%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL015+1 : TPTP v9.3.1. Released v4.0.0.
% 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 02:03:15 PM UTC 2026
% Result : Theorem 0.17s 5.65s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 45 unt; 1 def)
% Number of atoms : 45 ( 44 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 57 ( 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,conjecture,
composition(top,top) = top,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
composition(top,top) != top,
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f17,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f20,plain,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f21,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f22,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f23,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f25,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f26,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f27,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
composition(top,top) != top,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f30,definition,
sF0_fnc = composition(top,top),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f31,plain,
sF0_fnc != top,
inference(definition_folding,[],[f29,f30]) ).
fof(f49,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(paramodulation,[status(thm)],[f27,f17]) ).
fof(f51,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f23,f25]) ).
fof(f72,plain,
! [X0,X1] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(paramodulation,[status(thm)],[f21,f20]) ).
fof(f109,plain,
! [X0] : join(X0,top) = join(top,complement(complement(X0))),
inference(paramodulation,[status(thm)],[f27,f49]) ).
fof(f122,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f21,f51]) ).
fof(f136,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f23,f122]) ).
fof(f146,plain,
! [X0] : composition(one,X0) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f72,f136]) ).
fof(f147,plain,
one = converse(one),
inference(paramodulation,[status(thm)],[f21,f136]) ).
fof(f156,plain,
! [X0] : composition(one,X0) = X0,
inference(forward_demodulation,[status(thm)],[f136,f146]) ).
fof(f170,plain,
! [X0] : composition(join(X0,top),top) = join(composition(X0,top),sF0_fnc),
inference(paramodulation,[status(thm)],[f30,f22]) ).
fof(f244,plain,
! [X0] : join(composition(one,complement(composition(one,X0))),complement(X0)) = complement(X0),
inference(paramodulation,[status(thm)],[f147,f26]) ).
fof(f261,plain,
! [X0] : join(complement(composition(one,X0)),complement(X0)) = complement(X0),
inference(forward_demodulation,[status(thm)],[f156,f244]) ).
fof(f262,plain,
! [X0] : join(complement(X0),complement(X0)) = complement(X0),
inference(forward_demodulation,[status(thm)],[f156,f261]) ).
fof(f292,plain,
! [X0] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(paramodulation,[status(thm)],[f262,f49]) ).
fof(f314,plain,
! [X0] : join(X0,top) = top,
inference(backward_demodulation,[status(thm)],[f315,f109]) ).
fof(f315,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[status(thm)],[f27,f292]) ).
fof(f319,plain,
! [X0] : composition(top,top) = join(composition(X0,top),sF0_fnc),
inference(backward_demodulation,[status(thm)],[f314,f170]) ).
fof(f322,plain,
! [X0] : sF0_fnc = join(composition(X0,top),sF0_fnc),
inference(forward_demodulation,[status(thm)],[f30,f319]) ).
fof(f324,plain,
! [X0] : join(top,X0) = top,
inference(paramodulation,[status(thm)],[f16,f314]) ).
fof(f1030,plain,
sF0_fnc = join(top,sF0_fnc),
inference(paramodulation,[status(thm)],[f156,f322]) ).
fof(f1039,plain,
sF0_fnc = top,
inference(forward_demodulation,[status(thm)],[f324,f1030]) ).
fof(f1040,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1039,f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL015+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/5.40 % Computer : n020.cluster.edu
% 0.14/5.40 % Model : x86_64 x86_64
% 0.14/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.40 % Memory : 8046.5625MB
% 0.14/5.40 % OS : Linux 6.8.0-71-generic
% 0.14/5.40 % CPULimit : 300
% 0.14/5.40 % WCLimit : 300
% 0.14/5.40 % DateTime : Mon Sep 21 04:00:08 UTC 2026
% 0.14/5.41 % CPUTime :
% 0.14/5.42 % Drodi V4.1.1
% 0.17/5.65 % Refutation found
% 0.17/5.65 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/5.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/5.68 % Elapsed time: 0.265290 seconds
% 0.17/5.68 % CPU time: 1.749743 seconds
% 0.17/5.68 % Total memory used: 33.703 MB
% 0.17/5.68 % Net memory used: 32.871 MB
%------------------------------------------------------------------------------