%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP184-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 12:33:01 PM UTC 2026
% Result : Unsatisfiable 110.15s 14.48s
% Output : CNFRefutation 64.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 20
% Syntax : Number of formulae : 79 ( 79 unt; 6 def)
% Number of atoms : 79 ( 78 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 115 ( 115 !; 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(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(f8,axiom,
! [X] : least_upper_bound(X,X) = X,
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(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(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(f16,negated_conjecture,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f20,plain,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f23,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(f24,plain,
! [X0] : least_upper_bound(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f26,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f27,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f28,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(f29,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(f30,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(f31,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(f32,plain,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f33,definition,
sF1_fnc = least_upper_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f34,definition,
sF3_fnc = greatest_lower_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f35,definition,
sF2_fnc = inverse(sF3_fnc),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f36,definition,
sF0_fnc = multiply(sF1_fnc,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f37,definition,
sF5_fnc = inverse(sF3_fnc),
introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition]) ).
fof(f38,definition,
sF4_fnc = multiply(sF5_fnc,sF1_fnc),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f39,plain,
sF0_fnc != sF4_fnc,
inference(definition_folding,[],[f32,f38,f37,f36,f35,f34,f33]) ).
fof(f40,plain,
sF2_fnc = sF5_fnc,
inference(backward_demodulation,[status(thm)],[f37,f35]) ).
fof(f41,plain,
sF0_fnc = multiply(sF1_fnc,sF5_fnc),
inference(backward_demodulation,[status(thm)],[f40,f36]) ).
fof(f43,plain,
multiply(sF5_fnc,sF3_fnc) = identity,
inference(paramodulation,[status(thm)],[f37,f18]) ).
fof(f57,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f20,f26]) ).
fof(f80,plain,
! [X0,X1] : least_upper_bound(least_upper_bound(X0,X1),X0) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f27,f57]) ).
fof(f90,plain,
! [X0,X1] : least_upper_bound(X0,least_upper_bound(X0,X1)) = least_upper_bound(X0,X1),
inference(forward_demodulation,[status(thm)],[f21,f80]) ).
fof(f95,plain,
! [X0] : multiply(sF1_fnc,greatest_lower_bound(sF5_fnc,X0)) = greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,X0)),
inference(paramodulation,[status(thm)],[f41,f29]) ).
fof(f143,plain,
! [X0,X1,X2] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X1,X0),X2),
inference(paramodulation,[status(thm)],[f21,f23]) ).
fof(f187,plain,
! [X0,X1] : multiply(least_upper_bound(X0,identity),X1) = least_upper_bound(multiply(X0,X1),X1),
inference(paramodulation,[status(thm)],[f17,f30]) ).
fof(f197,plain,
! [X0,X1] : multiply(least_upper_bound(X0,identity),X1) = least_upper_bound(X1,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f21,f187]) ).
fof(f244,plain,
! [X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X0)) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f21,f90]) ).
fof(f902,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f18,f19]) ).
fof(f904,plain,
! [X0] : multiply(identity,X0) = multiply(sF5_fnc,multiply(sF3_fnc,X0)),
inference(paramodulation,[status(thm)],[f43,f19]) ).
fof(f918,plain,
! [X0] : X0 = multiply(sF5_fnc,multiply(sF3_fnc,X0)),
inference(forward_demodulation,[status(thm)],[f17,f904]) ).
fof(f919,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f17,f902]) ).
fof(f930,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f919,f919]) ).
fof(f931,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f18,f919]) ).
fof(f934,plain,
sF3_fnc = multiply(inverse(sF5_fnc),identity),
inference(paramodulation,[status(thm)],[f43,f919]) ).
fof(f942,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f930,f931]) ).
fof(f944,plain,
sF3_fnc = inverse(sF5_fnc),
inference(forward_demodulation,[status(thm)],[f942,f934]) ).
fof(f964,plain,
multiply(sF3_fnc,sF5_fnc) = identity,
inference(paramodulation,[status(thm)],[f944,f18]) ).
fof(f997,plain,
! [X0,X1] : multiply(greatest_lower_bound(X0,identity),X1) = greatest_lower_bound(multiply(X0,X1),X1),
inference(paramodulation,[status(thm)],[f17,f31]) ).
fof(f1021,plain,
! [X0,X1] : multiply(greatest_lower_bound(X0,identity),X1) = greatest_lower_bound(X1,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f20,f997]) ).
fof(f1149,plain,
! [X0,X1,X2,X3] : least_upper_bound(multiply(X0,X1),least_upper_bound(multiply(X0,X2),X3)) = least_upper_bound(multiply(X0,least_upper_bound(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f28,f23]) ).
fof(f1151,plain,
! [X0,X1,X2] : least_upper_bound(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,least_upper_bound(X2,X1)),
inference(paramodulation,[status(thm)],[f28,f21]) ).
fof(f7037,plain,
! [X0] : multiply(sF1_fnc,X0) = least_upper_bound(X0,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f33,f197]) ).
fof(f11110,plain,
! [X0] : multiply(sF3_fnc,X0) = greatest_lower_bound(X0,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f34,f1021]) ).
fof(f14202,plain,
! [X0,X1,X2] : least_upper_bound(multiply(X0,X1),multiply(X0,X2)) = least_upper_bound(multiply(X0,least_upper_bound(X1,X2)),multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f244,f1149]) ).
fof(f14431,plain,
! [X0,X1,X2] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,least_upper_bound(X1,X2)),multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f28,f14202]) ).
fof(f14432,plain,
! [X0,X1,X2] : multiply(X0,least_upper_bound(X1,X2)) = multiply(X0,least_upper_bound(least_upper_bound(X1,X2),X1)),
inference(forward_demodulation,[status(thm)],[f28,f14431]) ).
fof(f14433,plain,
! [X0,X1,X2] : multiply(X0,least_upper_bound(X1,X2)) = multiply(X0,least_upper_bound(X2,least_upper_bound(X1,X1))),
inference(forward_demodulation,[status(thm)],[f143,f14432]) ).
fof(f14434,plain,
! [X0,X1,X2] : multiply(X0,least_upper_bound(X1,X2)) = multiply(X0,least_upper_bound(X2,X1)),
inference(forward_demodulation,[status(thm)],[f24,f14433]) ).
fof(f25891,plain,
! [X0] : multiply(sF1_fnc,multiply(a,X0)) = multiply(a,least_upper_bound(multiply(a,X0),X0)),
inference(paramodulation,[status(thm)],[f7037,f1151]) ).
fof(f25935,plain,
! [X0] : multiply(sF1_fnc,multiply(a,X0)) = multiply(a,least_upper_bound(X0,multiply(a,X0))),
inference(forward_demodulation,[status(thm)],[f14434,f25891]) ).
fof(f25936,plain,
! [X0] : multiply(sF1_fnc,multiply(a,X0)) = multiply(a,multiply(sF1_fnc,X0)),
inference(forward_demodulation,[status(thm)],[f7037,f25935]) ).
fof(f28268,plain,
multiply(sF1_fnc,multiply(sF3_fnc,sF5_fnc)) = greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,multiply(a,sF5_fnc))),
inference(paramodulation,[status(thm)],[f11110,f95]) ).
fof(f28397,plain,
multiply(sF1_fnc,identity) = greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,multiply(a,sF5_fnc))),
inference(forward_demodulation,[status(thm)],[f964,f28268]) ).
fof(f28398,plain,
sF1_fnc = greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,multiply(a,sF5_fnc))),
inference(forward_demodulation,[status(thm)],[f942,f28397]) ).
fof(f28399,plain,
sF1_fnc = greatest_lower_bound(sF0_fnc,multiply(a,multiply(sF1_fnc,sF5_fnc))),
inference(forward_demodulation,[status(thm)],[f25936,f28398]) ).
fof(f28400,plain,
sF1_fnc = greatest_lower_bound(sF0_fnc,multiply(a,sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f41,f28399]) ).
fof(f28415,plain,
sF1_fnc = multiply(sF3_fnc,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f11110,f28400]) ).
fof(f28577,plain,
sF0_fnc = multiply(sF5_fnc,sF1_fnc),
inference(paramodulation,[status(thm)],[f28415,f918]) ).
fof(f28617,plain,
sF0_fnc = sF4_fnc,
inference(forward_demodulation,[status(thm)],[f38,f28577]) ).
fof(f28618,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f28617,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP184-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.45 % Computer : n017.cluster.edu
% 0.16/0.45 % Model : x86_64 x86_64
% 0.16/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.45 % Memory : 8046.5625MB
% 0.16/0.45 % OS : Linux 6.8.0-71-generic
% 0.16/0.45 % CPULimit : 300
% 0.16/0.45 % WCLimit : 300
% 0.16/0.45 % DateTime : Sun Sep 20 20:00:28 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.47 % Drodi V4.1.1
% 110.15/14.48 % Refutation found
% 110.15/14.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 110.15/14.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.38/15.15 % Elapsed time: 14.674923 seconds
% 6.38/15.15 % CPU time: 112.495366 seconds
% 6.38/15.15 % Total memory used: 615.667 MB
% 6.38/15.15 % Net memory used: 581.646 MB
%------------------------------------------------------------------------------