TSTP Solution File: SWV370+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWV370+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n013.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 12:41:30 EDT 2023
% Result : Theorem 0.15s 0.35s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 70 ( 5 unt; 0 def)
% Number of atoms : 193 ( 20 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 199 ( 76 ~; 87 |; 20 &)
% ( 13 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 148 (; 130 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [U,V,W] :
( contains_pq(insert_pq(U,V),W)
<=> ( contains_pq(U,W)
| V = W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [U,V,W,X] :
( contains_slb(insert_slb(U,pair(V,X)),W)
<=> ( contains_slb(U,W)
| V = W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [U,V,W,X] :
( contains_cpq(triple(U,V,W),X)
<=> contains_slb(V,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [U,V,W,X,Y] : i(triple(U,insert_slb(V,pair(X,Y)),W)) = insert_pq(i(triple(U,V,W)),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,conjecture,
! [U] :
( ! [V,W,X] :
( contains_cpq(triple(V,U,W),X)
<=> contains_pq(i(triple(V,U,W)),X) )
=> ! [Y,Z,X1,X2,X3] :
( contains_cpq(triple(Y,insert_slb(U,pair(X1,X2)),Z),X3)
<=> contains_pq(i(triple(Y,insert_slb(U,pair(X1,X2)),Z)),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,negated_conjecture,
~ ! [U] :
( ! [V,W,X] :
( contains_cpq(triple(V,U,W),X)
<=> contains_pq(i(triple(V,U,W)),X) )
=> ! [Y,Z,X1,X2,X3] :
( contains_cpq(triple(Y,insert_slb(U,pair(X1,X2)),Z),X3)
<=> contains_pq(i(triple(Y,insert_slb(U,pair(X1,X2)),Z)),X3) ) ),
inference(negated_conjecture,[status(cth)],[f63]) ).
fof(f79,plain,
! [U,V,W] :
( ( ~ contains_pq(insert_pq(U,V),W)
| contains_pq(U,W)
| V = W )
& ( contains_pq(insert_pq(U,V),W)
| ( ~ contains_pq(U,W)
& V != W ) ) ),
inference(NNF_transformation,[status(esa)],[f9]) ).
fof(f80,plain,
( ! [U,V,W] :
( ~ contains_pq(insert_pq(U,V),W)
| contains_pq(U,W)
| V = W )
& ! [U,V,W] :
( contains_pq(insert_pq(U,V),W)
| ( ~ contains_pq(U,W)
& V != W ) ) ),
inference(miniscoping,[status(esa)],[f79]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ~ contains_pq(insert_pq(X0,X1),X2)
| contains_pq(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[status(esa)],[f80]) ).
fof(f82,plain,
! [X0,X1,X2] :
( contains_pq(insert_pq(X0,X1),X2)
| ~ contains_pq(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f80]) ).
fof(f83,plain,
! [X0,X1,X2] :
( contains_pq(insert_pq(X0,X1),X2)
| X1 != X2 ),
inference(cnf_transformation,[status(esa)],[f80]) ).
fof(f106,plain,
! [U,V,W,X] :
( ( ~ contains_slb(insert_slb(U,pair(V,X)),W)
| contains_slb(U,W)
| V = W )
& ( contains_slb(insert_slb(U,pair(V,X)),W)
| ( ~ contains_slb(U,W)
& V != W ) ) ),
inference(NNF_transformation,[status(esa)],[f21]) ).
fof(f107,plain,
( ! [U,V,W] :
( ! [X] : ~ contains_slb(insert_slb(U,pair(V,X)),W)
| contains_slb(U,W)
| V = W )
& ! [U,V,W] :
( ! [X] : contains_slb(insert_slb(U,pair(V,X)),W)
| ( ~ contains_slb(U,W)
& V != W ) ) ),
inference(miniscoping,[status(esa)],[f106]) ).
fof(f108,plain,
! [X0,X1,X2,X3] :
( ~ contains_slb(insert_slb(X0,pair(X1,X2)),X3)
| contains_slb(X0,X3)
| X1 = X3 ),
inference(cnf_transformation,[status(esa)],[f107]) ).
fof(f109,plain,
! [X0,X1,X2,X3] :
( contains_slb(insert_slb(X0,pair(X1,X2)),X3)
| ~ contains_slb(X0,X3) ),
inference(cnf_transformation,[status(esa)],[f107]) ).
fof(f110,plain,
! [X0,X1,X2,X3] :
( contains_slb(insert_slb(X0,pair(X1,X2)),X3)
| X1 != X3 ),
inference(cnf_transformation,[status(esa)],[f107]) ).
fof(f155,plain,
! [U,V,W,X] :
( ( ~ contains_cpq(triple(U,V,W),X)
| contains_slb(V,X) )
& ( contains_cpq(triple(U,V,W),X)
| ~ contains_slb(V,X) ) ),
inference(NNF_transformation,[status(esa)],[f39]) ).
fof(f156,plain,
( ! [V,X] :
( ! [U,W] : ~ contains_cpq(triple(U,V,W),X)
| contains_slb(V,X) )
& ! [V,X] :
( ! [U,W] : contains_cpq(triple(U,V,W),X)
| ~ contains_slb(V,X) ) ),
inference(miniscoping,[status(esa)],[f155]) ).
fof(f157,plain,
! [X0,X1,X2,X3] :
( ~ contains_cpq(triple(X0,X1,X2),X3)
| contains_slb(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f156]) ).
fof(f158,plain,
! [X0,X1,X2,X3] :
( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_slb(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f156]) ).
fof(f193,plain,
! [X0,X1,X2,X3,X4] : i(triple(X0,insert_slb(X1,pair(X2,X3)),X4)) = insert_pq(i(triple(X0,X1,X4)),X2),
inference(cnf_transformation,[status(esa)],[f55]) ).
fof(f229,plain,
? [U] :
( ! [V,W,X] :
( contains_cpq(triple(V,U,W),X)
<=> contains_pq(i(triple(V,U,W)),X) )
& ? [Y,Z,X1,X2,X3] :
( contains_cpq(triple(Y,insert_slb(U,pair(X1,X2)),Z),X3)
<~> contains_pq(i(triple(Y,insert_slb(U,pair(X1,X2)),Z)),X3) ) ),
inference(pre_NNF_transformation,[status(esa)],[f64]) ).
fof(f230,plain,
? [U] :
( ! [V,W,X] :
( ( ~ contains_cpq(triple(V,U,W),X)
| contains_pq(i(triple(V,U,W)),X) )
& ( contains_cpq(triple(V,U,W),X)
| ~ contains_pq(i(triple(V,U,W)),X) ) )
& ? [Y,Z,X1,X2,X3] :
( ( contains_cpq(triple(Y,insert_slb(U,pair(X1,X2)),Z),X3)
| contains_pq(i(triple(Y,insert_slb(U,pair(X1,X2)),Z)),X3) )
& ( ~ contains_cpq(triple(Y,insert_slb(U,pair(X1,X2)),Z),X3)
| ~ contains_pq(i(triple(Y,insert_slb(U,pair(X1,X2)),Z)),X3) ) ) ),
inference(NNF_transformation,[status(esa)],[f229]) ).
fof(f231,plain,
? [U] :
( ! [V,W,X] :
( ~ contains_cpq(triple(V,U,W),X)
| contains_pq(i(triple(V,U,W)),X) )
& ! [V,W,X] :
( contains_cpq(triple(V,U,W),X)
| ~ contains_pq(i(triple(V,U,W)),X) )
& ? [Y,Z,X1,X2,X3] :
( ( contains_cpq(triple(Y,insert_slb(U,pair(X1,X2)),Z),X3)
| contains_pq(i(triple(Y,insert_slb(U,pair(X1,X2)),Z)),X3) )
& ( ~ contains_cpq(triple(Y,insert_slb(U,pair(X1,X2)),Z),X3)
| ~ contains_pq(i(triple(Y,insert_slb(U,pair(X1,X2)),Z)),X3) ) ) ),
inference(miniscoping,[status(esa)],[f230]) ).
fof(f232,plain,
( ! [V,W,X] :
( ~ contains_cpq(triple(V,sk0_4,W),X)
| contains_pq(i(triple(V,sk0_4,W)),X) )
& ! [V,W,X] :
( contains_cpq(triple(V,sk0_4,W),X)
| ~ contains_pq(i(triple(V,sk0_4,W)),X) )
& ( contains_cpq(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6),sk0_9)
| contains_pq(i(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6)),sk0_9) )
& ( ~ contains_cpq(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6),sk0_9)
| ~ contains_pq(i(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6)),sk0_9) ) ),
inference(skolemization,[status(esa)],[f231]) ).
fof(f233,plain,
! [X0,X1,X2] :
( ~ contains_cpq(triple(X0,sk0_4,X1),X2)
| contains_pq(i(triple(X0,sk0_4,X1)),X2) ),
inference(cnf_transformation,[status(esa)],[f232]) ).
fof(f234,plain,
! [X0,X1,X2] :
( contains_cpq(triple(X0,sk0_4,X1),X2)
| ~ contains_pq(i(triple(X0,sk0_4,X1)),X2) ),
inference(cnf_transformation,[status(esa)],[f232]) ).
fof(f235,plain,
( contains_cpq(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6),sk0_9)
| contains_pq(i(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6)),sk0_9) ),
inference(cnf_transformation,[status(esa)],[f232]) ).
fof(f236,plain,
( ~ contains_cpq(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6),sk0_9)
| ~ contains_pq(i(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6)),sk0_9) ),
inference(cnf_transformation,[status(esa)],[f232]) ).
fof(f237,plain,
( spl0_0
<=> contains_cpq(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6),sk0_9) ),
introduced(split_symbol_definition) ).
fof(f238,plain,
( contains_cpq(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6),sk0_9)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f239,plain,
( ~ contains_cpq(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6),sk0_9)
| spl0_0 ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f240,plain,
( spl0_1
<=> contains_pq(i(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6)),sk0_9) ),
introduced(split_symbol_definition) ).
fof(f241,plain,
( contains_pq(i(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6)),sk0_9)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f240]) ).
fof(f242,plain,
( ~ contains_pq(i(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6)),sk0_9)
| spl0_1 ),
inference(component_clause,[status(thm)],[f240]) ).
fof(f243,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f235,f237,f240]) ).
fof(f244,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f236,f237,f240]) ).
fof(f246,plain,
! [X0,X1] : contains_pq(insert_pq(X0,X1),X1),
inference(destructive_equality_resolution,[status(esa)],[f83]) ).
fof(f247,plain,
! [X0,X1,X2] : contains_slb(insert_slb(X0,pair(X1,X2)),X1),
inference(destructive_equality_resolution,[status(esa)],[f110]) ).
fof(f250,plain,
( contains_pq(insert_pq(i(triple(sk0_5,sk0_4,sk0_6)),sk0_7),sk0_9)
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f193,f241]) ).
fof(f256,plain,
( spl0_2
<=> contains_pq(i(triple(sk0_5,sk0_4,sk0_6)),sk0_9) ),
introduced(split_symbol_definition) ).
fof(f257,plain,
( contains_pq(i(triple(sk0_5,sk0_4,sk0_6)),sk0_9)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f256]) ).
fof(f259,plain,
( spl0_3
<=> sk0_7 = sk0_9 ),
introduced(split_symbol_definition) ).
fof(f260,plain,
( sk0_7 = sk0_9
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f262,plain,
( contains_pq(i(triple(sk0_5,sk0_4,sk0_6)),sk0_9)
| sk0_7 = sk0_9
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f250,f81]) ).
fof(f263,plain,
( spl0_2
| spl0_3
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f262,f256,f259,f240]) ).
fof(f264,plain,
( contains_cpq(triple(sk0_5,sk0_4,sk0_6),sk0_9)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f257,f234]) ).
fof(f265,plain,
( contains_slb(sk0_4,sk0_9)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f264,f157]) ).
fof(f266,plain,
( ~ contains_slb(insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_9)
| spl0_0 ),
inference(resolution,[status(thm)],[f239,f158]) ).
fof(f460,plain,
( ~ contains_slb(sk0_4,sk0_9)
| spl0_0 ),
inference(resolution,[status(thm)],[f109,f266]) ).
fof(f461,plain,
( $false
| ~ spl0_2
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f460,f265]) ).
fof(f462,plain,
( ~ spl0_2
| spl0_0 ),
inference(contradiction_clause,[status(thm)],[f461]) ).
fof(f463,plain,
( ~ contains_pq(insert_pq(i(triple(sk0_5,sk0_4,sk0_6)),sk0_7),sk0_9)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f193,f242]) ).
fof(f464,plain,
( ~ contains_pq(i(triple(sk0_5,sk0_4,sk0_6)),sk0_9)
| spl0_1 ),
inference(resolution,[status(thm)],[f463,f82]) ).
fof(f465,plain,
( ~ contains_cpq(triple(sk0_5,sk0_4,sk0_6),sk0_9)
| spl0_1 ),
inference(resolution,[status(thm)],[f464,f233]) ).
fof(f467,plain,
( ~ contains_slb(sk0_4,sk0_9)
| spl0_1 ),
inference(resolution,[status(thm)],[f465,f158]) ).
fof(f469,plain,
( contains_slb(insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_9)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f238,f157]) ).
fof(f470,plain,
( spl0_17
<=> contains_slb(sk0_4,sk0_9) ),
introduced(split_symbol_definition) ).
fof(f471,plain,
( contains_slb(sk0_4,sk0_9)
| ~ spl0_17 ),
inference(component_clause,[status(thm)],[f470]) ).
fof(f473,plain,
( contains_slb(sk0_4,sk0_9)
| sk0_7 = sk0_9
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f469,f108]) ).
fof(f474,plain,
( spl0_17
| spl0_3
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f473,f470,f259,f237]) ).
fof(f477,plain,
( ~ contains_slb(insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_7)
| ~ spl0_3
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f260,f266]) ).
fof(f478,plain,
( $false
| ~ spl0_3
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f477,f247]) ).
fof(f479,plain,
( ~ spl0_3
| spl0_0 ),
inference(contradiction_clause,[status(thm)],[f478]) ).
fof(f480,plain,
( $false
| ~ spl0_17
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f467,f471]) ).
fof(f481,plain,
( ~ spl0_17
| spl0_1 ),
inference(contradiction_clause,[status(thm)],[f480]) ).
fof(f488,plain,
( ~ contains_pq(insert_pq(i(triple(sk0_5,sk0_4,sk0_6)),sk0_7),sk0_7)
| ~ spl0_3
| spl0_1 ),
inference(backward_demodulation,[status(thm)],[f260,f463]) ).
fof(f489,plain,
( $false
| ~ spl0_3
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f488,f246]) ).
fof(f490,plain,
( ~ spl0_3
| spl0_1 ),
inference(contradiction_clause,[status(thm)],[f489]) ).
fof(f491,plain,
$false,
inference(sat_refutation,[status(thm)],[f243,f244,f263,f462,f474,f479,f481,f490]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWV370+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n013.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 11:33:20 EDT 2023
% 0.09/0.31 % CPUTime :
% 0.15/0.31 % Drodi V3.5.1
% 0.15/0.35 % Refutation found
% 0.15/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.37 % Elapsed time: 0.061903 seconds
% 0.15/0.37 % CPU time: 0.111358 seconds
% 0.15/0.37 % Memory used: 17.035 MB
%------------------------------------------------------------------------------