TSTP Solution File: REL048+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : REL048+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n014.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 : Tue Apr 30 20:37:37 EDT 2024
% Result : Theorem 2.87s 0.74s
% Output : CNFRefutation 2.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of formulae : 78 ( 65 unt; 0 def)
% Number of atoms : 95 ( 81 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 12 ~; 9 |; 4 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 97 ( 94 !; 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(f5,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
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,conjecture,
! [X0,X1,X2] :
( join(join(X0,X1),X2) = X2
=> ( join(X0,X2) = X2
& join(X1,X2) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [X0,X1,X2] :
( join(join(X0,X1),X2) = X2
=> ( join(X0,X2) = X2
& join(X1,X2) = X2 ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f17,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f18,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f19,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f20,plain,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f21,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f23,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f25,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f26,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f27,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f28,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f29,plain,
? [X0,X1,X2] :
( join(join(X0,X1),X2) = X2
& ( join(X0,X2) != X2
| join(X1,X2) != X2 ) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f30,plain,
( join(join(sk0_0,sk0_1),sk0_2) = sk0_2
& ( join(sk0_0,sk0_2) != sk0_2
| join(sk0_1,sk0_2) != sk0_2 ) ),
inference(skolemization,[status(esa)],[f29]) ).
fof(f31,plain,
join(join(sk0_0,sk0_1),sk0_2) = sk0_2,
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f32,plain,
( join(sk0_0,sk0_2) != sk0_2
| join(sk0_1,sk0_2) != sk0_2 ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f33,plain,
( spl0_0
<=> join(sk0_0,sk0_2) = sk0_2 ),
introduced(split_symbol_definition) ).
fof(f35,plain,
( join(sk0_0,sk0_2) != sk0_2
| spl0_0 ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f36,plain,
( spl0_1
<=> join(sk0_1,sk0_2) = sk0_2 ),
introduced(split_symbol_definition) ).
fof(f38,plain,
( join(sk0_1,sk0_2) != sk0_2
| spl0_1 ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f32,f33,f36]) ).
fof(f44,plain,
join(sk0_0,join(sk0_1,sk0_2)) = sk0_2,
inference(backward_demodulation,[status(thm)],[f17,f31]) ).
fof(f52,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X1,X0),X2),
inference(paramodulation,[status(thm)],[f16,f17]) ).
fof(f53,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X1,join(X0,X2)),
inference(forward_demodulation,[status(thm)],[f17,f52]) ).
fof(f133,plain,
! [X0] : join(X0,sk0_2) = join(sk0_0,join(X0,join(sk0_1,sk0_2))),
inference(paramodulation,[status(thm)],[f44,f53]) ).
fof(f244,plain,
! [X0] : meet(X0,complement(X0)) = complement(top),
inference(paramodulation,[status(thm)],[f27,f19]) ).
fof(f245,plain,
zero = complement(top),
inference(forward_demodulation,[status(thm)],[f28,f244]) ).
fof(f246,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f16,f19]) ).
fof(f247,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f19,f246]) ).
fof(f270,plain,
! [X0,X1] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(paramodulation,[status(thm)],[f21,f20]) ).
fof(f334,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(forward_demodulation,[status(thm)],[f16,f18]) ).
fof(f335,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f334]) ).
fof(f336,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f16,f335]) ).
fof(f344,plain,
! [X0,X1] : X0 = join(meet(X0,complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f336]) ).
fof(f345,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(X0,complement(X1))),
inference(forward_demodulation,[status(thm)],[f16,f344]) ).
fof(f346,plain,
! [X0] : X0 = join(meet(X0,complement(complement(X0))),complement(top)),
inference(paramodulation,[status(thm)],[f27,f336]) ).
fof(f347,plain,
! [X0] : X0 = join(complement(top),meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f16,f346]) ).
fof(f348,plain,
! [X0] : X0 = join(zero,meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f245,f347]) ).
fof(f402,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f23,f25]) ).
fof(f536,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(complement(X1),X0)),
inference(paramodulation,[status(thm)],[f247,f345]) ).
fof(f580,plain,
! [X0] : complement(complement(X0)) = join(meet(complement(complement(X0)),X0),zero),
inference(paramodulation,[status(thm)],[f28,f536]) ).
fof(f581,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(complement(complement(X0)),X0)),
inference(forward_demodulation,[status(thm)],[f16,f580]) ).
fof(f582,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f247,f581]) ).
fof(f583,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f348,f582]) ).
fof(f949,plain,
! [X0,X1] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f16,f26]) ).
fof(f960,plain,
! [X0,X1] : join(complement(X0),composition(X1,complement(composition(converse(X1),X0)))) = complement(X0),
inference(paramodulation,[status(thm)],[f23,f949]) ).
fof(f4088,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f21,f402]) ).
fof(f4089,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f23,f4088]) ).
fof(f4566,plain,
! [X0] : composition(one,X0) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f270,f4089]) ).
fof(f4567,plain,
! [X0] : composition(one,X0) = X0,
inference(forward_demodulation,[status(thm)],[f4089,f4566]) ).
fof(f4614,plain,
! [X0] : join(complement(X0),complement(composition(converse(one),X0))) = complement(X0),
inference(paramodulation,[status(thm)],[f4567,f960]) ).
fof(f4615,plain,
! [X0] : join(complement(X0),complement(X0)) = complement(X0),
inference(forward_demodulation,[status(thm)],[f4089,f4614]) ).
fof(f5494,plain,
! [X0] : join(X0,complement(complement(X0))) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f583,f4615]) ).
fof(f5495,plain,
! [X0] : join(X0,X0) = complement(complement(X0)),
inference(forward_demodulation,[status(thm)],[f583,f5494]) ).
fof(f5496,plain,
! [X0] : join(X0,X0) = X0,
inference(forward_demodulation,[status(thm)],[f583,f5495]) ).
fof(f5634,plain,
join(join(sk0_1,sk0_2),sk0_2) = join(sk0_0,join(sk0_1,sk0_2)),
inference(paramodulation,[status(thm)],[f5496,f133]) ).
fof(f5635,plain,
join(sk0_1,join(sk0_2,sk0_2)) = join(sk0_0,join(sk0_1,sk0_2)),
inference(forward_demodulation,[status(thm)],[f17,f5634]) ).
fof(f5636,plain,
join(sk0_1,sk0_2) = join(sk0_0,join(sk0_1,sk0_2)),
inference(forward_demodulation,[status(thm)],[f5496,f5635]) ).
fof(f5637,plain,
join(sk0_1,sk0_2) = sk0_2,
inference(forward_demodulation,[status(thm)],[f44,f5636]) ).
fof(f7067,plain,
join(sk0_0,sk0_2) = sk0_2,
inference(backward_demodulation,[status(thm)],[f5637,f44]) ).
fof(f7068,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f7067,f35]) ).
fof(f7069,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f7068]) ).
fof(f7092,plain,
( sk0_2 != sk0_2
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f5637,f38]) ).
fof(f7093,plain,
( $false
| spl0_1 ),
inference(trivial_equality_resolution,[status(esa)],[f7092]) ).
fof(f7094,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f7093]) ).
fof(f7095,plain,
$false,
inference(sat_refutation,[status(thm)],[f39,f7069,f7094]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : REL048+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 29 20:58:49 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.6.0
% 2.87/0.74 % Refutation found
% 2.87/0.74 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.87/0.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.87/0.76 % Elapsed time: 0.412023 seconds
% 2.87/0.76 % CPU time: 3.175336 seconds
% 2.87/0.76 % Total memory used: 74.617 MB
% 2.87/0.76 % Net memory used: 74.086 MB
%------------------------------------------------------------------------------