%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP167-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 12:32:56 PM UTC 2026
% Result : Unsatisfiable 265.67s 34.10s
% Output : CNFRefutation 261.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 17
% Syntax : Number of formulae : 135 ( 135 unt; 3 def)
% Number of atoms : 135 ( 134 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 151 ( 151 !; 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,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
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,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f33,definition,
sF1_fnc = least_upper_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f34,definition,
sF2_fnc = greatest_lower_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f35,definition,
sF0_fnc = multiply(sF1_fnc,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f36,plain,
a != sF0_fnc,
inference(definition_folding,[],[f32,f35,f34,f33]) ).
fof(f38,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f18,f19]) ).
fof(f42,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f17,f38]) ).
fof(f43,plain,
! [X0] : multiply(sF0_fnc,X0) = multiply(sF1_fnc,multiply(sF2_fnc,X0)),
inference(paramodulation,[status(thm)],[f35,f19]) ).
fof(f44,plain,
least_upper_bound(a,sF2_fnc) = a,
inference(paramodulation,[status(thm)],[f34,f26]) ).
fof(f47,plain,
greatest_lower_bound(a,sF1_fnc) = a,
inference(paramodulation,[status(thm)],[f33,f27]) ).
fof(f56,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f20,f26]) ).
fof(f60,plain,
least_upper_bound(identity,sF2_fnc) = identity,
inference(paramodulation,[status(thm)],[f34,f56]) ).
fof(f71,plain,
sF2_fnc = multiply(inverse(sF1_fnc),sF0_fnc),
inference(paramodulation,[status(thm)],[f35,f42]) ).
fof(f73,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f42,f42]) ).
fof(f74,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f18,f42]) ).
fof(f77,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f73,f74]) ).
fof(f95,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f21,f27]) ).
fof(f101,plain,
greatest_lower_bound(identity,sF1_fnc) = identity,
inference(paramodulation,[status(thm)],[f33,f95]) ).
fof(f120,plain,
least_upper_bound(sF1_fnc,identity) = sF1_fnc,
inference(paramodulation,[status(thm)],[f101,f56]) ).
fof(f122,plain,
least_upper_bound(identity,sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f21,f120]) ).
fof(f130,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X2,greatest_lower_bound(X0,X1)),
inference(paramodulation,[status(thm)],[f20,f22]) ).
fof(f137,plain,
! [X0] : greatest_lower_bound(a,greatest_lower_bound(sF1_fnc,X0)) = greatest_lower_bound(a,X0),
inference(paramodulation,[status(thm)],[f47,f22]) ).
fof(f138,plain,
! [X0] : greatest_lower_bound(a,greatest_lower_bound(identity,X0)) = greatest_lower_bound(sF2_fnc,X0),
inference(paramodulation,[status(thm)],[f34,f22]) ).
fof(f181,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f42,f73]) ).
fof(f182,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(paramodulation,[status(thm)],[f18,f73]) ).
fof(f183,plain,
! [X0] : multiply(X0,identity) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f77,f73]) ).
fof(f191,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f77,f183]) ).
fof(f201,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(paramodulation,[status(thm)],[f19,f182]) ).
fof(f268,plain,
! [X0] : least_upper_bound(a,least_upper_bound(sF2_fnc,X0)) = least_upper_bound(a,X0),
inference(paramodulation,[status(thm)],[f44,f23]) ).
fof(f280,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,least_upper_bound(X1,least_upper_bound(X2,X0))) = X0,
inference(paramodulation,[status(thm)],[f23,f95]) ).
fof(f462,plain,
! [X0,X1] : multiply(X0,least_upper_bound(identity,X1)) = least_upper_bound(X0,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f77,f28]) ).
fof(f467,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(f491,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,f467]) ).
fof(f620,plain,
! [X0] : multiply(sF1_fnc,greatest_lower_bound(sF2_fnc,X0)) = greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,X0)),
inference(paramodulation,[status(thm)],[f35,f29]) ).
fof(f633,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)],[f42,f29]) ).
fof(f634,plain,
! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X1,X0)) = greatest_lower_bound(multiply(inverse(X0),X1),identity),
inference(paramodulation,[status(thm)],[f18,f29]) ).
fof(f659,plain,
! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X1,X0)) = greatest_lower_bound(identity,multiply(inverse(X0),X1)),
inference(forward_demodulation,[status(thm)],[f20,f634]) ).
fof(f808,plain,
! [X0,X1] : multiply(least_upper_bound(identity,X0),X1) = least_upper_bound(X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f17,f30]) ).
fof(f820,plain,
! [X0,X1] : multiply(least_upper_bound(X0,identity),X1) = least_upper_bound(multiply(X0,X1),X1),
inference(paramodulation,[status(thm)],[f17,f30]) ).
fof(f846,plain,
! [X0,X1] : multiply(least_upper_bound(X0,identity),X1) = least_upper_bound(X1,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f21,f820]) ).
fof(f1046,plain,
! [X0,X1] : multiply(greatest_lower_bound(identity,X0),X1) = greatest_lower_bound(X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f17,f31]) ).
fof(f1058,plain,
! [X0,X1] : multiply(greatest_lower_bound(X0,identity),X1) = greatest_lower_bound(multiply(X0,X1),X1),
inference(paramodulation,[status(thm)],[f17,f31]) ).
fof(f1086,plain,
! [X0,X1] : multiply(greatest_lower_bound(X0,identity),X1) = greatest_lower_bound(X1,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f20,f1058]) ).
fof(f1612,plain,
! [X0,X1,X2] : greatest_lower_bound(greatest_lower_bound(X0,X1),least_upper_bound(X2,X0)) = greatest_lower_bound(X0,X1),
inference(paramodulation,[status(thm)],[f26,f280]) ).
fof(f1660,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(X1,least_upper_bound(X2,X0))) = greatest_lower_bound(X0,X1),
inference(forward_demodulation,[status(thm)],[f22,f1612]) ).
fof(f1937,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X2,greatest_lower_bound(X1,X0)),
inference(paramodulation,[status(thm)],[f20,f130]) ).
fof(f2186,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = multiply(inverse(X1),identity),
inference(paramodulation,[status(thm)],[f201,f42]) ).
fof(f2233,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f77,f2186]) ).
fof(f2252,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),inverse(inverse(X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f2233,f2233]) ).
fof(f2255,plain,
! [X0] : multiply(sF0_fnc,inverse(multiply(X0,sF2_fnc))) = multiply(sF1_fnc,inverse(X0)),
inference(paramodulation,[status(thm)],[f2233,f43]) ).
fof(f2267,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
inference(paramodulation,[status(thm)],[f2233,f42]) ).
fof(f2284,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f191,f2252]) ).
fof(f2323,plain,
! [X0,X1] : multiply(inverse(X0),X1) = inverse(multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f181,f2284]) ).
fof(f11207,plain,
multiply(inverse(sF1_fnc),sF1_fnc) = least_upper_bound(identity,multiply(inverse(sF1_fnc),identity)),
inference(paramodulation,[status(thm)],[f122,f491]) ).
fof(f11293,plain,
identity = least_upper_bound(identity,multiply(inverse(sF1_fnc),identity)),
inference(forward_demodulation,[status(thm)],[f18,f11207]) ).
fof(f11294,plain,
identity = least_upper_bound(identity,inverse(sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f77,f11293]) ).
fof(f22713,plain,
! [X0] : multiply(identity,X0) = least_upper_bound(X0,multiply(inverse(sF1_fnc),X0)),
inference(paramodulation,[status(thm)],[f11294,f808]) ).
fof(f22861,plain,
! [X0] : X0 = least_upper_bound(X0,multiply(inverse(sF1_fnc),X0)),
inference(forward_demodulation,[status(thm)],[f17,f22713]) ).
fof(f23131,plain,
sF0_fnc = least_upper_bound(sF0_fnc,sF2_fnc),
inference(paramodulation,[status(thm)],[f71,f22861]) ).
fof(f23354,plain,
greatest_lower_bound(sF2_fnc,sF0_fnc) = sF2_fnc,
inference(paramodulation,[status(thm)],[f23131,f95]) ).
fof(f23383,plain,
greatest_lower_bound(sF0_fnc,sF2_fnc) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f20,f23354]) ).
fof(f26767,plain,
! [X0] : multiply(sF1_fnc,X0) = least_upper_bound(X0,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f33,f846]) ).
fof(f28934,plain,
! [X0] : multiply(sF1_fnc,multiply(a,X0)) = multiply(a,least_upper_bound(X0,multiply(a,X0))),
inference(paramodulation,[status(thm)],[f28,f26767]) ).
fof(f28952,plain,
least_upper_bound(a,multiply(sF1_fnc,sF2_fnc)) = least_upper_bound(a,multiply(a,sF2_fnc)),
inference(paramodulation,[status(thm)],[f26767,f268]) ).
fof(f29022,plain,
! [X0] : multiply(sF1_fnc,multiply(a,X0)) = multiply(a,multiply(sF1_fnc,X0)),
inference(forward_demodulation,[status(thm)],[f26767,f28934]) ).
fof(f29055,plain,
least_upper_bound(a,sF0_fnc) = least_upper_bound(a,multiply(a,sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f35,f28952]) ).
fof(f38965,plain,
! [X0] : multiply(sF2_fnc,X0) = greatest_lower_bound(X0,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f34,f1086]) ).
fof(f39359,plain,
multiply(sF1_fnc,multiply(sF2_fnc,sF2_fnc)) = greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,multiply(a,sF2_fnc))),
inference(paramodulation,[status(thm)],[f38965,f620]) ).
fof(f39467,plain,
multiply(sF0_fnc,sF2_fnc) = greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,multiply(a,sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f43,f39359]) ).
fof(f39468,plain,
multiply(sF0_fnc,sF2_fnc) = greatest_lower_bound(sF0_fnc,multiply(a,multiply(sF1_fnc,sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f29022,f39467]) ).
fof(f39469,plain,
multiply(sF0_fnc,sF2_fnc) = greatest_lower_bound(sF0_fnc,multiply(a,sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f35,f39468]) ).
fof(f39488,plain,
multiply(sF0_fnc,sF2_fnc) = multiply(sF2_fnc,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f38965,f39469]) ).
fof(f39609,plain,
multiply(sF0_fnc,inverse(multiply(sF0_fnc,sF2_fnc))) = inverse(sF2_fnc),
inference(paramodulation,[status(thm)],[f39488,f2233]) ).
fof(f39640,plain,
multiply(sF1_fnc,inverse(sF0_fnc)) = inverse(sF2_fnc),
inference(forward_demodulation,[status(thm)],[f2255,f39609]) ).
fof(f39685,plain,
multiply(inverse(inverse(sF2_fnc)),sF1_fnc) = inverse(inverse(sF0_fnc)),
inference(paramodulation,[status(thm)],[f39640,f2284]) ).
fof(f39686,plain,
multiply(inverse(sF0_fnc),inverse(inverse(sF2_fnc))) = inverse(sF1_fnc),
inference(paramodulation,[status(thm)],[f39640,f2233]) ).
fof(f39735,plain,
multiply(sF2_fnc,sF1_fnc) = inverse(inverse(sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f191,f39685]) ).
fof(f39739,plain,
multiply(sF2_fnc,sF1_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f191,f39735]) ).
fof(f39740,plain,
inverse(multiply(inverse(sF2_fnc),sF0_fnc)) = inverse(sF1_fnc),
inference(forward_demodulation,[status(thm)],[f2267,f39686]) ).
fof(f39751,plain,
multiply(inverse(sF0_fnc),sF2_fnc) = inverse(sF1_fnc),
inference(forward_demodulation,[status(thm)],[f2323,f39740]) ).
fof(f45012,plain,
! [X0] : multiply(X0,identity) = least_upper_bound(X0,multiply(X0,sF2_fnc)),
inference(paramodulation,[status(thm)],[f60,f462]) ).
fof(f45260,plain,
least_upper_bound(a,sF0_fnc) = a,
inference(backward_demodulation,[status(thm)],[f45261,f29055]) ).
fof(f45261,plain,
! [X0] : X0 = least_upper_bound(X0,multiply(X0,sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f77,f45012]) ).
fof(f45551,plain,
! [X0] : greatest_lower_bound(sF0_fnc,greatest_lower_bound(X0,a)) = greatest_lower_bound(sF0_fnc,X0),
inference(paramodulation,[status(thm)],[f45260,f1660]) ).
fof(f45570,plain,
greatest_lower_bound(sF0_fnc,a) = sF0_fnc,
inference(paramodulation,[status(thm)],[f45260,f95]) ).
fof(f45589,plain,
! [X0] : greatest_lower_bound(a,greatest_lower_bound(X0,sF0_fnc)) = greatest_lower_bound(sF0_fnc,X0),
inference(forward_demodulation,[status(thm)],[f1937,f45551]) ).
fof(f45600,plain,
greatest_lower_bound(a,sF0_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f20,f45570]) ).
fof(f58537,plain,
greatest_lower_bound(sF2_fnc,sF0_fnc) = greatest_lower_bound(sF0_fnc,identity),
inference(paramodulation,[status(thm)],[f138,f45589]) ).
fof(f58617,plain,
greatest_lower_bound(sF0_fnc,sF2_fnc) = greatest_lower_bound(sF0_fnc,identity),
inference(forward_demodulation,[status(thm)],[f20,f58537]) ).
fof(f58618,plain,
sF2_fnc = greatest_lower_bound(sF0_fnc,identity),
inference(forward_demodulation,[status(thm)],[f23383,f58617]) ).
fof(f58620,plain,
sF2_fnc = greatest_lower_bound(identity,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f20,f58618]) ).
fof(f58698,plain,
! [X0] : multiply(sF2_fnc,X0) = greatest_lower_bound(X0,multiply(sF0_fnc,X0)),
inference(paramodulation,[status(thm)],[f58620,f1046]) ).
fof(f58719,plain,
multiply(inverse(sF0_fnc),sF2_fnc) = greatest_lower_bound(identity,multiply(inverse(sF0_fnc),identity)),
inference(paramodulation,[status(thm)],[f58620,f659]) ).
fof(f58756,plain,
inverse(sF1_fnc) = greatest_lower_bound(identity,multiply(inverse(sF0_fnc),identity)),
inference(forward_demodulation,[status(thm)],[f39751,f58719]) ).
fof(f58757,plain,
inverse(sF1_fnc) = greatest_lower_bound(identity,inverse(sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f77,f58756]) ).
fof(f59060,plain,
! [X0] : multiply(inverse(sF1_fnc),X0) = greatest_lower_bound(X0,multiply(inverse(sF0_fnc),X0)),
inference(paramodulation,[status(thm)],[f58757,f1046]) ).
fof(f59437,plain,
greatest_lower_bound(a,multiply(sF2_fnc,sF1_fnc)) = greatest_lower_bound(a,multiply(sF0_fnc,sF1_fnc)),
inference(paramodulation,[status(thm)],[f58698,f137]) ).
fof(f59542,plain,
greatest_lower_bound(a,sF0_fnc) = greatest_lower_bound(a,multiply(sF0_fnc,sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f39739,f59437]) ).
fof(f59543,plain,
sF0_fnc = greatest_lower_bound(a,multiply(sF0_fnc,sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f45600,f59542]) ).
fof(f59622,plain,
multiply(inverse(sF0_fnc),sF0_fnc) = greatest_lower_bound(multiply(inverse(sF0_fnc),a),sF1_fnc),
inference(paramodulation,[status(thm)],[f59543,f633]) ).
fof(f59661,plain,
identity = greatest_lower_bound(multiply(inverse(sF0_fnc),a),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f18,f59622]) ).
fof(f59662,plain,
identity = greatest_lower_bound(sF1_fnc,multiply(inverse(sF0_fnc),a)),
inference(forward_demodulation,[status(thm)],[f20,f59661]) ).
fof(f69101,plain,
greatest_lower_bound(a,identity) = greatest_lower_bound(a,multiply(inverse(sF0_fnc),a)),
inference(paramodulation,[status(thm)],[f59662,f137]) ).
fof(f69149,plain,
sF2_fnc = greatest_lower_bound(a,multiply(inverse(sF0_fnc),a)),
inference(forward_demodulation,[status(thm)],[f34,f69101]) ).
fof(f69160,plain,
sF2_fnc = multiply(inverse(sF1_fnc),a),
inference(forward_demodulation,[status(thm)],[f59060,f69149]) ).
fof(f69238,plain,
multiply(sF1_fnc,sF2_fnc) = a,
inference(paramodulation,[status(thm)],[f69160,f181]) ).
fof(f69277,plain,
sF0_fnc = a,
inference(forward_demodulation,[status(thm)],[f35,f69238]) ).
fof(f69278,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f69277,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP167-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n014.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.03/0.41 % DateTime : Sun Sep 20 20:03:04 UTC 2026
% 0.03/0.42 % CPUTime :
% 0.03/0.43 % Drodi V4.1.1
% 265.67/34.10 % Refutation found
% 265.67/34.10 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 265.67/34.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 61.75/35.49 % Elapsed time: 34.847707 seconds
% 61.75/35.49 % CPU time: 251.530396 seconds
% 61.75/35.49 % Total memory used: 19.398 GB
% 61.75/35.49 % Net memory used: 19.363 GB
%------------------------------------------------------------------------------