%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP184-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 135.08s 22.46s
% Output : CNFRefutation 118.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 58 ( 58 unt; 6 def)
% Number of atoms : 58 ( 57 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 : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 65 ( 65 !; 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(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(f17,hypothesis,
! [X] : inverse(inverse(X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,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(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(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(f32,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(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(f38,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)],[f19]) ).
fof(f39,definition,
sF1_fnc = least_upper_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f40,definition,
sF3_fnc = greatest_lower_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f41,definition,
sF2_fnc = inverse(sF3_fnc),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f42,definition,
sF0_fnc = multiply(sF1_fnc,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f43,definition,
sF5_fnc = inverse(sF3_fnc),
introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition]) ).
fof(f44,definition,
sF4_fnc = multiply(sF5_fnc,sF1_fnc),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f45,plain,
sF0_fnc != sF4_fnc,
inference(definition_folding,[],[f38,f44,f43,f42,f41,f40,f39]) ).
fof(f46,plain,
sF5_fnc = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f41,f43]) ).
fof(f47,plain,
sF4_fnc = multiply(sF2_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f46,f44]) ).
fof(f49,plain,
multiply(sF2_fnc,sF3_fnc) = identity,
inference(paramodulation,[status(thm)],[f41,f21]) ).
fof(f51,plain,
inverse(sF2_fnc) = sF3_fnc,
inference(paramodulation,[status(thm)],[f41,f36]) ).
fof(f53,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(paramodulation,[status(thm)],[f36,f21]) ).
fof(f55,plain,
multiply(sF3_fnc,sF2_fnc) = identity,
inference(paramodulation,[status(thm)],[f51,f21]) ).
fof(f64,plain,
! [X0] : multiply(identity,X0) = multiply(sF2_fnc,multiply(sF3_fnc,X0)),
inference(paramodulation,[status(thm)],[f49,f22]) ).
fof(f65,plain,
! [X0] : X0 = multiply(sF2_fnc,multiply(sF3_fnc,X0)),
inference(forward_demodulation,[status(thm)],[f20,f64]) ).
fof(f90,plain,
! [X0,X1] : multiply(identity,X0) = multiply(X1,multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f53,f22]) ).
fof(f91,plain,
! [X0,X1] : X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(forward_demodulation,[status(thm)],[f20,f90]) ).
fof(f189,plain,
! [X0] : X0 = multiply(X0,identity),
inference(paramodulation,[status(thm)],[f21,f91]) ).
fof(f618,plain,
! [X0] : multiply(sF1_fnc,greatest_lower_bound(sF2_fnc,X0)) = greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,X0)),
inference(paramodulation,[status(thm)],[f42,f32]) ).
fof(f820,plain,
! [X0,X1] : multiply(least_upper_bound(X0,identity),X1) = least_upper_bound(multiply(X0,X1),X1),
inference(paramodulation,[status(thm)],[f20,f33]) ).
fof(f852,plain,
! [X0,X1] : multiply(least_upper_bound(X0,identity),X1) = least_upper_bound(X1,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f24,f820]) ).
fof(f1032,plain,
! [X0,X1] : multiply(greatest_lower_bound(X0,identity),X1) = greatest_lower_bound(multiply(X0,X1),X1),
inference(paramodulation,[status(thm)],[f20,f34]) ).
fof(f1068,plain,
! [X0,X1] : multiply(greatest_lower_bound(X0,identity),X1) = greatest_lower_bound(X1,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f23,f1032]) ).
fof(f20621,plain,
! [X0] : multiply(sF1_fnc,X0) = least_upper_bound(X0,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f39,f852]) ).
fof(f31796,plain,
! [X0] : multiply(sF3_fnc,X0) = greatest_lower_bound(X0,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f40,f1068]) ).
fof(f39923,plain,
! [X0] : multiply(sF1_fnc,multiply(a,X0)) = multiply(a,least_upper_bound(X0,multiply(a,X0))),
inference(paramodulation,[status(thm)],[f31,f20621]) ).
fof(f40014,plain,
! [X0] : multiply(sF1_fnc,multiply(a,X0)) = multiply(a,multiply(sF1_fnc,X0)),
inference(forward_demodulation,[status(thm)],[f20621,f39923]) ).
fof(f47142,plain,
multiply(sF1_fnc,multiply(sF3_fnc,sF2_fnc)) = greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,multiply(a,sF2_fnc))),
inference(paramodulation,[status(thm)],[f31796,f618]) ).
fof(f47254,plain,
multiply(sF1_fnc,identity) = greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,multiply(a,sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f55,f47142]) ).
fof(f47255,plain,
sF1_fnc = greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,multiply(a,sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f189,f47254]) ).
fof(f47256,plain,
sF1_fnc = greatest_lower_bound(sF0_fnc,multiply(a,multiply(sF1_fnc,sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f40014,f47255]) ).
fof(f47257,plain,
sF1_fnc = greatest_lower_bound(sF0_fnc,multiply(a,sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f42,f47256]) ).
fof(f47278,plain,
sF1_fnc = multiply(sF3_fnc,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f31796,f47257]) ).
fof(f47617,plain,
sF0_fnc = multiply(sF2_fnc,sF1_fnc),
inference(paramodulation,[status(thm)],[f47278,f65]) ).
fof(f47704,plain,
sF0_fnc = sF4_fnc,
inference(forward_demodulation,[status(thm)],[f47,f47617]) ).
fof(f47705,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f47704,f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP184-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n020.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sun Sep 20 20:05:54 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 % Drodi V4.1.1
% 135.08/22.46 % Refutation found
% 135.08/22.46 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 135.08/22.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 67.77/23.82 % Elapsed time: 18.236903 seconds
% 67.77/23.82 % CPU time: 107.931184 seconds
% 67.77/23.82 % Total memory used: 661.141 MB
% 67.77/23.82 % Net memory used: 633.761 MB
%------------------------------------------------------------------------------