%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP170-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 8.42s 11.42s
% Output : CNFRefutation 8.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 62 ( 62 unt; 3 def)
% Number of atoms : 62 ( 61 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 : 5 ( 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 : 55 ( 55 !; 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(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/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] : greatest_lower_bound(X,X) = X,
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(f13,axiom,
! [X,Y,Z] : multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
least_upper_bound(a,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
least_upper_bound(c,d) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
greatest_lower_bound(multiply(a,c),multiply(b,d)) != multiply(a,c),
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(f24,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(f27,plain,
! [X0] : greatest_lower_bound(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f28,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f29,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,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(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f34,plain,
least_upper_bound(a,b) = b,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f35,plain,
least_upper_bound(c,d) = d,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f36,plain,
greatest_lower_bound(multiply(a,c),multiply(b,d)) != multiply(a,c),
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 = greatest_lower_bound(sF1_fnc,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f40,plain,
sF0_fnc != sF1_fnc,
inference(definition_folding,[],[f36,f39,f38,f37]) ).
fof(f57,plain,
greatest_lower_bound(a,b) = a,
inference(paramodulation,[status(thm)],[f34,f29]) ).
fof(f58,plain,
greatest_lower_bound(c,d) = c,
inference(paramodulation,[status(thm)],[f35,f29]) ).
fof(f75,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X2,greatest_lower_bound(X0,X1)),
inference(paramodulation,[status(thm)],[f22,f24]) ).
fof(f100,plain,
! [X0] : multiply(b,greatest_lower_bound(d,X0)) = greatest_lower_bound(sF2_fnc,multiply(b,X0)),
inference(paramodulation,[status(thm)],[f38,f31]) ).
fof(f104,plain,
! [X0] : multiply(a,greatest_lower_bound(X0,c)) = greatest_lower_bound(multiply(a,X0),sF1_fnc),
inference(paramodulation,[status(thm)],[f37,f31]) ).
fof(f143,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f23,f29]) ).
fof(f166,plain,
! [X0,X1] : greatest_lower_bound(greatest_lower_bound(X0,X1),X0) = greatest_lower_bound(X0,X1),
inference(paramodulation,[status(thm)],[f28,f143]) ).
fof(f176,plain,
! [X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X0)) = greatest_lower_bound(X0,X1),
inference(forward_demodulation,[status(thm)],[f24,f166]) ).
fof(f575,plain,
! [X0,X1] : multiply(greatest_lower_bound(b,X0),greatest_lower_bound(d,X1)) = greatest_lower_bound(greatest_lower_bound(sF2_fnc,multiply(b,X1)),multiply(X0,greatest_lower_bound(d,X1))),
inference(paramodulation,[status(thm)],[f100,f33]) ).
fof(f591,plain,
! [X0] : multiply(greatest_lower_bound(X0,a),c) = greatest_lower_bound(multiply(X0,c),sF1_fnc),
inference(paramodulation,[status(thm)],[f37,f33]) ).
fof(f604,plain,
! [X0,X1] : multiply(greatest_lower_bound(b,X0),greatest_lower_bound(d,X1)) = greatest_lower_bound(sF2_fnc,greatest_lower_bound(multiply(b,X1),multiply(X0,greatest_lower_bound(d,X1)))),
inference(forward_demodulation,[status(thm)],[f24,f575]) ).
fof(f711,plain,
greatest_lower_bound(sF2_fnc,sF0_fnc) = greatest_lower_bound(sF2_fnc,sF1_fnc),
inference(paramodulation,[status(thm)],[f39,f176]) ).
fof(f1030,plain,
! [X0] : greatest_lower_bound(X0,c) = greatest_lower_bound(d,greatest_lower_bound(X0,c)),
inference(paramodulation,[status(thm)],[f58,f75]) ).
fof(f1031,plain,
! [X0] : greatest_lower_bound(X0,a) = greatest_lower_bound(b,greatest_lower_bound(X0,a)),
inference(paramodulation,[status(thm)],[f57,f75]) ).
fof(f1034,plain,
! [X0] : greatest_lower_bound(X0,sF0_fnc) = greatest_lower_bound(sF2_fnc,greatest_lower_bound(X0,sF1_fnc)),
inference(paramodulation,[status(thm)],[f39,f75]) ).
fof(f2137,plain,
greatest_lower_bound(sF2_fnc,sF0_fnc) = greatest_lower_bound(sF1_fnc,sF2_fnc),
inference(paramodulation,[status(thm)],[f22,f711]) ).
fof(f2156,plain,
greatest_lower_bound(sF2_fnc,sF0_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f39,f2137]) ).
fof(f2168,plain,
sF0_fnc = greatest_lower_bound(sF2_fnc,sF1_fnc),
inference(backward_demodulation,[status(thm)],[f2156,f711]) ).
fof(f8594,plain,
greatest_lower_bound(c,c) = greatest_lower_bound(d,c),
inference(paramodulation,[status(thm)],[f27,f1030]) ).
fof(f8636,plain,
c = greatest_lower_bound(d,c),
inference(forward_demodulation,[status(thm)],[f27,f8594]) ).
fof(f9324,plain,
multiply(a,c) = greatest_lower_bound(multiply(a,d),sF1_fnc),
inference(paramodulation,[status(thm)],[f8636,f104]) ).
fof(f9355,plain,
sF1_fnc = greatest_lower_bound(multiply(a,d),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f37,f9324]) ).
fof(f9491,plain,
greatest_lower_bound(a,a) = greatest_lower_bound(b,a),
inference(paramodulation,[status(thm)],[f27,f1031]) ).
fof(f9532,plain,
a = greatest_lower_bound(b,a),
inference(forward_demodulation,[status(thm)],[f27,f9491]) ).
fof(f18658,plain,
multiply(a,c) = greatest_lower_bound(multiply(b,c),sF1_fnc),
inference(paramodulation,[status(thm)],[f9532,f591]) ).
fof(f18711,plain,
sF1_fnc = greatest_lower_bound(multiply(b,c),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f37,f18658]) ).
fof(f19130,plain,
greatest_lower_bound(multiply(b,c),sF0_fnc) = greatest_lower_bound(sF2_fnc,sF1_fnc),
inference(paramodulation,[status(thm)],[f18711,f1034]) ).
fof(f19165,plain,
greatest_lower_bound(multiply(b,c),sF0_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f2168,f19130]) ).
fof(f33187,plain,
multiply(greatest_lower_bound(b,a),greatest_lower_bound(d,c)) = greatest_lower_bound(sF2_fnc,greatest_lower_bound(multiply(b,c),greatest_lower_bound(multiply(a,d),sF1_fnc))),
inference(paramodulation,[status(thm)],[f104,f604]) ).
fof(f33319,plain,
multiply(a,greatest_lower_bound(d,c)) = greatest_lower_bound(sF2_fnc,greatest_lower_bound(multiply(b,c),greatest_lower_bound(multiply(a,d),sF1_fnc))),
inference(forward_demodulation,[status(thm)],[f9532,f33187]) ).
fof(f33320,plain,
greatest_lower_bound(multiply(a,d),sF1_fnc) = greatest_lower_bound(sF2_fnc,greatest_lower_bound(multiply(b,c),greatest_lower_bound(multiply(a,d),sF1_fnc))),
inference(forward_demodulation,[status(thm)],[f104,f33319]) ).
fof(f33321,plain,
sF1_fnc = greatest_lower_bound(sF2_fnc,greatest_lower_bound(multiply(b,c),greatest_lower_bound(multiply(a,d),sF1_fnc))),
inference(forward_demodulation,[status(thm)],[f9355,f33320]) ).
fof(f33322,plain,
sF1_fnc = greatest_lower_bound(sF2_fnc,greatest_lower_bound(multiply(b,c),sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f9355,f33321]) ).
fof(f33323,plain,
sF1_fnc = greatest_lower_bound(multiply(b,c),sF0_fnc),
inference(forward_demodulation,[status(thm)],[f1034,f33322]) ).
fof(f33324,plain,
sF1_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f19165,f33323]) ).
fof(f33325,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f33324,f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP170-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/10.31 % Computer : n012.cluster.edu
% 0.03/10.31 % Model : x86_64 x86_64
% 0.03/10.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/10.31 % Memory : 8046.5625MB
% 0.03/10.31 % OS : Linux 6.8.0-71-generic
% 0.03/10.31 % CPULimit : 300
% 0.03/10.31 % WCLimit : 300
% 0.03/10.31 % DateTime : Sun Sep 20 20:03:34 UTC 2026
% 0.03/10.31 % CPUTime :
% 0.03/10.32 % Drodi V4.1.1
% 8.42/11.42 % Refutation found
% 8.42/11.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 8.42/11.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 10.63/12.66 % Elapsed time: 2.130175 seconds
% 10.63/12.66 % CPU time: 7.294832 seconds
% 10.63/12.66 % Total memory used: 163.434 MB
% 10.63/12.66 % Net memory used: 160.420 MB
%------------------------------------------------------------------------------