%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP190-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 12:33:03 PM UTC 2026
% Result : Unsatisfiable 2.58s 0.82s
% Output : CNFRefutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 52 ( 52 unt; 3 def)
% Number of atoms : 52 ( 51 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 56 ( 56 !; 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(f5,axiom,
! [X,Y] : least_upper_bound(X,Y) = least_upper_bound(Y,X),
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(f8,axiom,
! [X] : least_upper_bound(X,X) = X,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
least_upper_bound(a,b) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
least_upper_bound(inverse(a),inverse(b)) != inverse(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f19,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f20,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f22,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f24,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(f25,plain,
! [X0] : least_upper_bound(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f29,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(f31,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(f33,plain,
least_upper_bound(a,b) = a,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f34,plain,
least_upper_bound(inverse(a),inverse(b)) != inverse(b),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f35,definition,
sF1_fnc = inverse(a),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f36,definition,
sF2_fnc = inverse(b),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f37,definition,
sF0_fnc = least_upper_bound(sF1_fnc,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f38,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f34,f37,f36,f35]) ).
fof(f50,plain,
! [X0,X1] : least_upper_bound(X0,least_upper_bound(X0,X1)) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f25,f24]) ).
fof(f64,plain,
! [X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X0)) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f22,f50]) ).
fof(f94,plain,
least_upper_bound(sF2_fnc,sF0_fnc) = least_upper_bound(sF2_fnc,sF1_fnc),
inference(paramodulation,[status(thm)],[f37,f64]) ).
fof(f118,plain,
least_upper_bound(sF2_fnc,sF0_fnc) = least_upper_bound(sF1_fnc,sF2_fnc),
inference(paramodulation,[status(thm)],[f22,f94]) ).
fof(f125,plain,
least_upper_bound(sF2_fnc,sF0_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f37,f118]) ).
fof(f132,plain,
sF0_fnc = least_upper_bound(sF2_fnc,sF1_fnc),
inference(backward_demodulation,[status(thm)],[f125,f94]) ).
fof(f180,plain,
! [X0,X1] : multiply(least_upper_bound(identity,X0),X1) = least_upper_bound(X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f18,f31]) ).
fof(f185,plain,
multiply(sF2_fnc,b) = identity,
inference(paramodulation,[status(thm)],[f36,f19]) ).
fof(f190,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1)),
inference(paramodulation,[status(thm)],[f19,f29]) ).
fof(f258,plain,
! [X0] : multiply(identity,X0) = multiply(sF2_fnc,multiply(b,X0)),
inference(paramodulation,[status(thm)],[f185,f20]) ).
fof(f259,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f268,plain,
! [X0] : X0 = multiply(sF2_fnc,multiply(b,X0)),
inference(forward_demodulation,[status(thm)],[f18,f258]) ).
fof(f269,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f18,f259]) ).
fof(f568,plain,
! [X0] : multiply(b,X0) = multiply(inverse(sF2_fnc),X0),
inference(paramodulation,[status(thm)],[f268,f269]) ).
fof(f570,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f269,f269]) ).
fof(f571,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f19,f269]) ).
fof(f1639,plain,
multiply(b,sF2_fnc) = identity,
inference(paramodulation,[status(thm)],[f19,f568]) ).
fof(f1841,plain,
! [X0] : X0 = multiply(X0,identity),
inference(backward_demodulation,[status(thm)],[f570,f571]) ).
fof(f5437,plain,
multiply(inverse(a),a) = least_upper_bound(identity,multiply(inverse(a),b)),
inference(paramodulation,[status(thm)],[f33,f190]) ).
fof(f5520,plain,
identity = least_upper_bound(identity,multiply(inverse(a),b)),
inference(forward_demodulation,[status(thm)],[f19,f5437]) ).
fof(f5521,plain,
identity = least_upper_bound(identity,multiply(sF1_fnc,b)),
inference(forward_demodulation,[status(thm)],[f35,f5520]) ).
fof(f5630,plain,
! [X0] : multiply(identity,X0) = least_upper_bound(X0,multiply(multiply(sF1_fnc,b),X0)),
inference(paramodulation,[status(thm)],[f5521,f180]) ).
fof(f5649,plain,
! [X0] : X0 = least_upper_bound(X0,multiply(multiply(sF1_fnc,b),X0)),
inference(forward_demodulation,[status(thm)],[f18,f5630]) ).
fof(f5650,plain,
! [X0] : X0 = least_upper_bound(X0,multiply(sF1_fnc,multiply(b,X0))),
inference(forward_demodulation,[status(thm)],[f20,f5649]) ).
fof(f5662,plain,
sF2_fnc = least_upper_bound(sF2_fnc,multiply(sF1_fnc,identity)),
inference(paramodulation,[status(thm)],[f1639,f5650]) ).
fof(f5708,plain,
sF2_fnc = least_upper_bound(sF2_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f1841,f5662]) ).
fof(f5709,plain,
sF2_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f132,f5708]) ).
fof(f5710,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5709,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP190-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n012.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 20 20:05:37 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 2.58/0.82 % Refutation found
% 2.58/0.82 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.58/0.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.58/0.86 % Elapsed time: 0.493354 seconds
% 2.58/0.86 % CPU time: 3.687222 seconds
% 2.58/0.86 % Total memory used: 68.714 MB
% 2.58/0.86 % Net memory used: 67.462 MB
%------------------------------------------------------------------------------