%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP170-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 40.34s 5.83s
% Output : CNFRefutation 40.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 57 ( 57 unt; 3 def)
% Number of atoms : 57 ( 56 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 ( 1 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 : 73 ( 73 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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/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(f9,axiom,
! [X] : greatest_lower_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(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(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,hypothesis,
greatest_lower_bound(a,b) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
greatest_lower_bound(c,d) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
greatest_lower_bound(multiply(a,c),multiply(b,d)) != multiply(a,c),
file('/export/starexec/sandbox2/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(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(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,
greatest_lower_bound(a,b) = a,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f35,plain,
greatest_lower_bound(c,d) = c,
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(f50,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(f56,plain,
! [X0] : greatest_lower_bound(sF1_fnc,greatest_lower_bound(sF2_fnc,X0)) = greatest_lower_bound(sF0_fnc,X0),
inference(paramodulation,[status(thm)],[f39,f24]) ).
fof(f59,plain,
! [X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X0,X1)) = greatest_lower_bound(X0,X1),
inference(paramodulation,[status(thm)],[f27,f24]) ).
fof(f71,plain,
greatest_lower_bound(sF1_fnc,sF0_fnc) = greatest_lower_bound(sF1_fnc,sF2_fnc),
inference(paramodulation,[status(thm)],[f39,f59]) ).
fof(f84,plain,
greatest_lower_bound(sF1_fnc,sF0_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f39,f71]) ).
fof(f102,plain,
! [X0] : multiply(b,greatest_lower_bound(d,X0)) = greatest_lower_bound(sF2_fnc,multiply(b,X0)),
inference(paramodulation,[status(thm)],[f38,f31]) ).
fof(f130,plain,
! [X0] : multiply(greatest_lower_bound(a,X0),c) = greatest_lower_bound(sF1_fnc,multiply(X0,c)),
inference(paramodulation,[status(thm)],[f37,f33]) ).
fof(f171,plain,
least_upper_bound(sF1_fnc,sF0_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f84,f28]) ).
fof(f174,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f22,f28]) ).
fof(f179,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f23,f29]) ).
fof(f201,plain,
! [X0,X1] : least_upper_bound(least_upper_bound(X0,X1),X0) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f29,f174]) ).
fof(f382,plain,
! [X0] : greatest_lower_bound(X0,c) = greatest_lower_bound(d,greatest_lower_bound(X0,c)),
inference(paramodulation,[status(thm)],[f35,f50]) ).
fof(f386,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,X1) = greatest_lower_bound(least_upper_bound(X2,X1),greatest_lower_bound(X0,X1)),
inference(paramodulation,[status(thm)],[f179,f50]) ).
fof(f654,plain,
! [X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X0)) = least_upper_bound(X0,X1),
inference(forward_demodulation,[status(thm)],[f25,f201]) ).
fof(f676,plain,
! [X0,X1] : greatest_lower_bound(least_upper_bound(X0,X1),least_upper_bound(X1,X0)) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f654,f179]) ).
fof(f1413,plain,
! [X0] : greatest_lower_bound(sF1_fnc,multiply(b,greatest_lower_bound(d,X0))) = greatest_lower_bound(sF0_fnc,multiply(b,X0)),
inference(paramodulation,[status(thm)],[f102,f56]) ).
fof(f5319,plain,
greatest_lower_bound(c,c) = greatest_lower_bound(d,c),
inference(paramodulation,[status(thm)],[f27,f382]) ).
fof(f5346,plain,
c = greatest_lower_bound(d,c),
inference(forward_demodulation,[status(thm)],[f27,f5319]) ).
fof(f6193,plain,
! [X0,X1] : greatest_lower_bound(X0,X0) = greatest_lower_bound(least_upper_bound(X1,X0),X0),
inference(paramodulation,[status(thm)],[f27,f386]) ).
fof(f6300,plain,
! [X0,X1] : X0 = greatest_lower_bound(least_upper_bound(X1,X0),X0),
inference(forward_demodulation,[status(thm)],[f27,f6193]) ).
fof(f11204,plain,
! [X0,X1] : greatest_lower_bound(least_upper_bound(greatest_lower_bound(X0,X1),X0),X0) = least_upper_bound(greatest_lower_bound(X0,X1),X0),
inference(paramodulation,[status(thm)],[f28,f676]) ).
fof(f11414,plain,
! [X0,X1] : X0 = least_upper_bound(greatest_lower_bound(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f6300,f11204]) ).
fof(f56269,plain,
greatest_lower_bound(sF1_fnc,multiply(b,c)) = greatest_lower_bound(sF0_fnc,multiply(b,c)),
inference(paramodulation,[status(thm)],[f5346,f1413]) ).
fof(f56385,plain,
multiply(greatest_lower_bound(a,b),c) = greatest_lower_bound(sF0_fnc,multiply(b,c)),
inference(forward_demodulation,[status(thm)],[f130,f56269]) ).
fof(f56386,plain,
multiply(a,c) = greatest_lower_bound(sF0_fnc,multiply(b,c)),
inference(forward_demodulation,[status(thm)],[f34,f56385]) ).
fof(f56387,plain,
sF1_fnc = greatest_lower_bound(sF0_fnc,multiply(b,c)),
inference(forward_demodulation,[status(thm)],[f37,f56386]) ).
fof(f56476,plain,
sF0_fnc = least_upper_bound(sF1_fnc,sF0_fnc),
inference(paramodulation,[status(thm)],[f56387,f11414]) ).
fof(f56516,plain,
sF0_fnc = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f171,f56476]) ).
fof(f56517,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f56516,f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP170-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n026.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 20:06:24 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 40.34/5.83 % Refutation found
% 40.34/5.83 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 40.34/5.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 24.35/7.11 % Elapsed time: 6.518925 seconds
% 24.35/7.11 % CPU time: 35.924947 seconds
% 24.35/7.11 % Total memory used: 225.567 MB
% 24.35/7.11 % Net memory used: 220.700 MB
%------------------------------------------------------------------------------