%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP178-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 12:32:59 PM UTC 2026
% Result : Unsatisfiable 14.71s 2.32s
% Output : CNFRefutation 15.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 18
% Syntax : Number of formulae : 77 ( 77 unt; 3 def)
% Number of atoms : 77 ( 76 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 : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 76 ( 76 !; 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,Y] : greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] : least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] : greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
least_upper_bound(identity,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
least_upper_bound(identity,c) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
greatest_lower_bound(a,b) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f23,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f24,plain,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f25,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f26,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(f27,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(f30,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f31,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f33,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(f35,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(f37,plain,
least_upper_bound(identity,b) = b,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f38,plain,
least_upper_bound(identity,c) = c,
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f39,plain,
greatest_lower_bound(a,b) = identity,
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f40,plain,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f41,definition,
sF1_fnc = multiply(b,c),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f42,definition,
sF0_fnc = greatest_lower_bound(a,sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f43,definition,
sF2_fnc = greatest_lower_bound(a,c),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f44,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f40,f43,f42,f41]) ).
fof(f46,plain,
least_upper_bound(b,identity) = b,
inference(forward_demodulation,[status(thm)],[f25,f37]) ).
fof(f47,plain,
least_upper_bound(c,identity) = c,
inference(forward_demodulation,[status(thm)],[f25,f38]) ).
fof(f48,plain,
greatest_lower_bound(b,a) = identity,
inference(forward_demodulation,[status(thm)],[f24,f39]) ).
fof(f49,plain,
sF2_fnc = greatest_lower_bound(c,a),
inference(forward_demodulation,[status(thm)],[f24,f43]) ).
fof(f69,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f24,f30]) ).
fof(f94,plain,
! [X0] : greatest_lower_bound(b,greatest_lower_bound(a,X0)) = greatest_lower_bound(identity,X0),
inference(paramodulation,[status(thm)],[f48,f26]) ).
fof(f96,plain,
! [X0] : greatest_lower_bound(a,greatest_lower_bound(sF1_fnc,X0)) = greatest_lower_bound(sF0_fnc,X0),
inference(paramodulation,[status(thm)],[f42,f26]) ).
fof(f113,plain,
! [X0] : multiply(b,greatest_lower_bound(c,X0)) = greatest_lower_bound(sF1_fnc,multiply(b,X0)),
inference(paramodulation,[status(thm)],[f41,f33]) ).
fof(f139,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f22,f23]) ).
fof(f141,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f21,f139]) ).
fof(f142,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f141,f141]) ).
fof(f143,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f22,f141]) ).
fof(f147,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)],[f141,f33]) ).
fof(f150,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f142,f143]) ).
fof(f195,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f25,f31]) ).
fof(f203,plain,
greatest_lower_bound(identity,c) = identity,
inference(paramodulation,[status(thm)],[f47,f195]) ).
fof(f220,plain,
greatest_lower_bound(c,identity) = identity,
inference(forward_demodulation,[status(thm)],[f24,f203]) ).
fof(f277,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f141,f142]) ).
fof(f326,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,least_upper_bound(X1,least_upper_bound(X2,X0))) = X0,
inference(paramodulation,[status(thm)],[f27,f195]) ).
fof(f827,plain,
! [X0] : multiply(greatest_lower_bound(b,X0),c) = greatest_lower_bound(sF1_fnc,multiply(X0,c)),
inference(paramodulation,[status(thm)],[f41,f35]) ).
fof(f1210,plain,
greatest_lower_bound(b,sF0_fnc) = greatest_lower_bound(identity,sF1_fnc),
inference(paramodulation,[status(thm)],[f42,f94]) ).
fof(f2356,plain,
multiply(b,identity) = greatest_lower_bound(sF1_fnc,multiply(b,identity)),
inference(paramodulation,[status(thm)],[f220,f113]) ).
fof(f2380,plain,
b = greatest_lower_bound(sF1_fnc,multiply(b,identity)),
inference(forward_demodulation,[status(thm)],[f150,f2356]) ).
fof(f2381,plain,
b = greatest_lower_bound(sF1_fnc,b),
inference(forward_demodulation,[status(thm)],[f150,f2380]) ).
fof(f2382,plain,
b = greatest_lower_bound(b,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f24,f2381]) ).
fof(f2414,plain,
least_upper_bound(sF1_fnc,b) = sF1_fnc,
inference(paramodulation,[status(thm)],[f2382,f69]) ).
fof(f2422,plain,
least_upper_bound(b,sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f25,f2414]) ).
fof(f2686,plain,
! [X0] : greatest_lower_bound(identity,least_upper_bound(X0,b)) = identity,
inference(paramodulation,[status(thm)],[f46,f326]) ).
fof(f2841,plain,
! [X0] : greatest_lower_bound(identity,least_upper_bound(b,X0)) = identity,
inference(paramodulation,[status(thm)],[f25,f2686]) ).
fof(f3004,plain,
greatest_lower_bound(identity,sF1_fnc) = identity,
inference(paramodulation,[status(thm)],[f2422,f2841]) ).
fof(f3033,plain,
greatest_lower_bound(b,sF0_fnc) = identity,
inference(backward_demodulation,[status(thm)],[f3004,f1210]) ).
fof(f18373,plain,
multiply(identity,c) = greatest_lower_bound(sF1_fnc,multiply(sF0_fnc,c)),
inference(paramodulation,[status(thm)],[f3033,f827]) ).
fof(f18429,plain,
c = greatest_lower_bound(sF1_fnc,multiply(sF0_fnc,c)),
inference(forward_demodulation,[status(thm)],[f21,f18373]) ).
fof(f21968,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(sF0_fnc,multiply(sF0_fnc,c)),
inference(paramodulation,[status(thm)],[f18429,f96]) ).
fof(f21987,plain,
greatest_lower_bound(c,a) = greatest_lower_bound(sF0_fnc,multiply(sF0_fnc,c)),
inference(forward_demodulation,[status(thm)],[f24,f21968]) ).
fof(f21988,plain,
sF2_fnc = greatest_lower_bound(sF0_fnc,multiply(sF0_fnc,c)),
inference(forward_demodulation,[status(thm)],[f49,f21987]) ).
fof(f30071,plain,
multiply(inverse(sF0_fnc),sF2_fnc) = greatest_lower_bound(multiply(inverse(sF0_fnc),sF0_fnc),c),
inference(paramodulation,[status(thm)],[f21988,f147]) ).
fof(f30090,plain,
multiply(inverse(sF0_fnc),sF2_fnc) = greatest_lower_bound(c,multiply(inverse(sF0_fnc),sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f24,f30071]) ).
fof(f30091,plain,
multiply(inverse(sF0_fnc),sF2_fnc) = greatest_lower_bound(c,identity),
inference(forward_demodulation,[status(thm)],[f22,f30090]) ).
fof(f30098,plain,
multiply(inverse(sF0_fnc),sF2_fnc) = identity,
inference(forward_demodulation,[status(thm)],[f220,f30091]) ).
fof(f30123,plain,
multiply(sF0_fnc,identity) = sF2_fnc,
inference(paramodulation,[status(thm)],[f30098,f277]) ).
fof(f30162,plain,
sF0_fnc = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f150,f30123]) ).
fof(f30163,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f30162,f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP178-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:03:56 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 14.71/2.32 % Refutation found
% 14.71/2.32 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 14.71/2.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 15.24/2.40 % Elapsed time: 2.009722 seconds
% 15.24/2.40 % CPU time: 15.730847 seconds
% 15.24/2.40 % Total memory used: 157.358 MB
% 15.24/2.40 % Net memory used: 154.989 MB
%------------------------------------------------------------------------------