(f3359,plain,
! [X0] : multiply(X0,negative_part(inverse(X0))) = negative_part(X0),
inference(forward_demodulation,[status(thm)],[f43,f3314]) ).
fof(f3415,plain,
! [X0,X1] : multiply(inverse(least_upper_bound(X0,X1)),least_upper_bound(X0,X1)) = positive_part(multiply(inverse(least_upper_bound(X0,X1)),X0)),
inference(paramodulation,[status(thm)],[f581,f647]) ).
fof(f3416,plain,
! [X0,X1] : multiply(inverse(least_upper_bound(X0,X1)),least_upper_bound(X1,X0)) = positive_part(multiply(inverse(least_upper_bound(X0,X1)),X1)),
inference(paramodulation,[status(thm)],[f456,f647]) ).
fof(f3458,plain,
! [X0,X1] : identity = positive_part(multiply(inverse(least_upper_bound(X0,X1)),X0)),
inference(forward_demodulation,[status(thm)],[f25,f3415]) ).
fof(f3544,plain,
! [X0] : multiply(X0,positive_part(negative_part(inverse(X0)))) = least_upper_bound(negative_part(X0),X0),
inference(paramodulation,[status(thm)],[f3359,f653]) ).
fof(f3569,plain,
! [X0] : multiply(X0,identity) = least_upper_bound(negative_part(X0),X0),
inference(forward_demodulation,[status(thm)],[f418,f3544]) ).
fof(f3570,plain,
! [X0] : X0 = least_upper_bound(negative_part(X0),X0),
inference(forward_demodulation,[status(thm)],[f73,f3569]) ).
fof(f3606,plain,
! [X0,X1] : least_upper_bound(negative_part(X0),least_upper_bound(X0,X1)) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f3570,f30]) ).
fof(f3877,plain,
! [X0] : multiply(positive_part(positive_part(X0)),inverse(positive_part(inverse(X0)))) = least_upper_bound(inverse(positive_part(inverse(X0))),X0),
inference(paramodulation,[status(thm)],[f2451,f2806]) ).
fof(f3913,plain,
! [X0] : multiply(positive_part(X0),inverse(positive_part(inverse(X0)))) = least_upper_bound(inverse(positive_part(inverse(X0))),X0),
inference(forward_demodulation,[status(thm)],[f421,f3877]) ).
fof(f3914,plain,
! [X0] : X0 = least_upper_bound(inverse(positive_part(inverse(X0))),X0),
inference(forward_demodulation,[status(thm)],[f2451,f3913]) ).
fof(f4610,plain,
! [X0] : multiply(negative_part(inverse(X0)),X0) = greatest_lower_bound(X0,identity),
inference(paramodulation,[status(thm)],[f25,f2873]) ).
fof(f4652,plain,
! [X0] : multiply(negative_part(inverse(X0)),X0) = negative_part(X0),
inference(forward_demodulation,[status(thm)],[f43,f4610]) ).
fof(f4706,plain,
! [X0] : X0 = multiply(inverse(negative_part(inverse(X0))),negative_part(X0)),
inference(paramodulation,[status(thm)],[f4652,f64]) ).
fof(f5115,plain,
! [X0,X1] : identity = positive_part(multiply(inverse(least_upper_bound(X0,X1)),X1)),
inference(paramodulation,[status(thm)],[f28,f3458]) ).
fof(f5165,plain,
! [X0,X1] : multiply(inverse(least_upper_bound(X0,X1)),least_upper_bound(X1,X0)) = identity,
inference(backward_demodulation,[status(thm)],[f5115,f3416]) ).
fof(f5370,plain,
! [X0,X1] : least_upper_bound(negative_part(X0),least_upper_bound(X1,X0)) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f28,f3606]) ).
fof(f6248,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(identity,X1)) = greatest_lower_bound(positive_part(X0),least_upper_bound(X0,X1)),
inference(paramodulation,[status(thm)],[f42,f44]) ).
fof(f6276,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,negative_part(X0))) = greatest_lower_bound(least_upper_bound(X0,X1),X0),
inference(paramodulation,[status(thm)],[f365,f44]) ).
fof(f6336,plain,
! [X0,X1] : least_upper_bound(X0,negative_part(X1)) = greatest_lower_bound(positive_part(X0),least_upper_bound(X0,X1)),
inference(forward_demodulation,[status(thm)],[f349,f6248]) ).
fof(f6356,plain,
! [X0,X1] : X0 = greatest_lower_bound(least_upper_bound(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f736,f6276]) ).
fof(f6451,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,positive_part(X0))) = least_upper_bound(greatest_lower_bound(X0,X1),X0),
inference(paramodulation,[status(thm)],[f373,f45]) ).
fof(f6530,plain,
! [X0,X1] : X0 = least_upper_bound(greatest_lower_bound(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f851,f6451]) ).
fof(f6592,plain,
! [X0,X1] : X0 = greatest_lower_bound(least_upper_bound(X1,X0),X0),
inference(paramodulation,[status(thm)],[f28,f6356]) ).
fof(f6676,plain,
! [X0,X1] : X0 = least_upper_bound(greatest_lower_bound(X1,X0),X0),
inference(paramodulation,[status(thm)],[f27,f6530]) ).
fof(f6774,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,least_upper_bound(X0,X1)),
inference(paramodulation,[status(thm)],[f6592,f6530]) ).
fof(f6876,plain,
! [X0,X1] : least_upper_bound(greatest_lower_bound(X0,X1),positive_part(X1)) = positive_part(X1),
inference(paramodulation,[status(thm)],[f6676,f593]) ).
fof(f7371,plain,
! [X0,X1,X2] : least_upper_bound(least_upper_bound(X0,X1),X2) = least_upper_bound(X2,least_upper_bound(X0,least_upper_bound(X1,X2))),
inference(paramodulation,[status(thm)],[f30,f6774]) ).
fof(f7382,plain,
! [X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X0)) = least_upper_bound(least_upper_bound(X1,X0),least_upper_bound(X0,X1)),
inference(paramodulation,[status(thm)],[f456,f6774]) ).
fof(f7450,plain,
! [X0,X1,X2] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X2,least_upper_bound(X0,least_upper_bound(X1,X2))),
inference(forward_demodulation,[status(thm)],[f30,f7371]) ).
fof(f7471,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(least_upper_bound(X0,X1),least_upper_bound(X1,X0)),
inference(forward_demodulation,[status(thm)],[f6774,f7382]) ).
fof(f7472,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X1,least_upper_bound(X1,X0))),
inference(forward_demodulation,[status(thm)],[f30,f7471]) ).
fof(f7473,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,least_upper_bound(X1,X0)),
inference(forward_demodulation,[status(thm)],[f7450,f7472]) ).
fof(f9231,plain,
! [X0] : multiply(inverse(negative_part(inverse(X0))),negative_part(negative_part(X0))) = greatest_lower_bound(X0,inverse(negative_part(inverse(X0)))),
inference(paramodulation,[status(thm)],[f4706,f2740]) ).
fof(f9298,plain,
! [X0] : multiply(inverse(negative_part(inverse(X0))),negative_part(X0)) = greatest_lower_bound(X0,inverse(negative_part(inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f426,f9231]) ).
fof(f9299,plain,
! [X0] : X0 = greatest_lower_bound(X0,inverse(negative_part(inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f4706,f9298]) ).
fof(f9322,plain,
! [X0] : inverse(X0) = greatest_lower_bound(inverse(X0),inverse(negative_part(X0))),
inference(paramodulation,[status(thm)],[f40,f9299]) ).
fof(f10039,plain,
! [X0,X1] : least_upper_bound(least_upper_bound(X0,X1),negative_part(X1)) = least_upper_bound(negative_part(X1),least_upper_bound(X1,X0)),
inference(paramodulation,[status(thm)],[f5370,f7473]) ).
fof(f10164,plain,
! [X0,X1] : least_upper_bound(X0,least_upper_bound(X1,negative_part(X1))) = least_upper_bound(negative_part(X1),least_upper_bound(X1,X0)),
inference(forward_demodulation,[status(thm)],[f30,f10039]) ).
fof(f10165,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(negative_part(X1),least_upper_bound(X1,X0)),
inference(forward_demodulation,[status(thm)],[f365,f10164]) ).
fof(f10584,plain,
! [X0] : least_upper_bound(inverse(X0),positive_part(inverse(negative_part(X0)))) = positive_part(inverse(negative_part(X0))),
inference(paramodulation,[status(thm)],[f9322,f6876]) ).
fof(f10649,plain,
! [X0] : least_upper_bound(inverse(X0),inverse(negative_part(X0))) = positive_part(inverse(negative_part(X0))),
inference(forward_demodulation,[status(thm)],[f2443,f10584]) ).
fof(f10650,plain,
! [X0] : least_upper_bound(inverse(X0),inverse(negative_part(X0))) = inverse(negative_part(X0)),
inference(forward_demodulation,[status(thm)],[f2443,f10649]) ).
fof(f11032,plain,
! [X0,X1] : least_upper_bound(X0,inverse(negative_part(X1))) = least_upper_bound(identity,least_upper_bound(inverse(negative_part(X1)),X0)),
inference(paramodulation,[status(thm)],[f2488,f10165]) ).
fof(f11133,plain,
! [X0,X1] : least_upper_bound(X0,inverse(negative_part(X1))) = positive_part(least_upper_bound(inverse(negative_part(X1)),X0)),
inference(forward_demodulation,[status(thm)],[f357,f11032]) ).
fof(f11134,plain,
! [X0,X1] : least_upper_bound(X0,inverse(negative_part(X1))) = least_upper_bound(inverse(negative_part(X1)),positive_part(X0)),
inference(forward_demodulation,[status(thm)],[f593,f11133]) ).
fof(f17787,plain,
! [X0,X1,X2] : least_upper_bound(greatest_lower_bound(X0,X1),least_upper_bound(X0,X2)) = least_upper_bound(X2,X0),
inference(paramodulation,[status(thm)],[f6530,f568]) ).
fof(f20833,plain,
! [X0,X1] : inverse(least_upper_bound(X0,X1)) = multiply(inverse(identity),inverse(least_upper_bound(X1,X0))),
inference(paramodulation,[status(thm)],[f5165,f165]) ).
fof(f21052,plain,
! [X0,X1] : inverse(least_upper_bound(X0,X1)) = inverse(multiply(least_upper_bound(X1,X0),identity)),
inference(forward_demodulation,[status(thm)],[f41,f20833]) ).
fof(f21053,plain,
! [X0,X1] : inverse(least_upper_bound(X0,X1)) = inverse(least_upper_bound(X1,X0)),
inference(forward_demodulation,[status(thm)],[f73,f21052]) ).
fof(f21160,plain,
! [X0,X1] : multiply(least_upper_bound(X0,X1),inverse(least_upper_bound(X1,X0))) = identity,
inference(paramodulation,[status(thm)],[f21053,f61]) ).
fof(f30201,plain,
! [X0] : least_upper_bound(inverse(positive_part(inverse(X0))),negative_part(X0)) = greatest_lower_bound(positive_part(inverse(positive_part(inverse(X0)))),X0),
inference(paramodulation,[status(thm)],[f3914,f6336]) ).
fof(f30361,plain,
! [X0] : least_upper_bound(inverse(positive_part(inverse(X0))),negative_part(X0)) = greatest_lower_bound(identity,X0),
inference(forward_demodulation,[status(thm)],[f1250,f30201]) ).
fof(f30362,plain,
! [X0] : least_upper_bound(inverse(positive_part(inverse(X0))),negative_part(X0)) = negative_part(X0),
inference(forward_demodulation,[status(thm)],[f349,f30361]) ).
fof(f35637,plain,
! [X0,X1] : multiply(least_upper_bound(least_upper_bound(X0,X1),X0),inverse(least_upper_bound(X0,X1))) = identity,
inference(paramodulation,[status(thm)],[f581,f21160]) ).
fof(f35929,plain,
! [X0,X1] : positive_part(multiply(X0,inverse(least_upper_bound(X0,X1)))) = identity,
inference(forward_demodulation,[status(thm)],[f2808,f35637]) ).
fof(f47436,plain,
! [X0,X1] : multiply(X0,identity) = least_upper_bound(X0,inverse(least_upper_bound(inverse(X0),X1))),
inference(paramodulation,[status(thm)],[f35929,f1162]) ).
fof(f47533,plain,
! [X0,X1] : X0 = least_upper_bound(X0,inverse(least_upper_bound(inverse(X0),X1))),
inference(forward_demodulation,[status(thm)],[f73,f47436]) ).
fof(f47759,plain,
! [X0,X1,X2] : least_upper_bound(greatest_lower_bound(X0,X1),X0) = least_upper_bound(inverse(least_upper_bound(inverse(X0),X2)),X0),
inference(paramodulation,[status(thm)],[f47533,f17787]) ).
fof(f47864,plain,
! [X0,X1] : X0 = least_upper_bound(inverse(least_upper_bound(inverse(X0),X1)),X0),
inference(forward_demodulation,[status(thm)],[f6530,f47759]) ).
fof(f103447,plain,
! [X0] : positive_part(inverse(X0)) = least_upper_bound(inverse(negative_part(X0)),positive_part(inverse(X0))),
inference(paramodulation,[status(thm)],[f30362,f47864]) ).
fof(f103651,plain,
! [X0] : positive_part(inverse(X0)) = least_upper_bound(inverse(X0),inverse(negative_part(X0))),
inference(forward_demodulation,[status(thm)],[f11134,f103447]) ).
fof(f103683,plain,
! [X0] : X0 = multiply(positive_part(X0),inverse(inverse(negative_part(X0)))),
inference(backward_demodulation,[status(thm)],[f104493,f2451]) ).
fof(f104493,plain,
! [X0] : positive_part(inverse(X0)) = inverse(negative_part(X0)),
inference(forward_demodulation,[status(thm)],[f10650,f103651]) ).
fof(f104837,plain,
a != a,
inference(backward_demodulation,[status(thm)],[f104839,f46]) ).
fof(f104839,plain,
! [X0] : X0 = multiply(positive_part(X0),negative_part(X0)),
inference(forward_demodulation,[status(thm)],[f40,f103683]) ).
fof(f106631,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f104837]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP167-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:08:43 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 177.76/22.86 % Refutation found
% 177.76/22.86 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 177.76/22.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 10.51/23.69 % Elapsed time: 23.324020 seconds
% 10.51/23.69 % CPU time: 180.383106 seconds
% 10.51/23.69 % Total memory used: 1.181 GB
% 10.51/23.69 % Net memory used: 1.108 GB
%------------------------------------------------------------------------------