%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP167-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 12:32:56 PM UTC 2026
% Result : Unsatisfiable 158.90s 20.42s
% Output : CNFRefutation 158.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 18
% Syntax : Number of formulae : 83 ( 83 unt; 3 def)
% Number of atoms : 83 ( 82 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; 5 con; 0-2 aty)
% Number of variables : 104 ( 104 !; 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(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(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(f14,axiom,
! [Y,Z,X] : multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X] : inverse(inverse(X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y] : inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f21,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f22,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] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f24,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] : 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(f26,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(f29,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f30,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f31,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(least_upper_bound(X0,X1),X2) = least_upper_bound(multiply(X0,X2),multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f34,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(f36,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f37,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f38,plain,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f39,definition,
sF1_fnc = least_upper_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f40,definition,
sF2_fnc = greatest_lower_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f41,definition,
sF0_fnc = multiply(sF1_fnc,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f42,plain,
a != sF0_fnc,
inference(definition_folding,[],[f38,f41,f40,f39]) ).
fof(f45,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(paramodulation,[status(thm)],[f36,f21]) ).
fof(f47,plain,
least_upper_bound(a,sF2_fnc) = a,
inference(paramodulation,[status(thm)],[f40,f29]) ).
fof(f55,plain,
! [X0] : multiply(sF0_fnc,X0) = multiply(sF1_fnc,multiply(sF2_fnc,X0)),
inference(paramodulation,[status(thm)],[f41,f22]) ).
fof(f56,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f21,f22]) ).
fof(f58,plain,
! [X0,X1] : multiply(identity,X0) = multiply(X1,multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f45,f22]) ).
fof(f62,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f20,f56]) ).
fof(f63,plain,
! [X0,X1] : X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(forward_demodulation,[status(thm)],[f20,f58]) ).
fof(f65,plain,
greatest_lower_bound(a,sF1_fnc) = a,
inference(paramodulation,[status(thm)],[f39,f30]) ).
fof(f74,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f23,f29]) ).
fof(f78,plain,
least_upper_bound(identity,sF2_fnc) = identity,
inference(paramodulation,[status(thm)],[f40,f74]) ).
fof(f93,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f24,f30]) ).
fof(f99,plain,
greatest_lower_bound(identity,sF1_fnc) = identity,
inference(paramodulation,[status(thm)],[f39,f93]) ).
fof(f118,plain,
least_upper_bound(sF1_fnc,identity) = sF1_fnc,
inference(paramodulation,[status(thm)],[f99,f74]) ).
fof(f120,plain,
least_upper_bound(identity,sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f24,f118]) ).
fof(f128,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f21,f62]) ).
fof(f133,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f36,f128]) ).
fof(f145,plain,
! [X0] : greatest_lower_bound(a,greatest_lower_bound(sF1_fnc,X0)) = greatest_lower_bound(a,X0),
inference(paramodulation,[status(thm)],[f65,f25]) ).
fof(f284,plain,
! [X0] : least_upper_bound(a,least_upper_bound(sF2_fnc,X0)) = least_upper_bound(a,X0),
inference(paramodulation,[status(thm)],[f47,f26]) ).
fof(f454,plain,
! [X0,X1] : multiply(X0,least_upper_bound(identity,X1)) = least_upper_bound(X0,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f133,f31]) ).
fof(f796,plain,
! [X0,X1] : multiply(least_upper_bound(identity,X0),X1) = least_upper_bound(X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f20,f33]) ).
fof(f809,plain,
! [X0,X1] : multiply(least_upper_bound(X0,identity),X1) = least_upper_bound(multiply(X0,X1),X1),
inference(paramodulation,[status(thm)],[f20,f33]) ).
fof(f837,plain,
! [X0,X1] : multiply(least_upper_bound(X0,identity),X1) = least_upper_bound(X1,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f24,f809]) ).
fof(f906,plain,
! [X0,X1] : inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f37,f63]) ).
fof(f1107,plain,
! [X0,X1] : multiply(greatest_lower_bound(X0,identity),X1) = greatest_lower_bound(multiply(X0,X1),X1),
inference(paramodulation,[status(thm)],[f20,f34]) ).
fof(f1138,plain,
! [X0,X1] : multiply(greatest_lower_bound(X0,identity),X1) = greatest_lower_bound(X1,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f23,f1107]) ).
fof(f21970,plain,
! [X0] : multiply(identity,X0) = least_upper_bound(X0,multiply(sF2_fnc,X0)),
inference(paramodulation,[status(thm)],[f78,f796]) ).
fof(f22114,plain,
! [X0] : X0 = least_upper_bound(X0,multiply(sF2_fnc,X0)),
inference(forward_demodulation,[status(thm)],[f20,f21970]) ).
fof(f25672,plain,
! [X0] : multiply(sF1_fnc,X0) = least_upper_bound(X0,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f39,f837]) ).
fof(f39525,plain,
! [X0] : multiply(X0,multiply(sF1_fnc,identity)) = least_upper_bound(X0,multiply(X0,multiply(a,identity))),
inference(paramodulation,[status(thm)],[f25672,f454]) ).
fof(f39731,plain,
! [X0,X1] : greatest_lower_bound(X0,multiply(X0,least_upper_bound(identity,X1))) = X0,
inference(paramodulation,[status(thm)],[f454,f30]) ).
fof(f39761,plain,
! [X0] : multiply(X0,sF1_fnc) = least_upper_bound(X0,multiply(X0,multiply(a,identity))),
inference(forward_demodulation,[status(thm)],[f133,f39525]) ).
fof(f39762,plain,
! [X0] : multiply(X0,sF1_fnc) = least_upper_bound(X0,multiply(X0,a)),
inference(forward_demodulation,[status(thm)],[f133,f39761]) ).
fof(f42309,plain,
! [X0] : greatest_lower_bound(X0,multiply(X0,sF1_fnc)) = X0,
inference(paramodulation,[status(thm)],[f120,f39731]) ).
fof(f46609,plain,
multiply(a,sF1_fnc) = multiply(sF1_fnc,a),
inference(paramodulation,[status(thm)],[f25672,f39762]) ).
fof(f46633,plain,
least_upper_bound(a,multiply(sF2_fnc,sF1_fnc)) = least_upper_bound(a,multiply(sF2_fnc,a)),
inference(paramodulation,[status(thm)],[f39762,f284]) ).
fof(f46799,plain,
least_upper_bound(a,multiply(sF2_fnc,sF1_fnc)) = a,
inference(forward_demodulation,[status(thm)],[f22114,f46633]) ).
fof(f47010,plain,
greatest_lower_bound(multiply(sF2_fnc,sF1_fnc),a) = multiply(sF2_fnc,sF1_fnc),
inference(paramodulation,[status(thm)],[f46799,f93]) ).
fof(f47043,plain,
greatest_lower_bound(a,multiply(sF2_fnc,sF1_fnc)) = multiply(sF2_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f23,f47010]) ).
fof(f51788,plain,
! [X0] : multiply(sF2_fnc,X0) = greatest_lower_bound(X0,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f40,f1138]) ).
fof(f52261,plain,
greatest_lower_bound(a,multiply(sF2_fnc,sF1_fnc)) = greatest_lower_bound(a,multiply(a,sF1_fnc)),
inference(paramodulation,[status(thm)],[f51788,f145]) ).
fof(f52374,plain,
multiply(sF2_fnc,sF1_fnc) = greatest_lower_bound(a,multiply(a,sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f47043,f52261]) ).
fof(f52387,plain,
multiply(sF2_fnc,sF1_fnc) = a,
inference(forward_demodulation,[status(thm)],[f42309,f52374]) ).
fof(f52484,plain,
multiply(sF0_fnc,sF1_fnc) = multiply(sF1_fnc,a),
inference(paramodulation,[status(thm)],[f52387,f55]) ).
fof(f52535,plain,
multiply(sF0_fnc,sF1_fnc) = multiply(a,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f46609,f52484]) ).
fof(f53743,plain,
inverse(sF0_fnc) = multiply(sF1_fnc,inverse(multiply(a,sF1_fnc))),
inference(paramodulation,[status(thm)],[f52535,f906]) ).
fof(f53844,plain,
inverse(sF0_fnc) = inverse(a),
inference(forward_demodulation,[status(thm)],[f906,f53743]) ).
fof(f53937,plain,
inverse(inverse(a)) = sF0_fnc,
inference(paramodulation,[status(thm)],[f53844,f36]) ).
fof(f54001,plain,
a = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f36,f53937]) ).
fof(f54002,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f54001,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP167-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:05:52 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 158.90/20.42 % Refutation found
% 158.90/20.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 158.90/20.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 21.25/21.64 % Elapsed time: 21.066614 seconds
% 21.25/21.64 % CPU time: 155.170558 seconds
% 21.25/21.64 % Total memory used: 913.459 MB
% 21.25/21.64 % Net memory used: 885.484 MB
%------------------------------------------------------------------------------