TSTP Solution File: REL010+2 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : REL010+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:32:17 EDT 2023
% Result : Theorem 4.89s 1.00s
% Output : CNFRefutation 4.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 14
% Syntax : Number of formulae : 94 ( 90 unt; 0 def)
% Number of atoms : 98 ( 97 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 114 (; 111 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X0,X1,X2] : join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [X0,X1,X2] :
( meet(composition(X0,X1),X2) = zero
=> meet(X1,composition(converse(X0),X2)) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( meet(composition(X0,X1),X2) = zero
=> meet(X1,composition(converse(X0),X2)) = zero ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f20,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f21,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f22,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f24,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f25,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f26,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f27,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f28,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f29,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f30,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f31,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f32,plain,
! [X0,X1,X2] : join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f35,plain,
? [X0,X1,X2] :
( meet(composition(X0,X1),X2) = zero
& meet(X1,composition(converse(X0),X2)) != zero ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f36,plain,
( meet(composition(sk0_0,sk0_1),sk0_2) = zero
& meet(sk0_1,composition(converse(sk0_0),sk0_2)) != zero ),
inference(skolemization,[status(esa)],[f35]) ).
fof(f37,plain,
meet(composition(sk0_0,sk0_1),sk0_2) = zero,
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f38,plain,
meet(sk0_1,composition(converse(sk0_0),sk0_2)) != zero,
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f39,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(forward_demodulation,[status(thm)],[f19,f21]) ).
fof(f40,plain,
! [X0,X1] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f19,f29]) ).
fof(f41,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(backward_demodulation,[status(thm)],[f22,f39]) ).
fof(f42,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f19,f41]) ).
fof(f46,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(paramodulation,[status(thm)],[f26,f27]) ).
fof(f49,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f472,plain,
! [X0,X1,X2] : join(meet(composition(converse(X0),X1),X2),composition(meet(converse(X0),composition(X2,converse(X1))),meet(X1,composition(X0,X2)))) = composition(meet(converse(X0),composition(X2,converse(X1))),meet(X1,composition(converse(converse(X0)),X2))),
inference(paramodulation,[status(thm)],[f26,f32]) ).
fof(f473,plain,
! [X0,X1,X2] : join(meet(composition(converse(X0),X1),X2),composition(meet(converse(X0),composition(X2,converse(X1))),meet(X1,composition(X0,X2)))) = composition(meet(converse(X0),composition(X2,converse(X1))),meet(X1,composition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f26,f472]) ).
fof(f535,plain,
! [X0] : converse(top) = join(X0,converse(complement(converse(X0)))),
inference(paramodulation,[status(thm)],[f30,f46]) ).
fof(f548,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f24,f49]) ).
fof(f549,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f26,f548]) ).
fof(f618,plain,
one = converse(one),
inference(paramodulation,[status(thm)],[f24,f549]) ).
fof(f663,plain,
! [X0] : X0 = composition(one,X0),
inference(backward_demodulation,[status(thm)],[f618,f549]) ).
fof(f753,plain,
! [X0] : meet(X0,complement(X0)) = complement(top),
inference(paramodulation,[status(thm)],[f30,f22]) ).
fof(f754,plain,
zero = complement(top),
inference(forward_demodulation,[status(thm)],[f31,f753]) ).
fof(f755,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f19,f22]) ).
fof(f756,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f22,f755]) ).
fof(f772,plain,
zero = meet(sk0_2,composition(sk0_0,sk0_1)),
inference(paramodulation,[status(thm)],[f37,f756]) ).
fof(f834,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(paramodulation,[status(thm)],[f30,f20]) ).
fof(f847,plain,
! [X0] : join(X0,top) = join(top,complement(complement(X0))),
inference(paramodulation,[status(thm)],[f30,f834]) ).
fof(f868,plain,
! [X0,X1] : composition(join(one,X0),X1) = join(X1,composition(X0,X1)),
inference(paramodulation,[status(thm)],[f663,f25]) ).
fof(f900,plain,
! [X0] : join(complement(X0),composition(one,complement(composition(one,X0)))) = complement(X0),
inference(paramodulation,[status(thm)],[f618,f40]) ).
fof(f901,plain,
! [X0] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f663,f900]) ).
fof(f902,plain,
! [X0] : join(complement(X0),complement(X0)) = complement(X0),
inference(forward_demodulation,[status(thm)],[f663,f901]) ).
fof(f1079,plain,
join(zero,complement(top)) = complement(top),
inference(paramodulation,[status(thm)],[f754,f902]) ).
fof(f1080,plain,
join(zero,zero) = complement(top),
inference(forward_demodulation,[status(thm)],[f754,f1079]) ).
fof(f1081,plain,
join(zero,zero) = zero,
inference(forward_demodulation,[status(thm)],[f754,f1080]) ).
fof(f1107,plain,
! [X0] : meet(X0,X0) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f902,f22]) ).
fof(f1108,plain,
! [X0] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(paramodulation,[status(thm)],[f902,f834]) ).
fof(f1109,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[status(thm)],[f30,f1108]) ).
fof(f1132,plain,
! [X0] : join(X0,top) = top,
inference(backward_demodulation,[status(thm)],[f1109,f847]) ).
fof(f1135,plain,
! [X0] : join(top,X0) = top,
inference(paramodulation,[status(thm)],[f19,f1132]) ).
fof(f1176,plain,
! [X0] : join(zero,join(zero,X0)) = join(zero,X0),
inference(paramodulation,[status(thm)],[f1081,f20]) ).
fof(f1247,plain,
! [X0] : join(zero,join(X0,zero)) = join(zero,X0),
inference(paramodulation,[status(thm)],[f19,f1176]) ).
fof(f1252,plain,
converse(top) = top,
inference(paramodulation,[status(thm)],[f1135,f535]) ).
fof(f2255,plain,
! [X0] : composition(top,X0) = join(X0,composition(top,X0)),
inference(paramodulation,[status(thm)],[f1132,f868]) ).
fof(f2327,plain,
composition(top,top) = top,
inference(paramodulation,[status(thm)],[f1135,f2255]) ).
fof(f2417,plain,
join(complement(top),composition(converse(top),complement(top))) = complement(top),
inference(paramodulation,[status(thm)],[f2327,f40]) ).
fof(f2418,plain,
composition(join(one,converse(top)),complement(top)) = complement(top),
inference(forward_demodulation,[status(thm)],[f868,f2417]) ).
fof(f2419,plain,
composition(join(one,top),complement(top)) = complement(top),
inference(forward_demodulation,[status(thm)],[f1252,f2418]) ).
fof(f2420,plain,
composition(top,complement(top)) = complement(top),
inference(forward_demodulation,[status(thm)],[f1132,f2419]) ).
fof(f2421,plain,
composition(top,zero) = complement(top),
inference(forward_demodulation,[status(thm)],[f754,f2420]) ).
fof(f2422,plain,
composition(top,zero) = zero,
inference(forward_demodulation,[status(thm)],[f754,f2421]) ).
fof(f2450,plain,
! [X0] : X0 = join(zero,complement(join(complement(X0),complement(X0)))),
inference(paramodulation,[status(thm)],[f31,f42]) ).
fof(f2451,plain,
! [X0] : X0 = join(zero,meet(X0,X0)),
inference(forward_demodulation,[status(thm)],[f22,f2450]) ).
fof(f2452,plain,
! [X0] : X0 = join(zero,complement(complement(X0))),
inference(forward_demodulation,[status(thm)],[f1107,f2451]) ).
fof(f3125,plain,
! [X0] : composition(join(X0,top),zero) = join(composition(X0,zero),zero),
inference(paramodulation,[status(thm)],[f2422,f25]) ).
fof(f3126,plain,
! [X0] : composition(top,zero) = join(composition(X0,zero),zero),
inference(forward_demodulation,[status(thm)],[f1132,f3125]) ).
fof(f3127,plain,
! [X0] : zero = join(composition(X0,zero),zero),
inference(forward_demodulation,[status(thm)],[f2422,f3126]) ).
fof(f3128,plain,
! [X0] : zero = join(zero,composition(X0,zero)),
inference(forward_demodulation,[status(thm)],[f19,f3127]) ).
fof(f3157,plain,
! [X0] : join(zero,X0) = join(zero,complement(complement(X0))),
inference(paramodulation,[status(thm)],[f2452,f1176]) ).
fof(f3158,plain,
! [X0] : join(zero,X0) = X0,
inference(forward_demodulation,[status(thm)],[f2452,f3157]) ).
fof(f3171,plain,
! [X0] : join(X0,zero) = join(zero,X0),
inference(backward_demodulation,[status(thm)],[f3158,f1247]) ).
fof(f3172,plain,
! [X0] : join(X0,zero) = X0,
inference(forward_demodulation,[status(thm)],[f3158,f3171]) ).
fof(f3239,plain,
! [X0] : zero = composition(X0,zero),
inference(backward_demodulation,[status(thm)],[f3158,f3128]) ).
fof(f5611,plain,
join(meet(composition(converse(sk0_0),sk0_2),sk0_1),composition(meet(converse(sk0_0),composition(sk0_1,converse(sk0_2))),zero)) = composition(meet(converse(sk0_0),composition(sk0_1,converse(sk0_2))),meet(sk0_2,composition(sk0_0,sk0_1))),
inference(paramodulation,[status(thm)],[f772,f473]) ).
fof(f5612,plain,
join(meet(sk0_1,composition(converse(sk0_0),sk0_2)),composition(meet(converse(sk0_0),composition(sk0_1,converse(sk0_2))),zero)) = composition(meet(converse(sk0_0),composition(sk0_1,converse(sk0_2))),meet(sk0_2,composition(sk0_0,sk0_1))),
inference(forward_demodulation,[status(thm)],[f756,f5611]) ).
fof(f5613,plain,
join(meet(sk0_1,composition(converse(sk0_0),sk0_2)),zero) = composition(meet(converse(sk0_0),composition(sk0_1,converse(sk0_2))),meet(sk0_2,composition(sk0_0,sk0_1))),
inference(forward_demodulation,[status(thm)],[f3239,f5612]) ).
fof(f5614,plain,
meet(sk0_1,composition(converse(sk0_0),sk0_2)) = composition(meet(converse(sk0_0),composition(sk0_1,converse(sk0_2))),meet(sk0_2,composition(sk0_0,sk0_1))),
inference(forward_demodulation,[status(thm)],[f3172,f5613]) ).
fof(f5615,plain,
meet(sk0_1,composition(converse(sk0_0),sk0_2)) = composition(meet(converse(sk0_0),composition(sk0_1,converse(sk0_2))),zero),
inference(forward_demodulation,[status(thm)],[f772,f5614]) ).
fof(f5616,plain,
meet(sk0_1,composition(converse(sk0_0),sk0_2)) = zero,
inference(forward_demodulation,[status(thm)],[f3239,f5615]) ).
fof(f5617,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5616,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL010+2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue May 30 10:19:04 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % Drodi V3.5.1
% 4.89/1.00 % Refutation found
% 4.89/1.00 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.89/1.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.89/1.05 % Elapsed time: 0.692300 seconds
% 4.89/1.05 % CPU time: 5.312364 seconds
% 4.89/1.05 % Memory used: 84.362 MB
%------------------------------------------------------------------------------