%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP186-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 12:33:02 PM UTC 2026
% Result : Unsatisfiable 172.90s 22.28s
% Output : CNFRefutation 120.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 20
% Syntax : Number of formulae : 161 ( 161 unt; 6 def)
% Number of atoms : 161 ( 160 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 : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 160 ( 160 !; 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(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(f16,negated_conjecture,
least_upper_bound(multiply(a,b),identity) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f20,plain,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f22,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(f23,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(f26,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f27,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f28,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(f29,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(f30,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(f31,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(f32,plain,
least_upper_bound(multiply(a,b),identity) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f33,definition,
sF1_fnc = multiply(a,b),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f34,definition,
sF0_fnc = least_upper_bound(sF1_fnc,identity),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f35,definition,
sF5_fnc = inverse(b),
introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition]) ).
fof(f36,definition,
sF4_fnc = greatest_lower_bound(a,sF5_fnc),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f37,definition,
sF3_fnc = inverse(sF4_fnc),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f38,definition,
sF2_fnc = multiply(a,sF3_fnc),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f39,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f32,f38,f37,f36,f35,f34,f33]) ).
fof(f40,plain,
sF0_fnc = least_upper_bound(identity,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f21,f34]) ).
fof(f41,plain,
multiply(sF3_fnc,sF4_fnc) = identity,
inference(paramodulation,[status(thm)],[f37,f18]) ).
fof(f42,plain,
multiply(sF5_fnc,b) = identity,
inference(paramodulation,[status(thm)],[f35,f18]) ).
fof(f44,plain,
! [X0] : multiply(identity,X0) = multiply(sF5_fnc,multiply(b,X0)),
inference(paramodulation,[status(thm)],[f42,f19]) ).
fof(f45,plain,
! [X0] : multiply(identity,X0) = multiply(sF3_fnc,multiply(sF4_fnc,X0)),
inference(paramodulation,[status(thm)],[f41,f19]) ).
fof(f47,plain,
! [X0] : multiply(sF1_fnc,X0) = multiply(a,multiply(b,X0)),
inference(paramodulation,[status(thm)],[f33,f19]) ).
fof(f48,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f18,f19]) ).
fof(f52,plain,
! [X0] : X0 = multiply(sF5_fnc,multiply(b,X0)),
inference(forward_demodulation,[status(thm)],[f17,f44]) ).
fof(f53,plain,
! [X0] : X0 = multiply(sF3_fnc,multiply(sF4_fnc,X0)),
inference(forward_demodulation,[status(thm)],[f17,f45]) ).
fof(f54,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f17,f48]) ).
fof(f55,plain,
least_upper_bound(a,sF4_fnc) = a,
inference(paramodulation,[status(thm)],[f36,f26]) ).
fof(f58,plain,
greatest_lower_bound(identity,sF0_fnc) = identity,
inference(paramodulation,[status(thm)],[f40,f27]) ).
fof(f85,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f21,f27]) ).
fof(f96,plain,
greatest_lower_bound(sF1_fnc,sF0_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f40,f85]) ).
fof(f106,plain,
greatest_lower_bound(sF0_fnc,sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f20,f96]) ).
fof(f127,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X0,X1),X2)) = greatest_lower_bound(X0,X2),
inference(paramodulation,[status(thm)],[f27,f22]) ).
fof(f154,plain,
! [X0] : multiply(b,X0) = multiply(inverse(sF5_fnc),X0),
inference(paramodulation,[status(thm)],[f52,f54]) ).
fof(f156,plain,
! [X0] : multiply(sF4_fnc,X0) = multiply(inverse(sF3_fnc),X0),
inference(paramodulation,[status(thm)],[f53,f54]) ).
fof(f160,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f54,f54]) ).
fof(f161,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f18,f54]) ).
fof(f168,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f160,f161]) ).
fof(f194,plain,
! [X0] : least_upper_bound(identity,least_upper_bound(sF1_fnc,X0)) = least_upper_bound(sF0_fnc,X0),
inference(paramodulation,[status(thm)],[f40,f23]) ).
fof(f197,plain,
! [X0,X1,X2] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X1,X0),X2),
inference(paramodulation,[status(thm)],[f21,f23]) ).
fof(f210,plain,
! [X0,X1,X2] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X1,least_upper_bound(X0,X2)),
inference(forward_demodulation,[status(thm)],[f23,f197]) ).
fof(f282,plain,
! [X0] : multiply(b,multiply(sF5_fnc,X0)) = X0,
inference(paramodulation,[status(thm)],[f54,f154]) ).
fof(f284,plain,
multiply(b,identity) = inverse(sF5_fnc),
inference(paramodulation,[status(thm)],[f168,f154]) ).
fof(f291,plain,
b = inverse(sF5_fnc),
inference(forward_demodulation,[status(thm)],[f168,f284]) ).
fof(f306,plain,
! [X0] : multiply(a,least_upper_bound(b,X0)) = least_upper_bound(sF1_fnc,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f33,f28]) ).
fof(f312,plain,
! [X0,X1] : multiply(X0,least_upper_bound(identity,X1)) = least_upper_bound(X0,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f168,f28]) ).
fof(f323,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X1,X0)) = least_upper_bound(multiply(inverse(X0),X1),identity),
inference(paramodulation,[status(thm)],[f18,f28]) ).
fof(f348,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X1,X0)) = least_upper_bound(identity,multiply(inverse(X0),X1)),
inference(forward_demodulation,[status(thm)],[f21,f323]) ).
fof(f374,plain,
! [X0] : multiply(sF4_fnc,multiply(sF3_fnc,X0)) = X0,
inference(paramodulation,[status(thm)],[f54,f156]) ).
fof(f424,plain,
! [X0] : multiply(a,greatest_lower_bound(sF3_fnc,X0)) = greatest_lower_bound(sF2_fnc,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f38,f29]) ).
fof(f434,plain,
! [X0,X1] : multiply(b,greatest_lower_bound(X0,multiply(sF5_fnc,X1))) = greatest_lower_bound(multiply(b,X0),X1),
inference(paramodulation,[status(thm)],[f282,f29]) ).
fof(f445,plain,
! [X0,X1,X2] : multiply(inverse(X0),greatest_lower_bound(X1,multiply(X0,X2))) = greatest_lower_bound(multiply(inverse(X0),X1),X2),
inference(paramodulation,[status(thm)],[f54,f29]) ).
fof(f573,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(paramodulation,[status(thm)],[f18,f160]) ).
fof(f574,plain,
! [X0] : multiply(X0,identity) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f168,f160]) ).
fof(f590,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f168,f574]) ).
fof(f612,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(paramodulation,[status(thm)],[f19,f573]) ).
fof(f672,plain,
! [X0,X1,X2] : multiply(least_upper_bound(X0,X1),X2) = least_upper_bound(multiply(X1,X2),multiply(X0,X2)),
inference(paramodulation,[status(thm)],[f21,f30]) ).
fof(f690,plain,
! [X0,X1] : multiply(least_upper_bound(identity,X0),X1) = least_upper_bound(X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f17,f30]) ).
fof(f692,plain,
! [X0,X1] : multiply(least_upper_bound(X0,X1),inverse(X0)) = least_upper_bound(identity,multiply(X1,inverse(X0))),
inference(paramodulation,[status(thm)],[f573,f30]) ).
fof(f723,plain,
! [X0,X1,X2] : multiply(least_upper_bound(X0,X1),X2) = multiply(least_upper_bound(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f30,f672]) ).
fof(f911,plain,
! [X0,X1,X2] : multiply(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(multiply(X1,X2),multiply(X0,X2)),
inference(paramodulation,[status(thm)],[f20,f31]) ).
fof(f923,plain,
! [X0] : multiply(greatest_lower_bound(a,X0),sF3_fnc) = greatest_lower_bound(sF2_fnc,multiply(X0,sF3_fnc)),
inference(paramodulation,[status(thm)],[f38,f31]) ).
fof(f924,plain,
! [X0] : multiply(greatest_lower_bound(a,X0),b) = greatest_lower_bound(sF1_fnc,multiply(X0,b)),
inference(paramodulation,[status(thm)],[f33,f31]) ).
fof(f964,plain,
! [X0,X1,X2] : multiply(greatest_lower_bound(X0,X1),X2) = multiply(greatest_lower_bound(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f31,f911]) ).
fof(f1119,plain,
! [X0] : multiply(sF1_fnc,multiply(sF5_fnc,X0)) = multiply(a,X0),
inference(paramodulation,[status(thm)],[f282,f47]) ).
fof(f3579,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = multiply(inverse(X1),identity),
inference(paramodulation,[status(thm)],[f612,f54]) ).
fof(f3664,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f168,f3579]) ).
fof(f3696,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),inverse(inverse(X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f3664,f3664]) ).
fof(f3701,plain,
! [X0] : inverse(multiply(X0,b)) = multiply(sF5_fnc,inverse(X0)),
inference(paramodulation,[status(thm)],[f3664,f52]) ).
fof(f3705,plain,
! [X0] : multiply(sF4_fnc,inverse(X0)) = inverse(multiply(X0,sF3_fnc)),
inference(paramodulation,[status(thm)],[f3664,f374]) ).
fof(f3760,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f590,f3696]) ).
fof(f3777,plain,
! [X0] : multiply(inverse(X0),sF5_fnc) = inverse(multiply(b,X0)),
inference(paramodulation,[status(thm)],[f52,f3760]) ).
fof(f4063,plain,
! [X0,X1] : identity = multiply(least_upper_bound(X0,X1),inverse(least_upper_bound(X1,X0))),
inference(paramodulation,[status(thm)],[f573,f723]) ).
fof(f5371,plain,
! [X0,X1] : identity = multiply(greatest_lower_bound(X0,X1),inverse(greatest_lower_bound(X1,X0))),
inference(paramodulation,[status(thm)],[f573,f964]) ).
fof(f5408,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(greatest_lower_bound(X1,X2),X0))) = inverse(greatest_lower_bound(X2,X1)),
inference(paramodulation,[status(thm)],[f964,f3664]) ).
fof(f5460,plain,
! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = inverse(greatest_lower_bound(X1,X0)),
inference(forward_demodulation,[status(thm)],[f3664,f5408]) ).
fof(f5484,plain,
! [X0,X1,X2] : inverse(multiply(greatest_lower_bound(X0,X1),X2)) = inverse(greatest_lower_bound(multiply(X1,X2),multiply(X0,X2))),
inference(paramodulation,[status(thm)],[f31,f5460]) ).
fof(f5509,plain,
! [X0,X1] : multiply(inverse(greatest_lower_bound(X0,X1)),greatest_lower_bound(X1,X0)) = identity,
inference(paramodulation,[status(thm)],[f5460,f18]) ).
fof(f5516,plain,
! [X0,X1,X2] : inverse(multiply(greatest_lower_bound(X0,X1),X2)) = inverse(multiply(greatest_lower_bound(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f31,f5484]) ).
fof(f9884,plain,
inverse(multiply(sF4_fnc,b)) = multiply(sF5_fnc,sF3_fnc),
inference(paramodulation,[status(thm)],[f37,f3701]) ).
fof(f11416,plain,
identity = multiply(least_upper_bound(sF4_fnc,a),inverse(a)),
inference(paramodulation,[status(thm)],[f55,f4063]) ).
fof(f11636,plain,
identity = multiply(least_upper_bound(a,sF4_fnc),inverse(a)),
inference(forward_demodulation,[status(thm)],[f723,f11416]) ).
fof(f11637,plain,
identity = least_upper_bound(identity,multiply(sF4_fnc,inverse(a))),
inference(forward_demodulation,[status(thm)],[f692,f11636]) ).
fof(f11638,plain,
identity = least_upper_bound(identity,inverse(multiply(a,sF3_fnc))),
inference(forward_demodulation,[status(thm)],[f3705,f11637]) ).
fof(f11639,plain,
identity = least_upper_bound(identity,inverse(sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f38,f11638]) ).
fof(f12136,plain,
multiply(inverse(inverse(sF2_fnc)),identity) = least_upper_bound(identity,multiply(inverse(inverse(sF2_fnc)),identity)),
inference(paramodulation,[status(thm)],[f11639,f348]) ).
fof(f12227,plain,
inverse(inverse(sF2_fnc)) = least_upper_bound(identity,multiply(inverse(inverse(sF2_fnc)),identity)),
inference(forward_demodulation,[status(thm)],[f168,f12136]) ).
fof(f12228,plain,
sF2_fnc = least_upper_bound(identity,multiply(inverse(inverse(sF2_fnc)),identity)),
inference(forward_demodulation,[status(thm)],[f590,f12227]) ).
fof(f12229,plain,
sF2_fnc = least_upper_bound(identity,inverse(inverse(sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f168,f12228]) ).
fof(f12230,plain,
sF2_fnc = least_upper_bound(identity,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f590,f12229]) ).
fof(f12281,plain,
! [X0] : least_upper_bound(identity,least_upper_bound(X0,sF2_fnc)) = least_upper_bound(X0,sF2_fnc),
inference(paramodulation,[status(thm)],[f12230,f210]) ).
fof(f14915,plain,
identity = multiply(sF4_fnc,inverse(greatest_lower_bound(sF5_fnc,a))),
inference(paramodulation,[status(thm)],[f36,f5371]) ).
fof(f15138,plain,
identity = inverse(multiply(greatest_lower_bound(sF5_fnc,a),sF3_fnc)),
inference(forward_demodulation,[status(thm)],[f3705,f14915]) ).
fof(f15139,plain,
identity = inverse(multiply(greatest_lower_bound(a,sF5_fnc),sF3_fnc)),
inference(forward_demodulation,[status(thm)],[f5516,f15138]) ).
fof(f15140,plain,
identity = inverse(greatest_lower_bound(sF2_fnc,multiply(sF5_fnc,sF3_fnc))),
inference(forward_demodulation,[status(thm)],[f923,f15139]) ).
fof(f21386,plain,
least_upper_bound(sF0_fnc,sF2_fnc) = least_upper_bound(sF1_fnc,sF2_fnc),
inference(paramodulation,[status(thm)],[f194,f12281]) ).
fof(f22734,plain,
multiply(identity,greatest_lower_bound(multiply(sF5_fnc,sF3_fnc),sF2_fnc)) = identity,
inference(paramodulation,[status(thm)],[f15140,f5509]) ).
fof(f22741,plain,
multiply(identity,sF5_fnc) = inverse(multiply(b,greatest_lower_bound(sF2_fnc,multiply(sF5_fnc,sF3_fnc)))),
inference(paramodulation,[status(thm)],[f15140,f3777]) ).
fof(f22757,plain,
greatest_lower_bound(multiply(sF5_fnc,sF3_fnc),sF2_fnc) = identity,
inference(forward_demodulation,[status(thm)],[f17,f22734]) ).
fof(f22759,plain,
greatest_lower_bound(sF2_fnc,multiply(sF5_fnc,sF3_fnc)) = identity,
inference(forward_demodulation,[status(thm)],[f20,f22757]) ).
fof(f22779,plain,
sF5_fnc = inverse(multiply(b,greatest_lower_bound(sF2_fnc,multiply(sF5_fnc,sF3_fnc)))),
inference(forward_demodulation,[status(thm)],[f17,f22741]) ).
fof(f22780,plain,
sF5_fnc = inverse(greatest_lower_bound(multiply(b,sF2_fnc),sF3_fnc)),
inference(forward_demodulation,[status(thm)],[f434,f22779]) ).
fof(f22781,plain,
sF5_fnc = inverse(greatest_lower_bound(sF3_fnc,multiply(b,sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f5460,f22780]) ).
fof(f23235,plain,
greatest_lower_bound(sF3_fnc,multiply(b,sF2_fnc)) = inverse(sF5_fnc),
inference(paramodulation,[status(thm)],[f22781,f590]) ).
fof(f23273,plain,
greatest_lower_bound(sF3_fnc,multiply(b,sF2_fnc)) = b,
inference(forward_demodulation,[status(thm)],[f291,f23235]) ).
fof(f23307,plain,
least_upper_bound(sF3_fnc,b) = sF3_fnc,
inference(paramodulation,[status(thm)],[f23273,f26]) ).
fof(f23361,plain,
least_upper_bound(b,sF3_fnc) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f21,f23307]) ).
fof(f23362,plain,
multiply(a,sF3_fnc) = least_upper_bound(sF1_fnc,multiply(a,sF3_fnc)),
inference(paramodulation,[status(thm)],[f23361,f306]) ).
fof(f23392,plain,
sF2_fnc = least_upper_bound(sF1_fnc,multiply(a,sF3_fnc)),
inference(forward_demodulation,[status(thm)],[f38,f23362]) ).
fof(f23393,plain,
sF2_fnc = least_upper_bound(sF1_fnc,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f38,f23392]) ).
fof(f23398,plain,
sF2_fnc = least_upper_bound(sF0_fnc,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f21386,f23393]) ).
fof(f23835,plain,
! [X0] : greatest_lower_bound(sF0_fnc,greatest_lower_bound(sF2_fnc,X0)) = greatest_lower_bound(sF0_fnc,X0),
inference(paramodulation,[status(thm)],[f23398,f127]) ).
fof(f24032,plain,
! [X0] : multiply(sF0_fnc,X0) = least_upper_bound(X0,multiply(sF1_fnc,X0)),
inference(paramodulation,[status(thm)],[f40,f690]) ).
fof(f33742,plain,
multiply(sF4_fnc,b) = greatest_lower_bound(sF1_fnc,multiply(sF5_fnc,b)),
inference(paramodulation,[status(thm)],[f36,f924]) ).
fof(f33816,plain,
multiply(sF4_fnc,b) = greatest_lower_bound(sF1_fnc,identity),
inference(forward_demodulation,[status(thm)],[f42,f33742]) ).
fof(f33820,plain,
inverse(greatest_lower_bound(identity,sF1_fnc)) = multiply(sF5_fnc,sF3_fnc),
inference(backward_demodulation,[status(thm)],[f33856,f9884]) ).
fof(f33856,plain,
multiply(sF4_fnc,b) = greatest_lower_bound(identity,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f20,f33816]) ).
fof(f40436,plain,
greatest_lower_bound(sF0_fnc,identity) = greatest_lower_bound(sF0_fnc,multiply(sF5_fnc,sF3_fnc)),
inference(paramodulation,[status(thm)],[f22759,f23835]) ).
fof(f40558,plain,
greatest_lower_bound(identity,sF0_fnc) = greatest_lower_bound(sF0_fnc,multiply(sF5_fnc,sF3_fnc)),
inference(forward_demodulation,[status(thm)],[f20,f40436]) ).
fof(f40559,plain,
identity = greatest_lower_bound(sF0_fnc,multiply(sF5_fnc,sF3_fnc)),
inference(forward_demodulation,[status(thm)],[f58,f40558]) ).
fof(f53990,plain,
! [X0] : multiply(X0,sF0_fnc) = least_upper_bound(X0,multiply(X0,sF1_fnc)),
inference(paramodulation,[status(thm)],[f40,f312]) ).
fof(f61794,plain,
multiply(sF1_fnc,sF0_fnc) = multiply(sF0_fnc,sF1_fnc),
inference(paramodulation,[status(thm)],[f24032,f53990]) ).
fof(f62388,plain,
multiply(inverse(sF5_fnc),identity) = greatest_lower_bound(multiply(inverse(sF5_fnc),sF0_fnc),sF3_fnc),
inference(paramodulation,[status(thm)],[f40559,f445]) ).
fof(f62735,plain,
inverse(sF5_fnc) = greatest_lower_bound(multiply(inverse(sF5_fnc),sF0_fnc),sF3_fnc),
inference(forward_demodulation,[status(thm)],[f168,f62388]) ).
fof(f62736,plain,
b = greatest_lower_bound(multiply(inverse(sF5_fnc),sF0_fnc),sF3_fnc),
inference(forward_demodulation,[status(thm)],[f291,f62735]) ).
fof(f62737,plain,
b = greatest_lower_bound(sF3_fnc,multiply(inverse(sF5_fnc),sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f20,f62736]) ).
fof(f62738,plain,
b = greatest_lower_bound(sF3_fnc,multiply(b,sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f291,f62737]) ).
fof(f63161,plain,
multiply(a,b) = greatest_lower_bound(sF2_fnc,multiply(a,multiply(b,sF0_fnc))),
inference(paramodulation,[status(thm)],[f62738,f424]) ).
fof(f63199,plain,
sF1_fnc = greatest_lower_bound(sF2_fnc,multiply(a,multiply(b,sF0_fnc))),
inference(forward_demodulation,[status(thm)],[f33,f63161]) ).
fof(f63200,plain,
sF1_fnc = greatest_lower_bound(sF2_fnc,multiply(sF1_fnc,sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f47,f63199]) ).
fof(f63201,plain,
sF1_fnc = greatest_lower_bound(sF2_fnc,multiply(sF0_fnc,sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f61794,f63200]) ).
fof(f63266,plain,
greatest_lower_bound(sF0_fnc,sF1_fnc) = greatest_lower_bound(sF0_fnc,multiply(sF0_fnc,sF1_fnc)),
inference(paramodulation,[status(thm)],[f63201,f23835]) ).
fof(f63306,plain,
sF1_fnc = greatest_lower_bound(sF0_fnc,multiply(sF0_fnc,sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f106,f63266]) ).
fof(f63362,plain,
multiply(inverse(sF0_fnc),sF1_fnc) = greatest_lower_bound(multiply(inverse(sF0_fnc),sF0_fnc),sF1_fnc),
inference(paramodulation,[status(thm)],[f63306,f445]) ).
fof(f63399,plain,
multiply(inverse(sF0_fnc),sF1_fnc) = greatest_lower_bound(sF1_fnc,multiply(inverse(sF0_fnc),sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f20,f63362]) ).
fof(f63400,plain,
multiply(inverse(sF0_fnc),sF1_fnc) = greatest_lower_bound(sF1_fnc,identity),
inference(forward_demodulation,[status(thm)],[f18,f63399]) ).
fof(f63433,plain,
multiply(inverse(sF0_fnc),sF1_fnc) = greatest_lower_bound(identity,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f20,f63400]) ).
fof(f76278,plain,
multiply(sF1_fnc,inverse(greatest_lower_bound(identity,sF1_fnc))) = inverse(inverse(sF0_fnc)),
inference(paramodulation,[status(thm)],[f63433,f3664]) ).
fof(f76359,plain,
multiply(sF1_fnc,multiply(sF5_fnc,sF3_fnc)) = inverse(inverse(sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f33820,f76278]) ).
fof(f76360,plain,
multiply(a,sF3_fnc) = inverse(inverse(sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f1119,f76359]) ).
fof(f76361,plain,
sF2_fnc = inverse(inverse(sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f38,f76360]) ).
fof(f76362,plain,
sF2_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f590,f76361]) ).
fof(f76363,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f76362,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP186-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 20:05:26 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 172.90/22.28 % Refutation found
% 172.90/22.28 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 172.90/22.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 81.43/24.32 % Elapsed time: 23.716769 seconds
% 81.43/24.32 % CPU time: 167.468865 seconds
% 81.43/24.32 % Total memory used: 20.977 GB
% 81.43/24.32 % Net memory used: 20.956 GB
%------------------------------------------------------------------------------