TSTP Solution File: SWC294+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWC294+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.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 20:45:14 EDT 2024
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 75 ( 15 unt; 0 def)
% Number of atoms : 209 ( 37 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 220 ( 86 ~; 83 |; 26 &)
% ( 14 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 9 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 39 ( 32 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( ssItem(V)
& cons(V,nil) = U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [U] :
( ssList(U)
=> ( segmentP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [U] :
( ssItem(U)
=> strictorderedP(cons(U,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox2/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)
| strictorderedP(U)
| ( ~ singletonP(W)
& neq(X,nil) ) ) ) ) ),
file('/export/starexec/sandbox2/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)
| strictorderedP(U)
| ( ~ singletonP(W)
& neq(X,nil) ) ) ) ) ),
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(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)
& ~ strictorderedP(U)
& ( singletonP(W)
| ~ neq(X,nil) ) ) ) ) ),
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)
& ~ strictorderedP(sk0_47)
& ( singletonP(sk0_49)
| ~ neq(sk0_50,nil) ) ),
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,
~ strictorderedP(sk0_47),
inference(cnf_transformation,[status(esa)],[f416]) ).
fof(f425,plain,
( singletonP(sk0_49)
| ~ neq(sk0_50,nil) ),
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)],[f425,f426,f429]) ).
fof(f465,plain,
segmentP(sk0_48,sk0_49),
inference(forward_demodulation,[status(thm)],[f421,f423]) ).
fof(f466,plain,
segmentP(sk0_48,sk0_47),
inference(forward_demodulation,[status(thm)],[f422,f465]) ).
fof(f477,plain,
( ~ neq(sk0_48,nil)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f421,f431]) ).
fof(f533,plain,
! [X0] :
( ~ ssList(X0)
| neq(sk0_48,X0)
| sk0_48 = X0 ),
inference(resolution,[status(thm)],[f220,f418]) ).
fof(f535,plain,
( spl0_11
<=> neq(sk0_48,nil) ),
introduced(split_symbol_definition) ).
fof(f536,plain,
( neq(sk0_48,nil)
| ~ spl0_11 ),
inference(component_clause,[status(thm)],[f535]) ).
fof(f538,plain,
( spl0_12
<=> sk0_48 = nil ),
introduced(split_symbol_definition) ).
fof(f539,plain,
( sk0_48 = nil
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f538]) ).
fof(f541,plain,
( neq(sk0_48,nil)
| sk0_48 = nil ),
inference(resolution,[status(thm)],[f533,f223]) ).
fof(f542,plain,
( spl0_11
| spl0_12 ),
inference(split_clause,[status(thm)],[f541,f535,f538]) ).
fof(f559,plain,
( $false
| spl0_1
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f536,f477]) ).
fof(f560,plain,
( spl0_1
| ~ spl0_11 ),
inference(contradiction_clause,[status(thm)],[f559]) ).
fof(f561,plain,
( singletonP(sk0_47)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f422,f427]) ).
fof(f570,plain,
( segmentP(nil,sk0_47)
| ~ spl0_12 ),
inference(backward_demodulation,[status(thm)],[f539,f466]) ).
fof(f591,plain,
( spl0_19
<=> sk0_47 = nil ),
introduced(split_symbol_definition) ).
fof(f592,plain,
( sk0_47 = nil
| ~ spl0_19 ),
inference(component_clause,[status(thm)],[f591]) ).
fof(f655,plain,
( spl0_25
<=> ssList(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f657,plain,
( ~ ssList(sk0_47)
| spl0_25 ),
inference(component_clause,[status(thm)],[f655]) ).
fof(f658,plain,
( spl0_26
<=> ssItem(sk0_4(sk0_47)) ),
introduced(split_symbol_definition) ).
fof(f659,plain,
( ssItem(sk0_4(sk0_47))
| ~ spl0_26 ),
inference(component_clause,[status(thm)],[f658]) ).
fof(f661,plain,
( ~ ssList(sk0_47)
| ssItem(sk0_4(sk0_47))
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f116,f561]) ).
fof(f662,plain,
( ~ spl0_25
| spl0_26
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f661,f655,f658,f426]) ).
fof(f663,plain,
( $false
| spl0_25 ),
inference(forward_subsumption_resolution,[status(thm)],[f657,f417]) ).
fof(f664,plain,
spl0_25,
inference(contradiction_clause,[status(thm)],[f663]) ).
fof(f665,plain,
( spl0_27
<=> cons(sk0_4(sk0_47),nil) = sk0_47 ),
introduced(split_symbol_definition) ).
fof(f666,plain,
( cons(sk0_4(sk0_47),nil) = sk0_47
| ~ spl0_27 ),
inference(component_clause,[status(thm)],[f665]) ).
fof(f668,plain,
( ~ ssList(sk0_47)
| cons(sk0_4(sk0_47),nil) = sk0_47
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f117,f561]) ).
fof(f669,plain,
( ~ spl0_25
| spl0_27
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f668,f655,f665,f426]) ).
fof(f694,plain,
( strictorderedP(cons(sk0_4(sk0_47),nil))
| ~ spl0_26 ),
inference(resolution,[status(thm)],[f659,f348]) ).
fof(f721,plain,
( strictorderedP(sk0_47)
| ~ spl0_27
| ~ spl0_26 ),
inference(forward_demodulation,[status(thm)],[f666,f694]) ).
fof(f722,plain,
( $false
| ~ spl0_27
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[status(thm)],[f721,f424]) ).
fof(f723,plain,
( ~ spl0_27
| ~ spl0_26 ),
inference(contradiction_clause,[status(thm)],[f722]) ).
fof(f725,plain,
( ~ ssList(sk0_47)
| nil = sk0_47
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f570,f326]) ).
fof(f726,plain,
( ~ spl0_25
| spl0_19
| ~ spl0_12 ),
inference(split_clause,[status(thm)],[f725,f655,f591,f538]) ).
fof(f749,plain,
( ~ strictorderedP(nil)
| ~ spl0_19 ),
inference(backward_demodulation,[status(thm)],[f592,f424]) ).
fof(f750,plain,
( $false
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[status(thm)],[f749,f349]) ).
fof(f751,plain,
~ spl0_19,
inference(contradiction_clause,[status(thm)],[f750]) ).
fof(f752,plain,
$false,
inference(sat_refutation,[status(thm)],[f432,f542,f560,f662,f664,f669,f723,f726,f751]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWC294+1 : TPTP v8.1.2. Released v2.4.0.
% 0.08/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n029.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 : Tue Apr 30 00:21:20 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.13/0.38 % Drodi V3.6.0
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.42 % Elapsed time: 0.040214 seconds
% 0.21/0.42 % CPU time: 0.069417 seconds
% 0.21/0.42 % Total memory used: 16.888 MB
% 0.21/0.42 % Net memory used: 16.849 MB
%------------------------------------------------------------------------------