%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP138-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 12:32:51 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 48 ( 48 unt; 2 def)
% Number of atoms : 48 ( 47 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 : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 39 ( 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X,Y] : greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] : least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] : greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
least_upper_bound(a,c) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
least_upper_bound(b,c) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
least_upper_bound(greatest_lower_bound(a,b),c) != greatest_lower_bound(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,plain,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f23,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] : 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(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(f28,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f29,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f34,plain,
least_upper_bound(a,c) = a,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f35,plain,
least_upper_bound(b,c) = b,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f36,plain,
least_upper_bound(greatest_lower_bound(a,b),c) != greatest_lower_bound(a,b),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f37,definition,
sF1_fnc = greatest_lower_bound(a,b),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f38,definition,
sF0_fnc = least_upper_bound(sF1_fnc,c),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f39,plain,
sF0_fnc != sF1_fnc,
inference(definition_folding,[],[f36,f38,f37]) ).
fof(f44,plain,
sF0_fnc = least_upper_bound(c,sF1_fnc),
inference(paramodulation,[status(thm)],[f38,f23]) ).
fof(f52,plain,
least_upper_bound(a,sF1_fnc) = a,
inference(paramodulation,[status(thm)],[f37,f28]) ).
fof(f53,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f22,f28]) ).
fof(f56,plain,
greatest_lower_bound(sF1_fnc,sF0_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f38,f29]) ).
fof(f58,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f23,f29]) ).
fof(f67,plain,
least_upper_bound(c,b) = b,
inference(paramodulation,[status(thm)],[f23,f35]) ).
fof(f75,plain,
least_upper_bound(b,sF1_fnc) = b,
inference(paramodulation,[status(thm)],[f37,f53]) ).
fof(f82,plain,
greatest_lower_bound(sF0_fnc,sF1_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f22,f56]) ).
fof(f94,plain,
! [X0] : greatest_lower_bound(a,greatest_lower_bound(b,X0)) = greatest_lower_bound(sF1_fnc,X0),
inference(paramodulation,[status(thm)],[f37,f24]) ).
fof(f118,plain,
! [X0] : least_upper_bound(a,least_upper_bound(c,X0)) = least_upper_bound(a,X0),
inference(paramodulation,[status(thm)],[f34,f25]) ).
fof(f119,plain,
! [X0] : least_upper_bound(sF1_fnc,least_upper_bound(c,X0)) = least_upper_bound(sF0_fnc,X0),
inference(paramodulation,[status(thm)],[f38,f25]) ).
fof(f144,plain,
! [X0,X1] : greatest_lower_bound(greatest_lower_bound(X0,X1),X0) = greatest_lower_bound(X0,X1),
inference(paramodulation,[status(thm)],[f28,f58]) ).
fof(f154,plain,
! [X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X0)) = greatest_lower_bound(X0,X1),
inference(forward_demodulation,[status(thm)],[f24,f144]) ).
fof(f1120,plain,
least_upper_bound(sF1_fnc,b) = least_upper_bound(sF0_fnc,b),
inference(paramodulation,[status(thm)],[f67,f119]) ).
fof(f2637,plain,
least_upper_bound(b,sF1_fnc) = least_upper_bound(sF0_fnc,b),
inference(paramodulation,[status(thm)],[f23,f1120]) ).
fof(f2652,plain,
b = least_upper_bound(sF0_fnc,b),
inference(forward_demodulation,[status(thm)],[f75,f2637]) ).
fof(f2676,plain,
greatest_lower_bound(sF0_fnc,b) = sF0_fnc,
inference(paramodulation,[status(thm)],[f2652,f29]) ).
fof(f2767,plain,
greatest_lower_bound(b,sF0_fnc) = sF0_fnc,
inference(paramodulation,[status(thm)],[f22,f2676]) ).
fof(f2790,plain,
greatest_lower_bound(a,sF0_fnc) = greatest_lower_bound(sF1_fnc,sF0_fnc),
inference(paramodulation,[status(thm)],[f2767,f94]) ).
fof(f2805,plain,
greatest_lower_bound(a,sF0_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f56,f2790]) ).
fof(f3086,plain,
greatest_lower_bound(sF0_fnc,sF1_fnc) = greatest_lower_bound(sF0_fnc,a),
inference(paramodulation,[status(thm)],[f2805,f154]) ).
fof(f3094,plain,
sF1_fnc = greatest_lower_bound(sF0_fnc,a),
inference(forward_demodulation,[status(thm)],[f82,f3086]) ).
fof(f3334,plain,
least_upper_bound(a,sF0_fnc) = least_upper_bound(a,sF1_fnc),
inference(paramodulation,[status(thm)],[f44,f118]) ).
fof(f3370,plain,
least_upper_bound(a,sF0_fnc) = a,
inference(forward_demodulation,[status(thm)],[f52,f3334]) ).
fof(f3404,plain,
greatest_lower_bound(sF0_fnc,a) = sF0_fnc,
inference(paramodulation,[status(thm)],[f3370,f58]) ).
fof(f3409,plain,
sF1_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f3094,f3404]) ).
fof(f3410,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3409,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP138-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.33 % Computer : n001.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Sun Sep 20 20:07:58 UTC 2026
% 0.07/0.33 % CPUTime :
% 0.07/0.34 % Drodi V4.1.1
% 0.11/0.38 % Refutation found
% 0.11/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.41 % Elapsed time: 0.070279 seconds
% 0.11/0.41 % CPU time: 0.322690 seconds
% 0.11/0.41 % Total memory used: 9.909 MB
% 0.11/0.41 % Net memory used: 9.716 MB
%------------------------------------------------------------------------------