%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL001+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 : n009.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 02:03:09 PM UTC 2026
% Result : Theorem 0.14s 0.55s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 77 ( 77 unt; 1 def)
% Number of atoms : 77 ( 76 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 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; 5 con; 0-2 aty)
% Number of variables : 94 ( 93 !; 1 ?)
% 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(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
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(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(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,conjecture,
! [X0] : join(zero,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [X0] : join(zero,X0) = X0,
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(f18,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f19,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(cnf_transformation,[status(thm)],[f4]) ).
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(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(f28,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f29,plain,
? [X0] : join(zero,X0) != X0,
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f30,plain,
join(zero,sK0_skl) != sK0_skl,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f29]) ).
fof(f31,plain,
join(zero,sK0_skl) != sK0_skl,
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,definition,
sF0_fnc = join(zero,sK0_skl),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f33,plain,
sF0_fnc != sK0_skl,
inference(definition_folding,[],[f31,f32]) ).
fof(f34,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(backward_demodulation,[status(thm)],[f19,f18]) ).
fof(f40,plain,
! [X0,X1] : join(X0,join(X1,complement(join(X0,X1)))) = top,
inference(paramodulation,[status(thm)],[f27,f17]) ).
fof(f41,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(paramodulation,[status(thm)],[f16,f17]) ).
fof(f44,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(paramodulation,[status(thm)],[f27,f17]) ).
fof(f54,plain,
sF0_fnc = join(sK0_skl,zero),
inference(paramodulation,[status(thm)],[f16,f32]) ).
fof(f61,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f23,f25]) ).
fof(f65,plain,
! [X0,X1] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(paramodulation,[status(thm)],[f21,f20]) ).
fof(f78,plain,
! [X0] : meet(X0,complement(X0)) = complement(top),
inference(paramodulation,[status(thm)],[f27,f19]) ).
fof(f79,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f16,f19]) ).
fof(f85,plain,
zero = complement(top),
inference(forward_demodulation,[status(thm)],[f28,f78]) ).
fof(f86,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f19,f79]) ).
fof(f239,plain,
! [X0] : join(X0,top) = join(top,complement(complement(X0))),
inference(paramodulation,[status(thm)],[f27,f44]) ).
fof(f254,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f21,f61]) ).
fof(f271,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f23,f254]) ).
fof(f285,plain,
! [X0] : composition(one,X0) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f65,f271]) ).
fof(f287,plain,
! [X0] : join(complement(composition(one,X0)),complement(X0)) = complement(X0),
inference(paramodulation,[status(thm)],[f271,f26]) ).
fof(f300,plain,
! [X0] : composition(one,X0) = X0,
inference(forward_demodulation,[status(thm)],[f271,f285]) ).
fof(f302,plain,
! [X0] : join(complement(X0),complement(X0)) = complement(X0),
inference(forward_demodulation,[status(thm)],[f300,f287]) ).
fof(f358,plain,
! [X0] : meet(X0,X0) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f302,f19]) ).
fof(f359,plain,
! [X0] : X0 = join(meet(X0,complement(X0)),complement(complement(X0))),
inference(paramodulation,[status(thm)],[f302,f34]) ).
fof(f360,plain,
! [X0] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(paramodulation,[status(thm)],[f302,f44]) ).
fof(f370,plain,
! [X0] : X0 = join(zero,complement(complement(X0))),
inference(forward_demodulation,[status(thm)],[f28,f359]) ).
fof(f371,plain,
! [X0] : join(X0,top) = top,
inference(backward_demodulation,[status(thm)],[f372,f239]) ).
fof(f372,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[status(thm)],[f27,f360]) ).
fof(f380,plain,
! [X0] : X0 = join(meet(X0,top),complement(top)),
inference(paramodulation,[status(thm)],[f371,f34]) ).
fof(f402,plain,
! [X0] : X0 = join(meet(X0,top),zero),
inference(forward_demodulation,[status(thm)],[f85,f380]) ).
fof(f514,plain,
meet(top,top) = complement(zero),
inference(paramodulation,[status(thm)],[f85,f358]) ).
fof(f516,plain,
! [X0] : X0 = join(complement(complement(X0)),complement(join(complement(X0),X0))),
inference(paramodulation,[status(thm)],[f358,f34]) ).
fof(f523,plain,
! [X0] : top = join(complement(X0),meet(X0,X0)),
inference(paramodulation,[status(thm)],[f358,f27]) ).
fof(f700,plain,
! [X0] : X0 = join(meet(top,X0),zero),
inference(paramodulation,[status(thm)],[f86,f402]) ).
fof(f702,plain,
! [X0,X1] : join(meet(X0,top),join(zero,X1)) = join(X1,X0),
inference(paramodulation,[status(thm)],[f402,f41]) ).
fof(f704,plain,
! [X0] : join(meet(X0,top),join(zero,complement(X0))) = top,
inference(paramodulation,[status(thm)],[f402,f40]) ).
fof(f711,plain,
! [X0] : X0 = join(complement(complement(X0)),complement(top)),
inference(backward_demodulation,[status(thm)],[f712,f516]) ).
fof(f712,plain,
! [X0] : join(complement(X0),X0) = top,
inference(forward_demodulation,[status(thm)],[f702,f704]) ).
fof(f714,plain,
! [X0] : X0 = join(complement(complement(X0)),zero),
inference(forward_demodulation,[status(thm)],[f85,f711]) ).
fof(f972,plain,
! [X0] : complement(X0) = join(meet(complement(X0),zero),complement(X0)),
inference(paramodulation,[status(thm)],[f714,f34]) ).
fof(f1140,plain,
! [X0] : X0 = join(meet(X0,meet(X0,X0)),complement(top)),
inference(paramodulation,[status(thm)],[f523,f34]) ).
fof(f1148,plain,
! [X0] : X0 = join(meet(X0,meet(X0,X0)),zero),
inference(forward_demodulation,[status(thm)],[f85,f1140]) ).
fof(f1175,plain,
top = meet(top,top),
inference(paramodulation,[status(thm)],[f700,f1148]) ).
fof(f1192,plain,
top = complement(zero),
inference(forward_demodulation,[status(thm)],[f514,f1175]) ).
fof(f1211,plain,
! [X0] : meet(X0,zero) = complement(join(complement(X0),top)),
inference(paramodulation,[status(thm)],[f1192,f19]) ).
fof(f1225,plain,
! [X0] : meet(X0,zero) = complement(top),
inference(forward_demodulation,[status(thm)],[f371,f1211]) ).
fof(f1228,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(backward_demodulation,[status(thm)],[f1229,f972]) ).
fof(f1229,plain,
! [X0] : meet(X0,zero) = zero,
inference(forward_demodulation,[status(thm)],[f85,f1225]) ).
fof(f1234,plain,
! [X0] : X0 = complement(complement(X0)),
inference(backward_demodulation,[status(thm)],[f1228,f370]) ).
fof(f1238,plain,
! [X0] : X0 = join(X0,zero),
inference(backward_demodulation,[status(thm)],[f1234,f714]) ).
fof(f1278,plain,
sF0_fnc = sK0_skl,
inference(backward_demodulation,[status(thm)],[f1238,f54]) ).
fof(f1359,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1278,f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL001+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.44 % Computer : n009.cluster.edu
% 0.09/0.44 % Model : x86_64 x86_64
% 0.09/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.44 % Memory : 8046.5625MB
% 0.09/0.44 % OS : Linux 6.8.0-71-generic
% 0.09/0.44 % CPULimit : 300
% 0.09/0.44 % WCLimit : 300
% 0.09/0.44 % DateTime : Mon Sep 21 03:57:28 UTC 2026
% 0.09/0.44 % CPUTime :
% 0.09/0.45 % Drodi V4.1.1
% 0.14/0.55 % Refutation found
% 0.14/0.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.57 % Elapsed time: 0.113891 seconds
% 0.14/0.57 % CPU time: 0.799370 seconds
% 0.14/0.57 % Total memory used: 20.466 MB
% 0.14/0.57 % Net memory used: 20.070 MB
%------------------------------------------------------------------------------