%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP170-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 12:32:57 PM UTC 2026
% Result : Unsatisfiable 19.08s 8.72s
% Output : CNFRefutation 19.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 42 ( 42 unt; 3 def)
% Number of atoms : 42 ( 41 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 44 ( 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(f16,hypothesis,
least_upper_bound(a,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
greatest_lower_bound(c,d) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
least_upper_bound(multiply(a,c),multiply(b,d)) != multiply(b,d),
file('/export/starexec/sandbox/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(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(f30,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(least_upper_bound(X0,X1),X2) = least_upper_bound(multiply(X0,X2),multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f34,plain,
least_upper_bound(a,b) = b,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f35,plain,
greatest_lower_bound(c,d) = c,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f36,plain,
least_upper_bound(multiply(a,c),multiply(b,d)) != multiply(b,d),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f37,definition,
sF1_fnc = multiply(a,c),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f38,definition,
sF2_fnc = multiply(b,d),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f39,definition,
sF0_fnc = least_upper_bound(sF1_fnc,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f40,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f36,f39,f38,f37]) ).
fof(f55,plain,
! [X0] : least_upper_bound(sF1_fnc,least_upper_bound(sF2_fnc,X0)) = least_upper_bound(sF0_fnc,X0),
inference(paramodulation,[status(thm)],[f39,f25]) ).
fof(f56,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)],[f23,f25]) ).
fof(f64,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)],[f25,f56]) ).
fof(f98,plain,
! [X0] : multiply(b,least_upper_bound(d,X0)) = least_upper_bound(sF2_fnc,multiply(b,X0)),
inference(paramodulation,[status(thm)],[f38,f30]) ).
fof(f126,plain,
! [X0] : multiply(least_upper_bound(a,X0),c) = least_upper_bound(sF1_fnc,multiply(X0,c)),
inference(paramodulation,[status(thm)],[f37,f32]) ).
fof(f163,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f22,f28]) ).
fof(f185,plain,
least_upper_bound(d,c) = d,
inference(paramodulation,[status(thm)],[f35,f163]) ).
fof(f1364,plain,
! [X0] : least_upper_bound(sF1_fnc,multiply(b,least_upper_bound(d,X0))) = least_upper_bound(sF0_fnc,multiply(b,X0)),
inference(paramodulation,[status(thm)],[f98,f55]) ).
fof(f1365,plain,
! [X0,X1] : least_upper_bound(sF2_fnc,least_upper_bound(X0,multiply(b,X1))) = least_upper_bound(X0,multiply(b,least_upper_bound(d,X1))),
inference(paramodulation,[status(thm)],[f98,f64]) ).
fof(f54044,plain,
least_upper_bound(sF1_fnc,multiply(b,d)) = least_upper_bound(sF0_fnc,multiply(b,c)),
inference(paramodulation,[status(thm)],[f185,f1364]) ).
fof(f54166,plain,
least_upper_bound(sF1_fnc,sF2_fnc) = least_upper_bound(sF0_fnc,multiply(b,c)),
inference(forward_demodulation,[status(thm)],[f38,f54044]) ).
fof(f54167,plain,
sF0_fnc = least_upper_bound(sF0_fnc,multiply(b,c)),
inference(forward_demodulation,[status(thm)],[f39,f54166]) ).
fof(f54589,plain,
least_upper_bound(sF2_fnc,multiply(least_upper_bound(a,b),c)) = least_upper_bound(sF1_fnc,multiply(b,least_upper_bound(d,c))),
inference(paramodulation,[status(thm)],[f126,f1365]) ).
fof(f54901,plain,
least_upper_bound(sF2_fnc,multiply(b,c)) = least_upper_bound(sF1_fnc,multiply(b,least_upper_bound(d,c))),
inference(forward_demodulation,[status(thm)],[f34,f54589]) ).
fof(f54902,plain,
multiply(b,least_upper_bound(d,c)) = least_upper_bound(sF1_fnc,multiply(b,least_upper_bound(d,c))),
inference(forward_demodulation,[status(thm)],[f98,f54901]) ).
fof(f54903,plain,
multiply(b,d) = least_upper_bound(sF1_fnc,multiply(b,least_upper_bound(d,c))),
inference(forward_demodulation,[status(thm)],[f185,f54902]) ).
fof(f54904,plain,
sF2_fnc = least_upper_bound(sF1_fnc,multiply(b,least_upper_bound(d,c))),
inference(forward_demodulation,[status(thm)],[f38,f54903]) ).
fof(f54905,plain,
sF2_fnc = least_upper_bound(sF0_fnc,multiply(b,c)),
inference(forward_demodulation,[status(thm)],[f1364,f54904]) ).
fof(f54906,plain,
sF2_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f54167,f54905]) ).
fof(f54907,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f54906,f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP170-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/6.17 % Computer : n010.cluster.edu
% 0.10/6.17 % Model : x86_64 x86_64
% 0.10/6.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/6.17 % Memory : 8046.5625MB
% 0.10/6.17 % OS : Linux 6.8.0-71-generic
% 0.10/6.17 % CPULimit : 300
% 0.10/6.17 % WCLimit : 300
% 0.10/6.17 % DateTime : Sun Sep 20 20:04:03 UTC 2026
% 0.10/6.18 % CPUTime :
% 0.10/6.19 % Drodi V4.1.1
% 19.08/8.72 % Refutation found
% 19.08/8.72 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 19.08/8.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 16.81/10.00 % Elapsed time: 3.603229 seconds
% 16.81/10.00 % CPU time: 16.372946 seconds
% 16.81/10.00 % Total memory used: 153.577 MB
% 16.81/10.00 % Net memory used: 150.228 MB
%------------------------------------------------------------------------------