TSTP Solution File: SWC348+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWC348+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n017.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 20:45:26 EDT 2024
% Result : Theorem 0.20s 0.37s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 20
% Syntax : Number of formulae : 95 ( 18 unt; 0 def)
% Number of atoms : 254 ( 37 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 254 ( 95 ~; 99 |; 28 &)
% ( 18 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 13 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 42 ( 35 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( ssItem(V)
& cons(V,nil) = U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [U] :
( ssList(U)
=> ( segmentP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [U] :
( ssItem(U)
=> strictorderedP(cons(U,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( V != X
| U != W
| ~ segmentP(X,W)
| ( ~ singletonP(W)
& neq(X,nil) )
| ( segmentP(V,U)
& strictorderedP(U) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( V != X
| U != W
| ~ segmentP(X,W)
| ( ~ singletonP(W)
& neq(X,nil) )
| ( segmentP(V,U)
& strictorderedP(U) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f113,plain,
! [U] :
( ~ ssList(U)
| ( singletonP(U)
<=> ? [V] :
( ssItem(V)
& cons(V,nil) = U ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f114,plain,
! [U] :
( ~ ssList(U)
| ( ( ~ singletonP(U)
| ? [V] :
( ssItem(V)
& cons(V,nil) = U ) )
& ( singletonP(U)
| ! [V] :
( ~ ssItem(V)
| cons(V,nil) != U ) ) ) ),
inference(NNF_transformation,[status(esa)],[f113]) ).
fof(f115,plain,
! [U] :
( ~ ssList(U)
| ( ( ~ singletonP(U)
| ( ssItem(sk0_4(U))
& cons(sk0_4(U),nil) = U ) )
& ( singletonP(U)
| ! [V] :
( ~ ssItem(V)
| cons(V,nil) != U ) ) ) ),
inference(skolemization,[status(esa)],[f114]) ).
fof(f116,plain,
! [X0] :
( ~ ssList(X0)
| ~ singletonP(X0)
| ssItem(sk0_4(X0)) ),
inference(cnf_transformation,[status(esa)],[f115]) ).
fof(f117,plain,
! [X0] :
( ~ ssList(X0)
| ~ singletonP(X0)
| cons(sk0_4(X0),nil) = X0 ),
inference(cnf_transformation,[status(esa)],[f115]) ).
fof(f217,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ( neq(U,V)
<=> U != V ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f218,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ( ( ~ neq(U,V)
| U != V )
& ( neq(U,V)
| U = V ) ) ) ),
inference(NNF_transformation,[status(esa)],[f217]) ).
fof(f220,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| neq(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f218]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f318,plain,
! [U] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(pre_NNF_transformation,[status(esa)],[f55]) ).
fof(f319,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f318]) ).
fof(f324,plain,
! [U] :
( ~ ssList(U)
| ( segmentP(nil,U)
<=> nil = U ) ),
inference(pre_NNF_transformation,[status(esa)],[f58]) ).
fof(f325,plain,
! [U] :
( ~ ssList(U)
| ( ( ~ segmentP(nil,U)
| nil = U )
& ( segmentP(nil,U)
| nil != U ) ) ),
inference(NNF_transformation,[status(esa)],[f324]) ).
fof(f326,plain,
! [X0] :
( ~ ssList(X0)
| ~ segmentP(nil,X0)
| nil = X0 ),
inference(cnf_transformation,[status(esa)],[f325]) ).
fof(f347,plain,
! [U] :
( ~ ssItem(U)
| strictorderedP(cons(U,nil)) ),
inference(pre_NNF_transformation,[status(esa)],[f68]) ).
fof(f348,plain,
! [X0] :
( ~ ssItem(X0)
| strictorderedP(cons(X0,nil)) ),
inference(cnf_transformation,[status(esa)],[f347]) ).
fof(f349,plain,
strictorderedP(nil),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f415,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& V = X
& U = W
& segmentP(X,W)
& ( singletonP(W)
| ~ neq(X,nil) )
& ( ~ segmentP(V,U)
| ~ strictorderedP(U) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f97]) ).
fof(f416,plain,
( ssList(sk0_47)
& ssList(sk0_48)
& ssList(sk0_49)
& ssList(sk0_50)
& sk0_48 = sk0_50
& sk0_47 = sk0_49
& segmentP(sk0_50,sk0_49)
& ( singletonP(sk0_49)
| ~ neq(sk0_50,nil) )
& ( ~ segmentP(sk0_48,sk0_47)
| ~ strictorderedP(sk0_47) ) ),
inference(skolemization,[status(esa)],[f415]) ).
fof(f417,plain,
ssList(sk0_47),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f418,plain,
ssList(sk0_48),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f421,plain,
sk0_48 = sk0_50,
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f422,plain,
sk0_47 = sk0_49,
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f423,plain,
segmentP(sk0_50,sk0_49),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f424,plain,
( singletonP(sk0_49)
| ~ neq(sk0_50,nil) ),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f425,plain,
( ~ segmentP(sk0_48,sk0_47)
| ~ strictorderedP(sk0_47) ),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f426,plain,
( spl0_0
<=> singletonP(sk0_49) ),
introduced(split_symbol_definition) ).
fof(f427,plain,
( singletonP(sk0_49)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f426]) ).
fof(f429,plain,
( spl0_1
<=> neq(sk0_50,nil) ),
introduced(split_symbol_definition) ).
fof(f431,plain,
( ~ neq(sk0_50,nil)
| spl0_1 ),
inference(component_clause,[status(thm)],[f429]) ).
fof(f432,plain,
( spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f424,f426,f429]) ).
fof(f433,plain,
( spl0_2
<=> segmentP(sk0_48,sk0_47) ),
introduced(split_symbol_definition) ).
fof(f435,plain,
( ~ segmentP(sk0_48,sk0_47)
| spl0_2 ),
inference(component_clause,[status(thm)],[f433]) ).
fof(f436,plain,
( spl0_3
<=> strictorderedP(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f438,plain,
( ~ strictorderedP(sk0_47)
| spl0_3 ),
inference(component_clause,[status(thm)],[f436]) ).
fof(f439,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f425,f433,f436]) ).
fof(f472,plain,
segmentP(sk0_48,sk0_49),
inference(forward_demodulation,[status(thm)],[f421,f423]) ).
fof(f473,plain,
segmentP(sk0_48,sk0_47),
inference(forward_demodulation,[status(thm)],[f422,f472]) ).
fof(f475,plain,
segmentP(sk0_48,sk0_48),
inference(resolution,[status(thm)],[f319,f418]) ).
fof(f476,plain,
segmentP(sk0_47,sk0_47),
inference(resolution,[status(thm)],[f319,f417]) ).
fof(f484,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f435,f473]) ).
fof(f485,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f484]) ).
fof(f486,plain,
( ~ neq(sk0_48,nil)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f421,f431]) ).
fof(f542,plain,
! [X0] :
( ~ ssList(X0)
| neq(sk0_48,X0)
| sk0_48 = X0 ),
inference(resolution,[status(thm)],[f220,f418]) ).
fof(f544,plain,
( spl0_13
<=> neq(sk0_48,nil) ),
introduced(split_symbol_definition) ).
fof(f545,plain,
( neq(sk0_48,nil)
| ~ spl0_13 ),
inference(component_clause,[status(thm)],[f544]) ).
fof(f547,plain,
( spl0_14
<=> sk0_48 = nil ),
introduced(split_symbol_definition) ).
fof(f548,plain,
( sk0_48 = nil
| ~ spl0_14 ),
inference(component_clause,[status(thm)],[f547]) ).
fof(f550,plain,
( neq(sk0_48,nil)
| sk0_48 = nil ),
inference(resolution,[status(thm)],[f542,f223]) ).
fof(f551,plain,
( spl0_13
| spl0_14 ),
inference(split_clause,[status(thm)],[f550,f544,f547]) ).
fof(f568,plain,
( $false
| spl0_1
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f545,f486]) ).
fof(f569,plain,
( spl0_1
| ~ spl0_13 ),
inference(contradiction_clause,[status(thm)],[f568]) ).
fof(f570,plain,
( singletonP(sk0_47)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f422,f427]) ).
fof(f579,plain,
( segmentP(nil,sk0_47)
| ~ spl0_14 ),
inference(backward_demodulation,[status(thm)],[f548,f473]) ).
fof(f600,plain,
( spl0_21
<=> sk0_47 = nil ),
introduced(split_symbol_definition) ).
fof(f601,plain,
( sk0_47 = nil
| ~ spl0_21 ),
inference(component_clause,[status(thm)],[f600]) ).
fof(f654,plain,
( spl0_30
<=> ssList(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f656,plain,
( ~ ssList(sk0_47)
| spl0_30 ),
inference(component_clause,[status(thm)],[f654]) ).
fof(f679,plain,
( $false
| spl0_30 ),
inference(forward_subsumption_resolution,[status(thm)],[f656,f417]) ).
fof(f680,plain,
spl0_30,
inference(contradiction_clause,[status(thm)],[f679]) ).
fof(f681,plain,
( spl0_35
<=> segmentP(sk0_48,sk0_48) ),
introduced(split_symbol_definition) ).
fof(f683,plain,
( ~ segmentP(sk0_48,sk0_48)
| spl0_35 ),
inference(component_clause,[status(thm)],[f681]) ).
fof(f701,plain,
( spl0_39
<=> segmentP(sk0_47,sk0_47) ),
introduced(split_symbol_definition) ).
fof(f703,plain,
( ~ segmentP(sk0_47,sk0_47)
| spl0_39 ),
inference(component_clause,[status(thm)],[f701]) ).
fof(f711,plain,
( $false
| spl0_35 ),
inference(forward_subsumption_resolution,[status(thm)],[f683,f475]) ).
fof(f712,plain,
spl0_35,
inference(contradiction_clause,[status(thm)],[f711]) ).
fof(f713,plain,
( $false
| spl0_39 ),
inference(forward_subsumption_resolution,[status(thm)],[f703,f476]) ).
fof(f714,plain,
spl0_39,
inference(contradiction_clause,[status(thm)],[f713]) ).
fof(f726,plain,
( spl0_41
<=> ssItem(sk0_4(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f727,plain,
( ssItem(sk0_4(sk0_47))
| ~ spl0_41 ),
inference(component_clause,[status(thm)],[f726]) ).
fof(f729,plain,
( ~ ssList(sk0_47)
| ssItem(sk0_4(sk0_47))
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f116,f570]) ).
fof(f730,plain,
( ~ spl0_30
| spl0_41
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f729,f654,f726,f426]) ).
fof(f731,plain,
( spl0_42
<=> cons(sk0_4(sk0_47),nil) = sk0_47 ),
introduced(split_symbol_definition) ).
fof(f732,plain,
( cons(sk0_4(sk0_47),nil) = sk0_47
| ~ spl0_42 ),
inference(component_clause,[status(thm)],[f731]) ).
fof(f734,plain,
( ~ ssList(sk0_47)
| cons(sk0_4(sk0_47),nil) = sk0_47
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f117,f570]) ).
fof(f735,plain,
( ~ spl0_30
| spl0_42
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f734,f654,f731,f426]) ).
fof(f790,plain,
( strictorderedP(cons(sk0_4(sk0_47),nil))
| ~ spl0_41 ),
inference(resolution,[status(thm)],[f727,f348]) ).
fof(f819,plain,
( strictorderedP(sk0_47)
| ~ spl0_42
| ~ spl0_41 ),
inference(forward_demodulation,[status(thm)],[f732,f790]) ).
fof(f820,plain,
( $false
| spl0_3
| ~ spl0_42
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[status(thm)],[f819,f438]) ).
fof(f821,plain,
( spl0_3
| ~ spl0_42
| ~ spl0_41 ),
inference(contradiction_clause,[status(thm)],[f820]) ).
fof(f827,plain,
( ~ ssList(sk0_47)
| nil = sk0_47
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f579,f326]) ).
fof(f828,plain,
( ~ spl0_30
| spl0_21
| ~ spl0_14 ),
inference(split_clause,[status(thm)],[f827,f654,f600,f547]) ).
fof(f841,plain,
( ~ strictorderedP(nil)
| ~ spl0_21
| spl0_3 ),
inference(backward_demodulation,[status(thm)],[f601,f438]) ).
fof(f842,plain,
( $false
| ~ spl0_21
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f841,f349]) ).
fof(f843,plain,
( ~ spl0_21
| spl0_3 ),
inference(contradiction_clause,[status(thm)],[f842]) ).
fof(f844,plain,
$false,
inference(sat_refutation,[status(thm)],[f432,f439,f485,f551,f569,f680,f712,f714,f730,f735,f821,f828,f843]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWC348+1 : TPTP v8.1.2. Released v2.4.0.
% 0.04/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 23:32:03 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.36 % Drodi V3.6.0
% 0.20/0.37 % Refutation found
% 0.20/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.38 % Elapsed time: 0.030831 seconds
% 0.20/0.38 % CPU time: 0.073088 seconds
% 0.20/0.38 % Total memory used: 17.006 MB
% 0.20/0.38 % Net memory used: 16.968 MB
%------------------------------------------------------------------------------