%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP185-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 12:33:02 PM UTC 2026
% Result : Unsatisfiable 4.84s 1.04s
% Output : CNFRefutation 4.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 19
% Syntax : Number of formulae : 80 ( 80 unt; 7 def)
% Number of atoms : 80 ( 79 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 73 ( 73 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] : least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] : greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
! [X] : inverse(inverse(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
file('/export/starexec/sandbox/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(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(f36,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f38,plain,
least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f39,definition,
sF2_fnc = multiply(a,b),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f40,definition,
sF1_fnc = least_upper_bound(sF2_fnc,identity),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f41,definition,
sF4_fnc = least_upper_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f42,definition,
sF5_fnc = least_upper_bound(b,identity),
introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition]) ).
fof(f43,definition,
sF3_fnc = multiply(sF4_fnc,sF5_fnc),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f44,definition,
sF0_fnc = least_upper_bound(sF1_fnc,sF3_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f45,definition,
sF6_fnc = multiply(sF4_fnc,sF5_fnc),
introduced(definition,[new_symbols(definition,[sF6_fnc])],[function_definition]) ).
fof(f46,plain,
sF0_fnc != sF6_fnc,
inference(definition_folding,[],[f38,f45,f44,f43,f42,f41,f40,f39]) ).
fof(f55,plain,
sF0_fnc != sF3_fnc,
inference(backward_demodulation,[status(thm)],[f56,f46]) ).
fof(f56,plain,
sF6_fnc = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f43,f45]) ).
fof(f70,plain,
! [X0] : least_upper_bound(a,least_upper_bound(identity,X0)) = least_upper_bound(sF4_fnc,X0),
inference(paramodulation,[status(thm)],[f41,f26]) ).
fof(f71,plain,
! [X0] : least_upper_bound(sF2_fnc,least_upper_bound(identity,X0)) = least_upper_bound(sF1_fnc,X0),
inference(paramodulation,[status(thm)],[f40,f26]) ).
fof(f72,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)],[f24,f26]) ).
fof(f80,plain,
! [X0,X1,X2] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X1,least_upper_bound(X0,X2)),
inference(forward_demodulation,[status(thm)],[f26,f72]) ).
fof(f113,plain,
! [X0] : multiply(sF4_fnc,least_upper_bound(sF5_fnc,X0)) = least_upper_bound(sF3_fnc,multiply(sF4_fnc,X0)),
inference(paramodulation,[status(thm)],[f43,f31]) ).
fof(f114,plain,
! [X0] : multiply(a,least_upper_bound(b,X0)) = least_upper_bound(sF2_fnc,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f39,f31]) ).
fof(f117,plain,
! [X0] : multiply(sF4_fnc,least_upper_bound(X0,sF5_fnc)) = least_upper_bound(multiply(sF4_fnc,X0),sF3_fnc),
inference(paramodulation,[status(thm)],[f43,f31]) ).
fof(f144,plain,
! [X0] : multiply(least_upper_bound(sF4_fnc,X0),sF5_fnc) = least_upper_bound(sF3_fnc,multiply(X0,sF5_fnc)),
inference(paramodulation,[status(thm)],[f43,f33]) ).
fof(f172,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f21,f22]) ).
fof(f173,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f20,f172]) ).
fof(f179,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f23,f29]) ).
fof(f192,plain,
greatest_lower_bound(a,sF4_fnc) = a,
inference(paramodulation,[status(thm)],[f41,f30]) ).
fof(f196,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f24,f30]) ).
fof(f347,plain,
least_upper_bound(sF4_fnc,a) = sF4_fnc,
inference(paramodulation,[status(thm)],[f192,f179]) ).
fof(f377,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,least_upper_bound(X1,least_upper_bound(X2,X0))) = X0,
inference(paramodulation,[status(thm)],[f26,f196]) ).
fof(f383,plain,
greatest_lower_bound(identity,sF5_fnc) = identity,
inference(paramodulation,[status(thm)],[f42,f196]) ).
fof(f385,plain,
greatest_lower_bound(identity,sF4_fnc) = identity,
inference(paramodulation,[status(thm)],[f41,f196]) ).
fof(f571,plain,
least_upper_bound(sF5_fnc,identity) = sF5_fnc,
inference(paramodulation,[status(thm)],[f383,f179]) ).
fof(f574,plain,
least_upper_bound(sF4_fnc,identity) = sF4_fnc,
inference(paramodulation,[status(thm)],[f385,f179]) ).
fof(f711,plain,
least_upper_bound(identity,sF5_fnc) = sF5_fnc,
inference(paramodulation,[status(thm)],[f24,f571]) ).
fof(f797,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f21,f173]) ).
fof(f818,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f36,f797]) ).
fof(f944,plain,
! [X0] : greatest_lower_bound(a,least_upper_bound(sF4_fnc,X0)) = a,
inference(paramodulation,[status(thm)],[f70,f30]) ).
fof(f1256,plain,
! [X0] : greatest_lower_bound(identity,least_upper_bound(X0,sF4_fnc)) = identity,
inference(paramodulation,[status(thm)],[f574,f377]) ).
fof(f1844,plain,
multiply(sF4_fnc,sF5_fnc) = least_upper_bound(sF3_fnc,multiply(sF4_fnc,identity)),
inference(paramodulation,[status(thm)],[f571,f113]) ).
fof(f1870,plain,
sF3_fnc = least_upper_bound(sF3_fnc,multiply(sF4_fnc,identity)),
inference(forward_demodulation,[status(thm)],[f43,f1844]) ).
fof(f1871,plain,
sF3_fnc = least_upper_bound(sF3_fnc,sF4_fnc),
inference(forward_demodulation,[status(thm)],[f818,f1870]) ).
fof(f2408,plain,
multiply(a,sF5_fnc) = least_upper_bound(sF2_fnc,multiply(a,identity)),
inference(paramodulation,[status(thm)],[f42,f114]) ).
fof(f2434,plain,
multiply(a,sF5_fnc) = least_upper_bound(sF2_fnc,a),
inference(forward_demodulation,[status(thm)],[f818,f2408]) ).
fof(f2499,plain,
multiply(sF4_fnc,sF5_fnc) = least_upper_bound(multiply(sF4_fnc,identity),sF3_fnc),
inference(paramodulation,[status(thm)],[f711,f117]) ).
fof(f2522,plain,
sF3_fnc = least_upper_bound(multiply(sF4_fnc,identity),sF3_fnc),
inference(forward_demodulation,[status(thm)],[f43,f2499]) ).
fof(f2523,plain,
sF3_fnc = least_upper_bound(sF4_fnc,sF3_fnc),
inference(forward_demodulation,[status(thm)],[f818,f2522]) ).
fof(f2579,plain,
greatest_lower_bound(a,sF3_fnc) = a,
inference(paramodulation,[status(thm)],[f2523,f944]) ).
fof(f2602,plain,
least_upper_bound(sF3_fnc,a) = sF3_fnc,
inference(paramodulation,[status(thm)],[f2579,f179]) ).
fof(f2847,plain,
greatest_lower_bound(identity,sF3_fnc) = identity,
inference(paramodulation,[status(thm)],[f1871,f1256]) ).
fof(f2876,plain,
least_upper_bound(sF3_fnc,identity) = sF3_fnc,
inference(paramodulation,[status(thm)],[f2847,f179]) ).
fof(f2879,plain,
least_upper_bound(identity,sF3_fnc) = sF3_fnc,
inference(paramodulation,[status(thm)],[f24,f2876]) ).
fof(f2899,plain,
least_upper_bound(sF2_fnc,sF3_fnc) = least_upper_bound(sF1_fnc,sF3_fnc),
inference(paramodulation,[status(thm)],[f2879,f71]) ).
fof(f2913,plain,
least_upper_bound(sF2_fnc,sF3_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f44,f2899]) ).
fof(f2921,plain,
multiply(sF4_fnc,sF5_fnc) = least_upper_bound(sF3_fnc,multiply(a,sF5_fnc)),
inference(paramodulation,[status(thm)],[f347,f144]) ).
fof(f2952,plain,
sF3_fnc = least_upper_bound(sF3_fnc,multiply(a,sF5_fnc)),
inference(forward_demodulation,[status(thm)],[f43,f2921]) ).
fof(f14466,plain,
sF3_fnc = least_upper_bound(sF3_fnc,least_upper_bound(sF2_fnc,a)),
inference(forward_demodulation,[status(thm)],[f2434,f2952]) ).
fof(f14467,plain,
sF3_fnc = least_upper_bound(sF2_fnc,least_upper_bound(sF3_fnc,a)),
inference(paramodulation,[status(thm)],[f80,f14466]) ).
fof(f14503,plain,
sF3_fnc = least_upper_bound(sF2_fnc,sF3_fnc),
inference(forward_demodulation,[status(thm)],[f2602,f14467]) ).
fof(f14504,plain,
sF3_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f2913,f14503]) ).
fof(f14505,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f14504,f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP185-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:05:19 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 4.84/1.04 % Refutation found
% 4.84/1.04 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.84/1.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 15.69/6.15 % Elapsed time: 5.790887 seconds
% 15.69/6.15 % CPU time: 33.546283 seconds
% 15.69/6.15 % Total memory used: 19.485 GB
% 15.69/6.15 % Net memory used: 19.484 GB
%------------------------------------------------------------------------------