%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP171-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 12:32:57 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 37 ( 37 unt; 2 def)
% Number of atoms : 37 ( 36 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 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 36 ( 36 !; 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(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(f16,hypothesis,
least_upper_bound(identity,a) = a,
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,negated_conjecture,
least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f21,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f23,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f25,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,X2] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f34,plain,
least_upper_bound(identity,a) = a,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f35,plain,
least_upper_bound(identity,b) = b,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f36,plain,
least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f37,definition,
sF1_fnc = multiply(a,b),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f38,definition,
sF0_fnc = least_upper_bound(identity,sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f39,plain,
sF0_fnc != sF1_fnc,
inference(definition_folding,[],[f36,f38,f37]) ).
fof(f53,plain,
least_upper_bound(b,identity) = b,
inference(paramodulation,[status(thm)],[f23,f35]) ).
fof(f64,plain,
! [X0] : least_upper_bound(identity,least_upper_bound(a,X0)) = least_upper_bound(a,X0),
inference(paramodulation,[status(thm)],[f34,f25]) ).
fof(f105,plain,
! [X0] : multiply(a,least_upper_bound(b,X0)) = least_upper_bound(sF1_fnc,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f37,f30]) ).
fof(f156,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f20,f21]) ).
fof(f157,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f19,f156]) ).
fof(f358,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f157,f157]) ).
fof(f359,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f20,f157]) ).
fof(f1630,plain,
multiply(a,b) = least_upper_bound(sF1_fnc,multiply(a,identity)),
inference(paramodulation,[status(thm)],[f53,f105]) ).
fof(f1655,plain,
sF1_fnc = least_upper_bound(sF1_fnc,multiply(a,identity)),
inference(forward_demodulation,[status(thm)],[f37,f1630]) ).
fof(f1778,plain,
! [X0] : X0 = multiply(X0,identity),
inference(backward_demodulation,[status(thm)],[f358,f359]) ).
fof(f2013,plain,
sF1_fnc = least_upper_bound(sF1_fnc,a),
inference(forward_demodulation,[status(thm)],[f1778,f1655]) ).
fof(f2014,plain,
sF1_fnc = least_upper_bound(a,sF1_fnc),
inference(paramodulation,[status(thm)],[f23,f2013]) ).
fof(f2036,plain,
least_upper_bound(identity,sF1_fnc) = least_upper_bound(a,sF1_fnc),
inference(paramodulation,[status(thm)],[f2014,f64]) ).
fof(f2048,plain,
sF0_fnc = least_upper_bound(a,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f38,f2036]) ).
fof(f2049,plain,
sF0_fnc = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f2014,f2048]) ).
fof(f2050,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2049,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP171-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.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 20:03:27 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.42 % Refutation found
% 0.13/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.078267 seconds
% 0.13/0.44 % CPU time: 0.493288 seconds
% 0.13/0.44 % Total memory used: 15.365 MB
% 0.13/0.44 % Net memory used: 15.146 MB
%------------------------------------------------------------------------------