%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP181-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 12:33:00 PM UTC 2026
% Result : Unsatisfiable 29.71s 4.36s
% Output : CNFRefutation 29.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 56 ( 56 unt; 0 def)
% Number of atoms : 56 ( 55 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 : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 70 ( 70 !; 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(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(f16,hypothesis,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
least_upper_bound(a,c) = least_upper_bound(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
! [X,Y] : inverse(least_upper_bound(X,Y)) = greatest_lower_bound(inverse(X),inverse(Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
a != b,
file('/export/starexec/sandbox2/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(f32,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(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(f36,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f37,plain,
least_upper_bound(a,c) = least_upper_bound(b,c),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f39,plain,
! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(X0),inverse(X1)),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f40,plain,
a != b,
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f48,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f22,f23]) ).
fof(f52,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f21,f48]) ).
fof(f53,plain,
greatest_lower_bound(b,c) = greatest_lower_bound(c,a),
inference(paramodulation,[status(thm)],[f36,f24]) ).
fof(f155,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f52,f52]) ).
fof(f156,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f22,f52]) ).
fof(f159,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f155,f156]) ).
fof(f196,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1)),
inference(paramodulation,[status(thm)],[f22,f32]) ).
fof(f227,plain,
! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X0,X1)) = greatest_lower_bound(identity,multiply(inverse(X0),X1)),
inference(paramodulation,[status(thm)],[f22,f33]) ).
fof(f231,plain,
! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X1,X0)) = greatest_lower_bound(multiply(inverse(X0),X1),identity),
inference(paramodulation,[status(thm)],[f22,f33]) ).
fof(f354,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f22,f159]) ).
fof(f696,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f52,f155]) ).
fof(f697,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(paramodulation,[status(thm)],[f22,f155]) ).
fof(f698,plain,
! [X0] : multiply(X0,identity) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f159,f155]) ).
fof(f714,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f159,f698]) ).
fof(f742,plain,
! [X0] : inverse(least_upper_bound(identity,X0)) = greatest_lower_bound(identity,inverse(X0)),
inference(paramodulation,[status(thm)],[f354,f39]) ).
fof(f1318,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(paramodulation,[status(thm)],[f23,f697]) ).
fof(f5209,plain,
multiply(inverse(a),least_upper_bound(b,c)) = least_upper_bound(identity,multiply(inverse(a),c)),
inference(paramodulation,[status(thm)],[f37,f196]) ).
fof(f6483,plain,
multiply(inverse(c),greatest_lower_bound(b,c)) = greatest_lower_bound(identity,multiply(inverse(c),a)),
inference(paramodulation,[status(thm)],[f53,f227]) ).
fof(f6542,plain,
greatest_lower_bound(multiply(inverse(c),b),identity) = greatest_lower_bound(identity,multiply(inverse(c),a)),
inference(forward_demodulation,[status(thm)],[f231,f6483]) ).
fof(f8186,plain,
greatest_lower_bound(identity,multiply(inverse(c),b)) = greatest_lower_bound(identity,multiply(inverse(c),a)),
inference(paramodulation,[status(thm)],[f24,f6542]) ).
fof(f19956,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = multiply(inverse(X1),identity),
inference(paramodulation,[status(thm)],[f1318,f52]) ).
fof(f20043,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f159,f19956]) ).
fof(f20102,plain,
multiply(least_upper_bound(b,c),inverse(least_upper_bound(identity,multiply(inverse(a),c)))) = inverse(inverse(a)),
inference(paramodulation,[status(thm)],[f5209,f20043]) ).
fof(f20107,plain,
! [X0,X1] : multiply(least_upper_bound(X0,X1),inverse(least_upper_bound(identity,multiply(inverse(X0),X1)))) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f196,f20043]) ).
fof(f20116,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),inverse(inverse(X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f20043,f20043]) ).
fof(f20194,plain,
multiply(least_upper_bound(b,c),greatest_lower_bound(identity,inverse(multiply(inverse(a),c)))) = inverse(inverse(a)),
inference(forward_demodulation,[status(thm)],[f742,f20102]) ).
fof(f20196,plain,
multiply(least_upper_bound(b,c),greatest_lower_bound(identity,inverse(multiply(inverse(a),c)))) = a,
inference(forward_demodulation,[status(thm)],[f714,f20194]) ).
fof(f20209,plain,
! [X0,X1] : multiply(least_upper_bound(X0,X1),greatest_lower_bound(identity,inverse(multiply(inverse(X0),X1)))) = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f742,f20107]) ).
fof(f20211,plain,
! [X0,X1] : multiply(least_upper_bound(X0,X1),greatest_lower_bound(identity,inverse(multiply(inverse(X0),X1)))) = X0,
inference(forward_demodulation,[status(thm)],[f714,f20209]) ).
fof(f20224,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f714,f20116]) ).
fof(f22698,plain,
! [X0,X1] : multiply(inverse(X0),X1) = inverse(multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f696,f20224]) ).
fof(f22781,plain,
multiply(least_upper_bound(b,c),greatest_lower_bound(identity,multiply(inverse(c),a))) = a,
inference(backward_demodulation,[status(thm)],[f22698,f20196]) ).
fof(f22794,plain,
! [X0,X1] : multiply(least_upper_bound(X0,X1),greatest_lower_bound(identity,multiply(inverse(X1),X0))) = X0,
inference(backward_demodulation,[status(thm)],[f22698,f20211]) ).
fof(f22865,plain,
multiply(least_upper_bound(b,c),greatest_lower_bound(identity,multiply(inverse(c),b))) = a,
inference(forward_demodulation,[status(thm)],[f8186,f22781]) ).
fof(f22894,plain,
b = a,
inference(backward_demodulation,[status(thm)],[f22794,f22865]) ).
fof(f22906,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f22894,f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP181-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n011.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 20 20:04:41 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.46 % Drodi V4.1.1
% 29.71/4.36 % Refutation found
% 29.71/4.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 29.71/4.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.08/4.45 % Elapsed time: 3.984080 seconds
% 2.08/4.45 % CPU time: 31.054524 seconds
% 2.08/4.45 % Total memory used: 216.587 MB
% 2.08/4.45 % Net memory used: 208.690 MB
%------------------------------------------------------------------------------