%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP193-2 : 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 12:33:04 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.48s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 35 unt; 0 def)
% Number of atoms : 35 ( 34 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
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(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(f9,axiom,
! [X] : greatest_lower_bound(X,X) = X,
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,
greatest_lower_bound(identity,b) = identity,
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,hypothesis,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f25,plain,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f27,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(f30,plain,
! [X0] : greatest_lower_bound(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f36,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(f38,plain,
greatest_lower_bound(identity,b) = identity,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f40,plain,
greatest_lower_bound(a,b) = identity,
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f41,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f42,plain,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f47,plain,
greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) = greatest_lower_bound(a,multiply(b,c)),
inference(forward_demodulation,[status(thm)],[f27,f41]) ).
fof(f48,plain,
greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(identity,greatest_lower_bound(a,c)))) = greatest_lower_bound(a,multiply(b,c)),
inference(forward_demodulation,[status(thm)],[f40,f47]) ).
fof(f49,plain,
greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(forward_demodulation,[status(thm)],[f22,f48]) ).
fof(f57,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)],[f25,f27]) ).
fof(f67,plain,
! [X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X0,X1)) = greatest_lower_bound(X0,X1),
inference(paramodulation,[status(thm)],[f30,f27]) ).
fof(f71,plain,
greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(multiply(b,c),a))) = greatest_lower_bound(a,multiply(b,c)),
inference(backward_demodulation,[status(thm)],[f57,f49]) ).
fof(f76,plain,
greatest_lower_bound(a,greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c)))) = greatest_lower_bound(a,multiply(b,c)),
inference(forward_demodulation,[status(thm)],[f57,f71]) ).
fof(f77,plain,
greatest_lower_bound(a,greatest_lower_bound(c,multiply(b,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(forward_demodulation,[status(thm)],[f67,f76]) ).
fof(f384,plain,
! [X0,X1,X2] : multiply(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(multiply(X1,X2),multiply(X0,X2)),
inference(paramodulation,[status(thm)],[f25,f36]) ).
fof(f397,plain,
! [X0,X1,X2] : multiply(greatest_lower_bound(X0,X1),X2) = multiply(greatest_lower_bound(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f36,f384]) ).
fof(f406,plain,
! [X0,X1] : multiply(greatest_lower_bound(X0,identity),X1) = greatest_lower_bound(multiply(X0,X1),X1),
inference(paramodulation,[status(thm)],[f22,f36]) ).
fof(f411,plain,
greatest_lower_bound(a,multiply(greatest_lower_bound(b,identity),c)) = greatest_lower_bound(a,multiply(b,c)),
inference(backward_demodulation,[status(thm)],[f412,f77]) ).
fof(f412,plain,
! [X0,X1] : multiply(greatest_lower_bound(X0,identity),X1) = greatest_lower_bound(X1,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f25,f406]) ).
fof(f416,plain,
greatest_lower_bound(a,multiply(greatest_lower_bound(identity,b),c)) = greatest_lower_bound(a,multiply(b,c)),
inference(forward_demodulation,[status(thm)],[f397,f411]) ).
fof(f417,plain,
greatest_lower_bound(a,multiply(identity,c)) = greatest_lower_bound(a,multiply(b,c)),
inference(forward_demodulation,[status(thm)],[f38,f416]) ).
fof(f418,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(a,multiply(b,c)),
inference(forward_demodulation,[status(thm)],[f22,f417]) ).
fof(f419,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f418,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP193-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.41 % Computer : n011.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sun Sep 20 20:05:40 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.43 % Drodi V4.1.1
% 0.14/0.48 % Refutation found
% 0.14/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.50 % Elapsed time: 0.076305 seconds
% 0.14/0.50 % CPU time: 0.339048 seconds
% 0.14/0.50 % Total memory used: 12.385 MB
% 0.14/0.50 % Net memory used: 12.305 MB
%------------------------------------------------------------------------------