TSTP Solution File: SWC023+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWC023+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n025.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 May 21 04:40:40 EDT 2024
% Result : Theorem 0.14s 0.40s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 169
% Syntax : Number of formulae : 749 ( 53 unt; 0 def)
% Number of atoms : 3595 ( 720 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 4514 (1668 ~;1679 |; 794 &)
% ( 79 <=>; 294 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 42 ( 40 usr; 3 prp; 0-2 aty)
% Number of functors : 57 ( 57 usr; 7 con; 0-2 aty)
% Number of variables : 1738 (1400 !; 338 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f810,plain,
$false,
inference(avatar_sat_refutation,[],[f667,f788,f809]) ).
fof(f809,plain,
~ spl71_1,
inference(avatar_contradiction_clause,[],[f808]) ).
fof(f808,plain,
( $false
| ~ spl71_1 ),
inference(subsumption_resolution,[],[f807,f649]) ).
fof(f649,plain,
frontsegP(nil,nil),
inference(global_subsumption,[],[f385,f384,f383,f382,f395,f394,f393,f392,f391,f390,f389,f388,f387,f386,f396,f397,f398,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f422,f421,f424,f646,f426,f425,f429,f428,f645,f430,f431,f432,f433,f434,f437,f644,f435,f643,f439,f438,f442,f441,f447,f617,f445,f444,f448,f450,f449,f455,f619,f453,f452,f456,f459,f458,f457,f460,f461,f462,f463,f464,f465,f466,f467,f470,f469,f468,f471,f472,f473,f475,f474,f477,f476,f621,f479,f478,f481,f489,f488,f487,f486,f485,f484,f622,f490,f491,f500,f499,f498,f497,f496,f495,f494,f642,f501,f502,f512,f511,f510,f509,f508,f507,f506,f505,f625,f513,f514,f524,f523,f522,f521,f520,f519,f518,f517,f626,f525,f526,f536,f535,f534,f533,f532,f531,f530,f529,f627,f537,f539,f538,f547,f546,f545,f544,f543,f542,f541,f628,f548,f550,f549,f558,f557,f556,f555,f554,f553,f552,f629,f559,f630,f647,f560,f631,f648,f562,f632]) ).
fof(f632,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f565]) ).
fof(f565,plain,
! [X0] :
( frontsegP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f357,plain,
! [X0] :
( ( ( frontsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ frontsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f178]) ).
fof(f178,plain,
! [X0] :
( ( frontsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0] :
( ssList(X0)
=> ( frontsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).
fof(f562,plain,
! [X0] :
( ~ rearsegP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f356]) ).
fof(f356,plain,
! [X0] :
( ( ( rearsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ rearsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f177]) ).
fof(f177,plain,
! [X0] :
( ( rearsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0] :
( ssList(X0)
=> ( rearsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).
fof(f648,plain,
rearsegP(nil,nil),
inference(global_subsumption,[],[f385,f384,f383,f382,f395,f394,f393,f392,f391,f390,f389,f388,f387,f386,f396,f397,f398,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f422,f421,f424,f646,f426,f425,f429,f428,f645,f430,f431,f432,f433,f434,f437,f644,f435,f643,f439,f438,f442,f441,f447,f617,f445,f444,f448,f450,f449,f455,f619,f453,f452,f456,f459,f458,f457,f460,f461,f462,f463,f464,f465,f466,f467,f470,f469,f468,f471,f472,f473,f475,f474,f477,f476,f621,f479,f478,f481,f489,f488,f487,f486,f485,f484,f622,f490,f491,f500,f499,f498,f497,f496,f495,f494,f642,f501,f502,f512,f511,f510,f509,f508,f507,f506,f505,f625,f513,f514,f524,f523,f522,f521,f520,f519,f518,f517,f626,f525,f526,f536,f535,f534,f533,f532,f531,f530,f529,f627,f537,f539,f538,f547,f546,f545,f544,f543,f542,f541,f628,f548,f550,f549,f558,f557,f556,f555,f554,f553,f552,f629,f559,f630,f647,f560,f631]) ).
fof(f631,plain,
( rearsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f563]) ).
fof(f563,plain,
! [X0] :
( rearsegP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f356]) ).
fof(f560,plain,
! [X0] :
( ~ segmentP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f355]) ).
fof(f355,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f176]) ).
fof(f176,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
fof(f647,plain,
segmentP(nil,nil),
inference(global_subsumption,[],[f385,f384,f383,f382,f395,f394,f393,f392,f391,f390,f389,f388,f387,f386,f396,f397,f398,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f422,f421,f424,f646,f426,f425,f429,f428,f645,f430,f431,f432,f433,f434,f437,f644,f435,f643,f439,f438,f442,f441,f447,f617,f445,f444,f448,f450,f449,f455,f619,f453,f452,f456,f459,f458,f457,f460,f461,f462,f463,f464,f465,f466,f467,f470,f469,f468,f471,f472,f473,f475,f474,f477,f476,f621,f479,f478,f481,f489,f488,f487,f486,f485,f484,f622,f490,f491,f500,f499,f498,f497,f496,f495,f494,f642,f501,f502,f512,f511,f510,f509,f508,f507,f506,f505,f625,f513,f514,f524,f523,f522,f521,f520,f519,f518,f517,f626,f525,f526,f536,f535,f534,f533,f532,f531,f530,f529,f627,f537,f539,f538,f547,f546,f545,f544,f543,f542,f541,f628,f548,f550,f549,f558,f557,f556,f555,f554,f553,f552,f629,f559,f630]) ).
fof(f630,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f561]) ).
fof(f561,plain,
! [X0] :
( segmentP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f355]) ).
fof(f559,plain,
! [X0] :
( sP18(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f252]) ).
fof(f252,plain,
! [X0] :
( sP18(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f175,f251,f250]) ).
fof(f250,plain,
! [X0] :
( sP17(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
fof(f251,plain,
! [X0] :
( ( strictorderedP(X0)
<=> sP17(X0) )
| ~ sP18(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).
fof(f175,plain,
! [X0] :
( ( strictorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f174]) ).
fof(f174,plain,
! [X0] :
( ( strictorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( ssList(X0)
=> ( strictorderedP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> lt(X1,X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax12) ).
fof(f629,plain,
! [X10,X8,X6,X9,X7] :
( lt(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP17(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f551]) ).
fof(f551,plain,
! [X10,X0,X8,X6,X9,X7] :
( lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP17(X0) ),
inference(cnf_transformation,[],[f354]) ).
fof(f354,plain,
! [X0] :
( ( sP17(X0)
| ( ~ lt(sK58(X0),sK59(X0))
& app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),sK62(X0))) = X0
& ssList(sK62(X0))
& ssList(sK61(X0))
& ssList(sK60(X0))
& ssItem(sK59(X0))
& ssItem(sK58(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP17(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK58,sK59,sK60,sK61,sK62])],[f348,f353,f352,f351,f350,f349]) ).
fof(f349,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK58(X0),X2)
& app(app(X3,cons(sK58(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK58(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f350,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK58(X0),X2)
& app(app(X3,cons(sK58(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK58(X0),sK59(X0))
& app(app(X3,cons(sK58(X0),X4)),cons(sK59(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK59(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f351,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK58(X0),sK59(X0))
& app(app(X3,cons(sK58(X0),X4)),cons(sK59(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ lt(sK58(X0),sK59(X0))
& app(app(sK60(X0),cons(sK58(X0),X4)),cons(sK59(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK60(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f352,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK58(X0),sK59(X0))
& app(app(sK60(X0),cons(sK58(X0),X4)),cons(sK59(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ lt(sK58(X0),sK59(X0))
& app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),X5)) = X0
& ssList(X5) )
& ssList(sK61(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f353,plain,
! [X0] :
( ? [X5] :
( ~ lt(sK58(X0),sK59(X0))
& app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),X5)) = X0
& ssList(X5) )
=> ( ~ lt(sK58(X0),sK59(X0))
& app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),sK62(X0))) = X0
& ssList(sK62(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
! [X0] :
( ( sP17(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP17(X0) ) ),
inference(rectify,[],[f347]) ).
fof(f347,plain,
! [X0] :
( ( sP17(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP17(X0) ) ),
inference(nnf_transformation,[],[f250]) ).
fof(f552,plain,
! [X0] :
( ssItem(sK58(X0))
| sP17(X0) ),
inference(cnf_transformation,[],[f354]) ).
fof(f553,plain,
! [X0] :
( ssItem(sK59(X0))
| sP17(X0) ),
inference(cnf_transformation,[],[f354]) ).
fof(f554,plain,
! [X0] :
( ssList(sK60(X0))
| sP17(X0) ),
inference(cnf_transformation,[],[f354]) ).
fof(f555,plain,
! [X0] :
( ssList(sK61(X0))
| sP17(X0) ),
inference(cnf_transformation,[],[f354]) ).
fof(f556,plain,
! [X0] :
( ssList(sK62(X0))
| sP17(X0) ),
inference(cnf_transformation,[],[f354]) ).
fof(f557,plain,
! [X0] :
( sP17(X0)
| app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),sK62(X0))) = X0 ),
inference(cnf_transformation,[],[f354]) ).
fof(f558,plain,
! [X0] :
( ~ lt(sK58(X0),sK59(X0))
| sP17(X0) ),
inference(cnf_transformation,[],[f354]) ).
fof(f549,plain,
! [X0] :
( ~ sP18(X0)
| ~ strictorderedP(X0)
| sP17(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f346,plain,
! [X0] :
( ( ( strictorderedP(X0)
| ~ sP17(X0) )
& ( sP17(X0)
| ~ strictorderedP(X0) ) )
| ~ sP18(X0) ),
inference(nnf_transformation,[],[f251]) ).
fof(f550,plain,
! [X0] :
( ~ sP18(X0)
| ~ sP17(X0)
| strictorderedP(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f548,plain,
! [X0] :
( sP16(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f249]) ).
fof(f249,plain,
! [X0] :
( sP16(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f173,f248,f247]) ).
fof(f247,plain,
! [X0] :
( sP15(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f248,plain,
! [X0] :
( ( totalorderedP(X0)
<=> sP15(X0) )
| ~ sP16(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f173,plain,
! [X0] :
( ( totalorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f172]) ).
fof(f172,plain,
! [X0] :
( ( totalorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( ssList(X0)
=> ( totalorderedP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> leq(X1,X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11) ).
fof(f628,plain,
! [X10,X8,X6,X9,X7] :
( leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP15(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f540]) ).
fof(f540,plain,
! [X10,X0,X8,X6,X9,X7] :
( leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP15(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f345,plain,
! [X0] :
( ( sP15(X0)
| ( ~ leq(sK53(X0),sK54(X0))
& app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),sK57(X0))) = X0
& ssList(sK57(X0))
& ssList(sK56(X0))
& ssList(sK55(X0))
& ssItem(sK54(X0))
& ssItem(sK53(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP15(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57])],[f339,f344,f343,f342,f341,f340]) ).
fof(f340,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK53(X0),X2)
& app(app(X3,cons(sK53(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK53(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f341,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK53(X0),X2)
& app(app(X3,cons(sK53(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK53(X0),sK54(X0))
& app(app(X3,cons(sK53(X0),X4)),cons(sK54(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK54(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f342,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK53(X0),sK54(X0))
& app(app(X3,cons(sK53(X0),X4)),cons(sK54(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK53(X0),sK54(X0))
& app(app(sK55(X0),cons(sK53(X0),X4)),cons(sK54(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK55(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f343,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK53(X0),sK54(X0))
& app(app(sK55(X0),cons(sK53(X0),X4)),cons(sK54(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK53(X0),sK54(X0))
& app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),X5)) = X0
& ssList(X5) )
& ssList(sK56(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f344,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK53(X0),sK54(X0))
& app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK53(X0),sK54(X0))
& app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),sK57(X0))) = X0
& ssList(sK57(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f339,plain,
! [X0] :
( ( sP15(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP15(X0) ) ),
inference(rectify,[],[f338]) ).
fof(f338,plain,
! [X0] :
( ( sP15(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP15(X0) ) ),
inference(nnf_transformation,[],[f247]) ).
fof(f541,plain,
! [X0] :
( ssItem(sK53(X0))
| sP15(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f542,plain,
! [X0] :
( ssItem(sK54(X0))
| sP15(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f543,plain,
! [X0] :
( ssList(sK55(X0))
| sP15(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f544,plain,
! [X0] :
( ssList(sK56(X0))
| sP15(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f545,plain,
! [X0] :
( ssList(sK57(X0))
| sP15(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f546,plain,
! [X0] :
( sP15(X0)
| app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),sK57(X0))) = X0 ),
inference(cnf_transformation,[],[f345]) ).
fof(f547,plain,
! [X0] :
( ~ leq(sK53(X0),sK54(X0))
| sP15(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f538,plain,
! [X0] :
( ~ sP16(X0)
| ~ totalorderedP(X0)
| sP15(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f337,plain,
! [X0] :
( ( ( totalorderedP(X0)
| ~ sP15(X0) )
& ( sP15(X0)
| ~ totalorderedP(X0) ) )
| ~ sP16(X0) ),
inference(nnf_transformation,[],[f248]) ).
fof(f539,plain,
! [X0] :
( ~ sP16(X0)
| ~ sP15(X0)
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f537,plain,
! [X0] :
( sP14(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f246]) ).
fof(f246,plain,
! [X0] :
( sP14(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f171,f245,f244]) ).
fof(f244,plain,
! [X0] :
( sP13(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f245,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> sP13(X0) )
| ~ sP14(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f171,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f170]) ).
fof(f170,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ssList(X0)
=> ( cyclefreeP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> ~ ( leq(X2,X1)
& leq(X1,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8) ).
fof(f627,plain,
! [X10,X8,X6,X9,X7] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP13(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f528]) ).
fof(f528,plain,
! [X10,X0,X8,X6,X9,X7] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP13(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f336,plain,
! [X0] :
( ( sP13(X0)
| ( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),sK52(X0))) = X0
& ssList(sK52(X0))
& ssList(sK51(X0))
& ssList(sK50(X0))
& ssItem(sK49(X0))
& ssItem(sK48(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP13(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48,sK49,sK50,sK51,sK52])],[f330,f335,f334,f333,f332,f331]) ).
fof(f331,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,X1)
& leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,sK48(X0))
& leq(sK48(X0),X2)
& app(app(X3,cons(sK48(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK48(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f332,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,sK48(X0))
& leq(sK48(X0),X2)
& app(app(X3,cons(sK48(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(X3,cons(sK48(X0),X4)),cons(sK49(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK49(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f333,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(X3,cons(sK48(X0),X4)),cons(sK49(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(sK50(X0),cons(sK48(X0),X4)),cons(sK49(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK50(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f334,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(sK50(X0),cons(sK48(X0),X4)),cons(sK49(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),X5)) = X0
& ssList(X5) )
& ssList(sK51(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f335,plain,
! [X0] :
( ? [X5] :
( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),X5)) = X0
& ssList(X5) )
=> ( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),sK52(X0))) = X0
& ssList(sK52(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f330,plain,
! [X0] :
( ( sP13(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,X1)
& leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP13(X0) ) ),
inference(rectify,[],[f329]) ).
fof(f329,plain,
! [X0] :
( ( sP13(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,X1)
& leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP13(X0) ) ),
inference(nnf_transformation,[],[f244]) ).
fof(f529,plain,
! [X0] :
( ssItem(sK48(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f530,plain,
! [X0] :
( ssItem(sK49(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f531,plain,
! [X0] :
( ssList(sK50(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f532,plain,
! [X0] :
( ssList(sK51(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f533,plain,
! [X0] :
( ssList(sK52(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f534,plain,
! [X0] :
( sP13(X0)
| app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),sK52(X0))) = X0 ),
inference(cnf_transformation,[],[f336]) ).
fof(f535,plain,
! [X0] :
( leq(sK48(X0),sK49(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f536,plain,
! [X0] :
( leq(sK49(X0),sK48(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f526,plain,
! [X0] :
( ~ sP14(X0)
| ~ cyclefreeP(X0)
| sP13(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f328,plain,
! [X0] :
( ( ( cyclefreeP(X0)
| ~ sP13(X0) )
& ( sP13(X0)
| ~ cyclefreeP(X0) ) )
| ~ sP14(X0) ),
inference(nnf_transformation,[],[f245]) ).
fof(f525,plain,
! [X0] :
( sP12(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f243]) ).
fof(f243,plain,
! [X0] :
( sP12(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f169,f242,f241]) ).
fof(f241,plain,
! [X0] :
( sP11(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f242,plain,
! [X0] :
( ( strictorderP(X0)
<=> sP11(X0) )
| ~ sP12(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f169,plain,
! [X0] :
( ( strictorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f168]) ).
fof(f168,plain,
! [X0] :
( ( strictorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( ssList(X0)
=> ( strictorderP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> ( lt(X2,X1)
| lt(X1,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10) ).
fof(f626,plain,
! [X10,X8,X6,X9,X7] :
( lt(X7,X6)
| lt(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP11(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f516]) ).
fof(f516,plain,
! [X10,X0,X8,X6,X9,X7] :
( lt(X7,X6)
| lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP11(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f327,plain,
! [X0] :
( ( sP11(X0)
| ( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),sK47(X0))) = X0
& ssList(sK47(X0))
& ssList(sK46(X0))
& ssList(sK45(X0))
& ssItem(sK44(X0))
& ssItem(sK43(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X7,X6)
| lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP11(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK43,sK44,sK45,sK46,sK47])],[f321,f326,f325,f324,f323,f322]) ).
fof(f322,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,X1)
& ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,sK43(X0))
& ~ lt(sK43(X0),X2)
& app(app(X3,cons(sK43(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK43(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f323,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,sK43(X0))
& ~ lt(sK43(X0),X2)
& app(app(X3,cons(sK43(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(X3,cons(sK43(X0),X4)),cons(sK44(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK44(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f324,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(X3,cons(sK43(X0),X4)),cons(sK44(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(sK45(X0),cons(sK43(X0),X4)),cons(sK44(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK45(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f325,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(sK45(X0),cons(sK43(X0),X4)),cons(sK44(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),X5)) = X0
& ssList(X5) )
& ssList(sK46(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f326,plain,
! [X0] :
( ? [X5] :
( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),X5)) = X0
& ssList(X5) )
=> ( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),sK47(X0))) = X0
& ssList(sK47(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f321,plain,
! [X0] :
( ( sP11(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,X1)
& ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X7,X6)
| lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP11(X0) ) ),
inference(rectify,[],[f320]) ).
fof(f320,plain,
! [X0] :
( ( sP11(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,X1)
& ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP11(X0) ) ),
inference(nnf_transformation,[],[f241]) ).
fof(f517,plain,
! [X0] :
( ssItem(sK43(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f518,plain,
! [X0] :
( ssItem(sK44(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f519,plain,
! [X0] :
( ssList(sK45(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f520,plain,
! [X0] :
( ssList(sK46(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f521,plain,
! [X0] :
( ssList(sK47(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f522,plain,
! [X0] :
( sP11(X0)
| app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),sK47(X0))) = X0 ),
inference(cnf_transformation,[],[f327]) ).
fof(f523,plain,
! [X0] :
( ~ lt(sK43(X0),sK44(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f524,plain,
! [X0] :
( ~ lt(sK44(X0),sK43(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f514,plain,
! [X0] :
( ~ sP12(X0)
| ~ strictorderP(X0)
| sP11(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f319,plain,
! [X0] :
( ( ( strictorderP(X0)
| ~ sP11(X0) )
& ( sP11(X0)
| ~ strictorderP(X0) ) )
| ~ sP12(X0) ),
inference(nnf_transformation,[],[f242]) ).
fof(f513,plain,
! [X0] :
( sP10(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f240]) ).
fof(f240,plain,
! [X0] :
( sP10(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f167,f239,f238]) ).
fof(f238,plain,
! [X0] :
( sP9(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f239,plain,
! [X0] :
( ( totalorderP(X0)
<=> sP9(X0) )
| ~ sP10(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f167,plain,
! [X0] :
( ( totalorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f166]) ).
fof(f166,plain,
! [X0] :
( ( totalorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( ssList(X0)
=> ( totalorderP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> ( leq(X2,X1)
| leq(X1,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax9) ).
fof(f625,plain,
! [X10,X8,X6,X9,X7] :
( leq(X7,X6)
| leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP9(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f504]) ).
fof(f504,plain,
! [X10,X0,X8,X6,X9,X7] :
( leq(X7,X6)
| leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f318,plain,
! [X0] :
( ( sP9(X0)
| ( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),sK42(X0))) = X0
& ssList(sK42(X0))
& ssList(sK41(X0))
& ssList(sK40(X0))
& ssItem(sK39(X0))
& ssItem(sK38(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X7,X6)
| leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP9(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39,sK40,sK41,sK42])],[f312,f317,f316,f315,f314,f313]) ).
fof(f313,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,X1)
& ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,sK38(X0))
& ~ leq(sK38(X0),X2)
& app(app(X3,cons(sK38(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK38(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f314,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,sK38(X0))
& ~ leq(sK38(X0),X2)
& app(app(X3,cons(sK38(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(X3,cons(sK38(X0),X4)),cons(sK39(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK39(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f315,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(X3,cons(sK38(X0),X4)),cons(sK39(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(sK40(X0),cons(sK38(X0),X4)),cons(sK39(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK40(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f316,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(sK40(X0),cons(sK38(X0),X4)),cons(sK39(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),X5)) = X0
& ssList(X5) )
& ssList(sK41(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f317,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),sK42(X0))) = X0
& ssList(sK42(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f312,plain,
! [X0] :
( ( sP9(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,X1)
& ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X7,X6)
| leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP9(X0) ) ),
inference(rectify,[],[f311]) ).
fof(f311,plain,
! [X0] :
( ( sP9(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,X1)
& ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP9(X0) ) ),
inference(nnf_transformation,[],[f238]) ).
fof(f505,plain,
! [X0] :
( ssItem(sK38(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f506,plain,
! [X0] :
( ssItem(sK39(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f507,plain,
! [X0] :
( ssList(sK40(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f508,plain,
! [X0] :
( ssList(sK41(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f509,plain,
! [X0] :
( ssList(sK42(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f510,plain,
! [X0] :
( sP9(X0)
| app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),sK42(X0))) = X0 ),
inference(cnf_transformation,[],[f318]) ).
fof(f511,plain,
! [X0] :
( ~ leq(sK38(X0),sK39(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f512,plain,
! [X0] :
( ~ leq(sK39(X0),sK38(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f502,plain,
! [X0] :
( ~ sP10(X0)
| ~ totalorderP(X0)
| sP9(X0) ),
inference(cnf_transformation,[],[f310]) ).
fof(f310,plain,
! [X0] :
( ( ( totalorderP(X0)
| ~ sP9(X0) )
& ( sP9(X0)
| ~ totalorderP(X0) ) )
| ~ sP10(X0) ),
inference(nnf_transformation,[],[f239]) ).
fof(f501,plain,
! [X0] :
( sP8(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f237]) ).
fof(f237,plain,
! [X0] :
( sP8(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f165,f236,f235]) ).
fof(f235,plain,
! [X0] :
( sP7(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f236,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> sP7(X0) )
| ~ sP8(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f165,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f164]) ).
fof(f164,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( ssList(X0)
=> ( duplicatefreeP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> X1 != X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax13) ).
fof(f642,plain,
! [X10,X8,X9,X7] :
( ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ sP7(app(app(X8,cons(X7,X9)),cons(X7,X10))) ),
inference(duplicate_literal_removal,[],[f624]) ).
fof(f624,plain,
! [X10,X8,X9,X7] :
( ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X7)
| ~ sP7(app(app(X8,cons(X7,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f623]) ).
fof(f623,plain,
! [X10,X0,X8,X9,X7] :
( app(app(X8,cons(X7,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X7)
| ~ sP7(X0) ),
inference(equality_resolution,[],[f493]) ).
fof(f493,plain,
! [X10,X0,X8,X6,X9,X7] :
( X6 != X7
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f309,plain,
! [X0] :
( ( sP7(X0)
| ( sK33(X0) = sK34(X0)
& app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),sK37(X0))) = X0
& ssList(sK37(X0))
& ssList(sK36(X0))
& ssList(sK35(X0))
& ssItem(sK34(X0))
& ssItem(sK33(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( X6 != X7
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP7(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34,sK35,sK36,sK37])],[f303,f308,f307,f306,f305,f304]) ).
fof(f304,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( X1 = X2
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK33(X0) = X2
& app(app(X3,cons(sK33(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK33(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f305,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK33(X0) = X2
& app(app(X3,cons(sK33(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK33(X0) = sK34(X0)
& app(app(X3,cons(sK33(X0),X4)),cons(sK34(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK34(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f306,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK33(X0) = sK34(X0)
& app(app(X3,cons(sK33(X0),X4)),cons(sK34(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( sK33(X0) = sK34(X0)
& app(app(sK35(X0),cons(sK33(X0),X4)),cons(sK34(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK35(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f307,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( sK33(X0) = sK34(X0)
& app(app(sK35(X0),cons(sK33(X0),X4)),cons(sK34(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( sK33(X0) = sK34(X0)
& app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),X5)) = X0
& ssList(X5) )
& ssList(sK36(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f308,plain,
! [X0] :
( ? [X5] :
( sK33(X0) = sK34(X0)
& app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),X5)) = X0
& ssList(X5) )
=> ( sK33(X0) = sK34(X0)
& app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),sK37(X0))) = X0
& ssList(sK37(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f303,plain,
! [X0] :
( ( sP7(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( X1 = X2
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( X6 != X7
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP7(X0) ) ),
inference(rectify,[],[f302]) ).
fof(f302,plain,
! [X0] :
( ( sP7(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( X1 = X2
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP7(X0) ) ),
inference(nnf_transformation,[],[f235]) ).
fof(f494,plain,
! [X0] :
( ssItem(sK33(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f495,plain,
! [X0] :
( ssItem(sK34(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f496,plain,
! [X0] :
( ssList(sK35(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f497,plain,
! [X0] :
( ssList(sK36(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f498,plain,
! [X0] :
( ssList(sK37(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f499,plain,
! [X0] :
( sP7(X0)
| app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),sK37(X0))) = X0 ),
inference(cnf_transformation,[],[f309]) ).
fof(f500,plain,
! [X0] :
( sP7(X0)
| sK33(X0) = sK34(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f491,plain,
! [X0] :
( ~ sP8(X0)
| ~ duplicatefreeP(X0)
| sP7(X0) ),
inference(cnf_transformation,[],[f301]) ).
fof(f301,plain,
! [X0] :
( ( ( duplicatefreeP(X0)
| ~ sP7(X0) )
& ( sP7(X0)
| ~ duplicatefreeP(X0) ) )
| ~ sP8(X0) ),
inference(nnf_transformation,[],[f236]) ).
fof(f490,plain,
! [X0] :
( sP6(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f234]) ).
fof(f234,plain,
! [X0] :
( sP6(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f163,f233,f232]) ).
fof(f232,plain,
! [X0] :
( sP5(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f233,plain,
! [X0] :
( ( equalelemsP(X0)
<=> sP5(X0) )
| ~ sP6(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f163,plain,
! [X0] :
( ( equalelemsP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f162]) ).
fof(f162,plain,
! [X0] :
( ( equalelemsP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ssList(X0)
=> ( equalelemsP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( app(X3,cons(X1,cons(X2,X4))) = X0
=> X1 = X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax14) ).
fof(f622,plain,
! [X8,X6,X7,X5] :
( X5 = X6
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssItem(X5)
| ~ sP5(app(X7,cons(X5,cons(X6,X8)))) ),
inference(equality_resolution,[],[f483]) ).
fof(f483,plain,
! [X0,X8,X6,X7,X5] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssItem(X5)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f300,plain,
! [X0] :
( ( sP5(X0)
| ( sK29(X0) != sK30(X0)
& app(sK31(X0),cons(sK29(X0),cons(sK30(X0),sK32(X0)))) = X0
& ssList(sK32(X0))
& ssList(sK31(X0))
& ssItem(sK30(X0))
& ssItem(sK29(X0)) ) )
& ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
| ~ ssItem(X5) )
| ~ sP5(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30,sK31,sK32])],[f295,f299,f298,f297,f296]) ).
fof(f296,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( X1 != X2
& app(X3,cons(X1,cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( sK29(X0) != X2
& app(X3,cons(sK29(X0),cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK29(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f297,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( sK29(X0) != X2
& app(X3,cons(sK29(X0),cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( sK29(X0) != sK30(X0)
& app(X3,cons(sK29(X0),cons(sK30(X0),X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(sK30(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f298,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( sK29(X0) != sK30(X0)
& app(X3,cons(sK29(X0),cons(sK30(X0),X4))) = X0
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( sK29(X0) != sK30(X0)
& app(sK31(X0),cons(sK29(X0),cons(sK30(X0),X4))) = X0
& ssList(X4) )
& ssList(sK31(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f299,plain,
! [X0] :
( ? [X4] :
( sK29(X0) != sK30(X0)
& app(sK31(X0),cons(sK29(X0),cons(sK30(X0),X4))) = X0
& ssList(X4) )
=> ( sK29(X0) != sK30(X0)
& app(sK31(X0),cons(sK29(X0),cons(sK30(X0),sK32(X0)))) = X0
& ssList(sK32(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f295,plain,
! [X0] :
( ( sP5(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( X1 != X2
& app(X3,cons(X1,cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
| ~ ssItem(X5) )
| ~ sP5(X0) ) ),
inference(rectify,[],[f294]) ).
fof(f294,plain,
! [X0] :
( ( sP5(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( X1 != X2
& app(X3,cons(X1,cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP5(X0) ) ),
inference(nnf_transformation,[],[f232]) ).
fof(f484,plain,
! [X0] :
( ssItem(sK29(X0))
| sP5(X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f485,plain,
! [X0] :
( ssItem(sK30(X0))
| sP5(X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f486,plain,
! [X0] :
( ssList(sK31(X0))
| sP5(X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f487,plain,
! [X0] :
( ssList(sK32(X0))
| sP5(X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f488,plain,
! [X0] :
( sP5(X0)
| app(sK31(X0),cons(sK29(X0),cons(sK30(X0),sK32(X0)))) = X0 ),
inference(cnf_transformation,[],[f300]) ).
fof(f489,plain,
! [X0] :
( sK29(X0) != sK30(X0)
| sP5(X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f481,plain,
! [X0] :
( ~ sP6(X0)
| ~ equalelemsP(X0)
| sP5(X0) ),
inference(cnf_transformation,[],[f293]) ).
fof(f293,plain,
! [X0] :
( ( ( equalelemsP(X0)
| ~ sP5(X0) )
& ( sP5(X0)
| ~ equalelemsP(X0) ) )
| ~ sP6(X0) ),
inference(nnf_transformation,[],[f233]) ).
fof(f478,plain,
! [X0] :
( ssItem(sK28(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f292,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ( cons(sK28(X0),nil) = X0
& ssItem(sK28(X0)) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f290,f291]) ).
fof(f291,plain,
! [X0] :
( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
=> ( cons(sK28(X0),nil) = X0
& ssItem(sK28(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f290,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f289]) ).
fof(f289,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f161]) ).
fof(f161,plain,
! [X0] :
( ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f479,plain,
! [X0] :
( cons(sK28(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f621,plain,
! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(equality_resolution,[],[f480]) ).
fof(f480,plain,
! [X0,X1] :
( singletonP(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f476,plain,
! [X0] :
( ssList(sK27(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f288]) ).
fof(f288,plain,
! [X0] :
( ( tl(X0) = sK27(X0)
& ssList(sK27(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f160,f287]) ).
fof(f287,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
=> ( tl(X0) = sK27(X0)
& ssList(sK27(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f160,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f159]) ).
fof(f159,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax76) ).
fof(f477,plain,
! [X0] :
( tl(X0) = sK27(X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f288]) ).
fof(f474,plain,
! [X0] :
( ssItem(sK26(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f286]) ).
fof(f286,plain,
! [X0] :
( ( hd(X0) = sK26(X0)
& ssItem(sK26(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f158,f285]) ).
fof(f285,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
=> ( hd(X0) = sK26(X0)
& ssItem(sK26(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f158,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f157]) ).
fof(f157,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax75) ).
fof(f475,plain,
! [X0] :
( hd(X0) = sK26(X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f286]) ).
fof(f473,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f155]) ).
fof(f155,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78) ).
fof(f472,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f153]) ).
fof(f153,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
fof(f471,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f152,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f151]) ).
fof(f151,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
fof(f468,plain,
! [X0] :
( ssList(sK24(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f284]) ).
fof(f284,plain,
! [X0] :
( ( cons(sK25(X0),sK24(X0)) = X0
& ssItem(sK25(X0))
& ssList(sK24(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25])],[f150,f283,f282]) ).
fof(f282,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
=> ( ? [X2] :
( cons(X2,sK24(X0)) = X0
& ssItem(X2) )
& ssList(sK24(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f283,plain,
! [X0] :
( ? [X2] :
( cons(X2,sK24(X0)) = X0
& ssItem(X2) )
=> ( cons(sK25(X0),sK24(X0)) = X0
& ssItem(sK25(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f150,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f149]) ).
fof(f149,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ssList(X0)
=> ( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
fof(f469,plain,
! [X0] :
( ssItem(sK25(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f284]) ).
fof(f470,plain,
! [X0] :
( cons(sK25(X0),sK24(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f284]) ).
fof(f467,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
fof(f466,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).
fof(f465,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0] :
( ssList(X0)
=> rearsegP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).
fof(f464,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
fof(f463,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).
fof(f462,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).
fof(f461,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0] :
( ssList(X0)
=> rearsegP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).
fof(f460,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f141,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
fof(f457,plain,
! [X2,X0,X1] :
( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f281]) ).
fof(f281,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f280]) ).
fof(f280,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f140]) ).
fof(f140,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).
fof(f458,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f281]) ).
fof(f459,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f281]) ).
fof(f456,plain,
! [X0,X1] :
( sP4(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f231]) ).
fof(f231,plain,
! [X0] :
( ! [X1] :
( sP4(X0,X1)
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(definition_folding,[],[f139,f230,f229]) ).
fof(f229,plain,
! [X1,X0] :
( sP3(X1,X0)
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f230,plain,
! [X0,X1] :
( ( strictorderedP(cons(X0,X1))
<=> sP3(X1,X0) )
| ~ sP4(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f139,plain,
! [X0] :
( ! [X1] :
( ( strictorderedP(cons(X0,X1))
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ( strictorderedP(cons(X0,X1))
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax70) ).
fof(f452,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| nil = X0
| strictorderedP(X0) ),
inference(cnf_transformation,[],[f279]) ).
fof(f279,plain,
! [X0,X1] :
( ( sP3(X0,X1)
| ( ( ~ lt(X1,hd(X0))
| ~ strictorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( lt(X1,hd(X0))
& strictorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP3(X0,X1) ) ),
inference(rectify,[],[f278]) ).
fof(f278,plain,
! [X1,X0] :
( ( sP3(X1,X0)
| ( ( ~ lt(X0,hd(X1))
| ~ strictorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP3(X1,X0) ) ),
inference(flattening,[],[f277]) ).
fof(f277,plain,
! [X1,X0] :
( ( sP3(X1,X0)
| ( ( ~ lt(X0,hd(X1))
| ~ strictorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP3(X1,X0) ) ),
inference(nnf_transformation,[],[f229]) ).
fof(f453,plain,
! [X0,X1] :
( lt(X1,hd(X0))
| nil = X0
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f279]) ).
fof(f619,plain,
! [X1] : sP3(nil,X1),
inference(equality_resolution,[],[f454]) ).
fof(f454,plain,
! [X0,X1] :
( sP3(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f279]) ).
fof(f455,plain,
! [X0,X1] :
( sP3(X0,X1)
| ~ lt(X1,hd(X0))
| ~ strictorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f279]) ).
fof(f449,plain,
! [X0,X1] :
( sP3(X1,X0)
| ~ strictorderedP(cons(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f276]) ).
fof(f276,plain,
! [X0,X1] :
( ( ( strictorderedP(cons(X0,X1))
| ~ sP3(X1,X0) )
& ( sP3(X1,X0)
| ~ strictorderedP(cons(X0,X1)) ) )
| ~ sP4(X0,X1) ),
inference(nnf_transformation,[],[f230]) ).
fof(f450,plain,
! [X0,X1] :
( strictorderedP(cons(X0,X1))
| ~ sP3(X1,X0)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f276]) ).
fof(f448,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f228]) ).
fof(f228,plain,
! [X0] :
( ! [X1] :
( sP2(X0,X1)
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(definition_folding,[],[f138,f227,f226]) ).
fof(f226,plain,
! [X1,X0] :
( sP1(X1,X0)
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f227,plain,
! [X0,X1] :
( ( totalorderedP(cons(X0,X1))
<=> sP1(X1,X0) )
| ~ sP2(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f138,plain,
! [X0] :
( ! [X1] :
( ( totalorderedP(cons(X0,X1))
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ( totalorderedP(cons(X0,X1))
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax67) ).
fof(f444,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| nil = X0
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f275]) ).
fof(f275,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ( ( ~ leq(X1,hd(X0))
| ~ totalorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( leq(X1,hd(X0))
& totalorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP1(X0,X1) ) ),
inference(rectify,[],[f274]) ).
fof(f274,plain,
! [X1,X0] :
( ( sP1(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP1(X1,X0) ) ),
inference(flattening,[],[f273]) ).
fof(f273,plain,
! [X1,X0] :
( ( sP1(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP1(X1,X0) ) ),
inference(nnf_transformation,[],[f226]) ).
fof(f445,plain,
! [X0,X1] :
( leq(X1,hd(X0))
| nil = X0
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f275]) ).
fof(f617,plain,
! [X1] : sP1(nil,X1),
inference(equality_resolution,[],[f446]) ).
fof(f446,plain,
! [X0,X1] :
( sP1(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f275]) ).
fof(f447,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ leq(X1,hd(X0))
| ~ totalorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f275]) ).
fof(f441,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ totalorderedP(cons(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f272]) ).
fof(f272,plain,
! [X0,X1] :
( ( ( totalorderedP(cons(X0,X1))
| ~ sP1(X1,X0) )
& ( sP1(X1,X0)
| ~ totalorderedP(cons(X0,X1)) ) )
| ~ sP2(X0,X1) ),
inference(nnf_transformation,[],[f227]) ).
fof(f442,plain,
! [X0,X1] :
( totalorderedP(cons(X0,X1))
| ~ sP1(X1,X0)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f272]) ).
fof(f438,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f271]) ).
fof(f271,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1 )
& ( ( frontsegP(X2,X3)
& X0 = X1 )
| ~ frontsegP(cons(X0,X2),cons(X1,X3)) ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f270]) ).
fof(f270,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1 )
& ( ( frontsegP(X2,X3)
& X0 = X1 )
| ~ frontsegP(cons(X0,X2),cons(X1,X3)) ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f137]) ).
fof(f137,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( frontsegP(cons(X0,X2),cons(X1,X3))
<=> ( frontsegP(X2,X3)
& X0 = X1 ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(cons(X0,X2),cons(X1,X3))
<=> ( frontsegP(X2,X3)
& X0 = X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax44) ).
fof(f439,plain,
! [X2,X3,X0,X1] :
( frontsegP(X2,X3)
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f271]) ).
fof(f643,plain,
! [X2,X3,X1] :
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f616]) ).
fof(f616,plain,
! [X2,X3,X1] :
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f440]) ).
fof(f440,plain,
! [X2,X3,X0,X1] :
( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f271]) ).
fof(f435,plain,
! [X2,X0,X1] :
( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f269]) ).
fof(f269,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f268]) ).
fof(f268,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax37) ).
fof(f644,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f615]) ).
fof(f615,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f436]) ).
fof(f436,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f269]) ).
fof(f437,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f269]) ).
fof(f434,plain,
! [X2,X0,X1] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f134]) ).
fof(f134,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( lt(X1,X2)
& lt(X0,X1) )
=> lt(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax34) ).
fof(f433,plain,
! [X2,X0,X1] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f132]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f91]) ).
fof(f91,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( lt(X1,X2)
& leq(X0,X1) )
=> lt(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax91) ).
fof(f432,plain,
! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f130]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( leq(X1,X2)
& leq(X0,X1) )
=> leq(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax30) ).
fof(f431,plain,
! [X2,X0,X1] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f128]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f88]) ).
fof(f88,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( geq(X1,X2)
& geq(X0,X1) )
=> geq(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax88) ).
fof(f430,plain,
! [X2,X0,X1] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f126]) ).
fof(f126,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f95]) ).
fof(f95,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( gt(X1,X2)
& gt(X0,X1) )
=> gt(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax95) ).
fof(f645,plain,
! [X1] :
( ~ lt(X1,X1)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f614]) ).
fof(f614,plain,
! [X1] :
( ~ lt(X1,X1)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f427]) ).
fof(f427,plain,
! [X0,X1] :
( X0 != X1
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f267]) ).
fof(f267,plain,
! [X0] :
( ! [X1] :
( ( ( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1 )
& ( ( leq(X0,X1)
& X0 != X1 )
| ~ lt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f266]) ).
fof(f266,plain,
! [X0] :
( ! [X1] :
( ( ( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1 )
& ( ( leq(X0,X1)
& X0 != X1 )
| ~ lt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( ( lt(X0,X1)
<=> ( leq(X0,X1)
& X0 != X1 ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f93]) ).
fof(f93,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( lt(X0,X1)
<=> ( leq(X0,X1)
& X0 != X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax93) ).
fof(f428,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f267]) ).
fof(f429,plain,
! [X0,X1] :
( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f267]) ).
fof(f425,plain,
! [X0,X1] :
( leq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f265]) ).
fof(f265,plain,
! [X0] :
( ! [X1] :
( ( ( geq(X0,X1)
| ~ leq(X1,X0) )
& ( leq(X1,X0)
| ~ geq(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0] :
( ! [X1] :
( ( geq(X0,X1)
<=> leq(X1,X0) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( geq(X0,X1)
<=> leq(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax32) ).
fof(f426,plain,
! [X0,X1] :
( geq(X0,X1)
| ~ leq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f265]) ).
fof(f646,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f613]) ).
fof(f613,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f423]) ).
fof(f423,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f264]) ).
fof(f264,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
fof(f424,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f264]) ).
fof(f421,plain,
! [X0,X1] :
( lt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f263]) ).
fof(f263,plain,
! [X0] :
( ! [X1] :
( ( ( gt(X0,X1)
| ~ lt(X1,X0) )
& ( lt(X1,X0)
| ~ gt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0] :
( ! [X1] :
( ( gt(X0,X1)
<=> lt(X1,X0) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( gt(X0,X1)
<=> lt(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax35) ).
fof(f422,plain,
! [X0,X1] :
( gt(X0,X1)
| ~ lt(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f263]) ).
fof(f420,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f120]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( ( leq(X1,X0)
& leq(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax29) ).
fof(f419,plain,
! [X0,X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f118]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f87]) ).
fof(f87,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( ( geq(X1,X0)
& geq(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax87) ).
fof(f418,plain,
! [X0,X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f116]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( lt(X0,X1)
=> ~ lt(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax33) ).
fof(f417,plain,
! [X0,X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0] :
( ! [X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f114]) ).
fof(f114,plain,
! [X0] :
( ! [X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f92]) ).
fof(f92,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( leq(X0,X1)
=> ( lt(X0,X1)
| X0 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax92) ).
fof(f416,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0] :
( ! [X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f112]) ).
fof(f112,plain,
! [X0] :
( ! [X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f94]) ).
fof(f94,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( gt(X0,X1)
=> ~ gt(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax94) ).
fof(f415,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,axiom,
! [X0] :
( ssItem(X0)
=> totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax65) ).
fof(f414,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,axiom,
! [X0] :
( ssItem(X0)
=> strictorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax68) ).
fof(f413,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0] :
( ssItem(X0)
=> strictorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax63) ).
fof(f412,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,axiom,
! [X0] :
( ssItem(X0)
=> totalorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax61) ).
fof(f411,plain,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,axiom,
! [X0] :
( ssItem(X0)
=> cyclefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax59) ).
fof(f410,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,axiom,
! [X0] :
( ssItem(X0)
=> duplicatefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax71) ).
fof(f409,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,axiom,
! [X0] :
( ssItem(X0)
=> equalelemsP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax73) ).
fof(f408,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] :
( ssItem(X0)
=> leq(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).
fof(f407,plain,
! [X0] :
( geq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0] :
( geq(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f89]) ).
fof(f89,axiom,
! [X0] :
( ssItem(X0)
=> geq(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax89) ).
fof(f406,plain,
! [X0] :
( ~ lt(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0] :
( ~ lt(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f90]) ).
fof(f90,axiom,
! [X0] :
( ssItem(X0)
=> ~ lt(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax90) ).
fof(f405,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
fof(f404,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f403,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f66]) ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax66) ).
fof(f402,plain,
strictorderedP(nil),
inference(cnf_transformation,[],[f69]) ).
fof(f69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax69) ).
fof(f401,plain,
totalorderP(nil),
inference(cnf_transformation,[],[f62]) ).
fof(f62,axiom,
totalorderP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax62) ).
fof(f400,plain,
strictorderP(nil),
inference(cnf_transformation,[],[f64]) ).
fof(f64,axiom,
strictorderP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax64) ).
fof(f399,plain,
cyclefreeP(nil),
inference(cnf_transformation,[],[f60]) ).
fof(f60,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60) ).
fof(f398,plain,
duplicatefreeP(nil),
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax72) ).
fof(f397,plain,
equalelemsP(nil),
inference(cnf_transformation,[],[f74]) ).
fof(f74,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax74) ).
fof(f396,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
fof(f386,plain,
ssList(sK20),
inference(cnf_transformation,[],[f262]) ).
fof(f262,plain,
( ( ( nil = sK22
& nil = sK23 )
| sP0(sK22,sK23) )
& ! [X4] :
( ~ frontsegP(sK20,X4)
| ~ frontsegP(sK21,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK21,nil)
& sK20 = sK22
& sK21 = sK23
& ssList(sK23)
& ssList(sK22)
& ssList(sK21)
& ssList(sK20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23])],[f257,f261,f260,f259,f258]) ).
fof(f258,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP0(X2,X3) )
& ! [X4] :
( ~ frontsegP(X0,X4)
| ~ frontsegP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP0(X2,X3) )
& ! [X4] :
( ~ frontsegP(sK20,X4)
| ~ frontsegP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil)
& sK20 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f259,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP0(X2,X3) )
& ! [X4] :
( ~ frontsegP(sK20,X4)
| ~ frontsegP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil)
& sK20 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP0(X2,X3) )
& ! [X4] :
( ~ frontsegP(sK20,X4)
| ~ frontsegP(sK21,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK21,nil)
& sK20 = X2
& sK21 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f260,plain,
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP0(X2,X3) )
& ! [X4] :
( ~ frontsegP(sK20,X4)
| ~ frontsegP(sK21,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK21,nil)
& sK20 = X2
& sK21 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( nil = sK22
& nil = X3 )
| sP0(sK22,X3) )
& ! [X4] :
( ~ frontsegP(sK20,X4)
| ~ frontsegP(sK21,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK21,nil)
& sK20 = sK22
& sK21 = X3
& ssList(X3) )
& ssList(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f261,plain,
( ? [X3] :
( ( ( nil = sK22
& nil = X3 )
| sP0(sK22,X3) )
& ! [X4] :
( ~ frontsegP(sK20,X4)
| ~ frontsegP(sK21,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK21,nil)
& sK20 = sK22
& sK21 = X3
& ssList(X3) )
=> ( ( ( nil = sK22
& nil = sK23 )
| sP0(sK22,sK23) )
& ! [X4] :
( ~ frontsegP(sK20,X4)
| ~ frontsegP(sK21,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK21,nil)
& sK20 = sK22
& sK21 = sK23
& ssList(sK23) ) ),
introduced(choice_axiom,[]) ).
fof(f257,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP0(X2,X3) )
& ! [X4] :
( ~ frontsegP(X0,X4)
| ~ frontsegP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(rectify,[],[f225]) ).
fof(f225,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP0(X2,X3) )
& ! [X5] :
( ~ frontsegP(X0,X5)
| ~ frontsegP(X1,X5)
| ~ neq(X5,nil)
| ~ ssList(X5) )
& neq(X1,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f100,f224]) ).
fof(f224,plain,
! [X2,X3] :
( ? [X4] :
( frontsegP(X2,X4)
& frontsegP(X3,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ sP0(X2,X3) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f100,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| ? [X4] :
( frontsegP(X2,X4)
& frontsegP(X3,X4)
& neq(X4,nil)
& ssList(X4) ) )
& ! [X5] :
( ~ frontsegP(X0,X5)
| ~ frontsegP(X1,X5)
| ~ neq(X5,nil)
| ~ ssList(X5) )
& neq(X1,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| ? [X4] :
( frontsegP(X2,X4)
& frontsegP(X3,X4)
& neq(X4,nil)
& ssList(X4) ) )
& ! [X5] :
( ~ frontsegP(X0,X5)
| ~ frontsegP(X1,X5)
| ~ neq(X5,nil)
| ~ ssList(X5) )
& neq(X1,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssList(X4)
=> ( ~ frontsegP(X2,X4)
| ~ frontsegP(X3,X4)
| ~ neq(X4,nil) ) ) )
| ? [X5] :
( frontsegP(X0,X5)
& frontsegP(X1,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X5] :
( ssList(X5)
=> ( ~ frontsegP(X2,X5)
| ~ frontsegP(X3,X5)
| ~ neq(X5,nil) ) ) )
| ? [X4] :
( frontsegP(X0,X4)
& frontsegP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X5] :
( ssList(X5)
=> ( ~ frontsegP(X2,X5)
| ~ frontsegP(X3,X5)
| ~ neq(X5,nil) ) ) )
| ? [X4] :
( frontsegP(X0,X4)
& frontsegP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f387,plain,
ssList(sK21),
inference(cnf_transformation,[],[f262]) ).
fof(f388,plain,
ssList(sK22),
inference(cnf_transformation,[],[f262]) ).
fof(f389,plain,
ssList(sK23),
inference(cnf_transformation,[],[f262]) ).
fof(f390,plain,
sK21 = sK23,
inference(cnf_transformation,[],[f262]) ).
fof(f391,plain,
sK20 = sK22,
inference(cnf_transformation,[],[f262]) ).
fof(f392,plain,
neq(sK21,nil),
inference(cnf_transformation,[],[f262]) ).
fof(f393,plain,
! [X4] :
( ~ frontsegP(sK21,X4)
| ~ frontsegP(sK20,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f262]) ).
fof(f394,plain,
( nil = sK23
| sP0(sK22,sK23) ),
inference(cnf_transformation,[],[f262]) ).
fof(f395,plain,
( nil = sK22
| sP0(sK22,sK23) ),
inference(cnf_transformation,[],[f262]) ).
fof(f382,plain,
! [X0,X1] :
( ssList(sK19(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f256]) ).
fof(f256,plain,
! [X0,X1] :
( ( frontsegP(X0,sK19(X0,X1))
& frontsegP(X1,sK19(X0,X1))
& neq(sK19(X0,X1),nil)
& ssList(sK19(X0,X1)) )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f254,f255]) ).
fof(f255,plain,
! [X0,X1] :
( ? [X2] :
( frontsegP(X0,X2)
& frontsegP(X1,X2)
& neq(X2,nil)
& ssList(X2) )
=> ( frontsegP(X0,sK19(X0,X1))
& frontsegP(X1,sK19(X0,X1))
& neq(sK19(X0,X1),nil)
& ssList(sK19(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f254,plain,
! [X0,X1] :
( ? [X2] :
( frontsegP(X0,X2)
& frontsegP(X1,X2)
& neq(X2,nil)
& ssList(X2) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f253]) ).
fof(f253,plain,
! [X2,X3] :
( ? [X4] :
( frontsegP(X2,X4)
& frontsegP(X3,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ sP0(X2,X3) ),
inference(nnf_transformation,[],[f224]) ).
fof(f383,plain,
! [X0,X1] :
( neq(sK19(X0,X1),nil)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f256]) ).
fof(f384,plain,
! [X0,X1] :
( frontsegP(X1,sK19(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f256]) ).
fof(f385,plain,
! [X0,X1] :
( frontsegP(X0,sK19(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f256]) ).
fof(f807,plain,
( ~ frontsegP(nil,nil)
| ~ spl71_1 ),
inference(forward_demodulation,[],[f800,f662]) ).
fof(f662,plain,
( nil = sK21
| ~ spl71_1 ),
inference(avatar_component_clause,[],[f660]) ).
fof(f660,plain,
( spl71_1
<=> nil = sK21 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_1])]) ).
fof(f800,plain,
~ frontsegP(nil,sK21),
inference(superposition,[],[f780,f789]) ).
fof(f789,plain,
nil = sK20,
inference(global_subsumption,[],[f395,f394,f416,f417,f418,f419,f420,f422,f421,f424,f426,f425,f429,f428,f645,f430,f431,f432,f433,f434,f437,f644,f435,f643,f439,f438,f442,f441,f447,f445,f450,f449,f455,f453,f459,f458,f457,f470,f473,f475,f477,f621,f479,f488,f622,f499,f642,f510,f625,f522,f626,f534,f627,f546,f628,f557,f629,f630,f631,f632,f567,f568,f569,f570,f571,f633,f574,f573,f572,f577,f578,f579,f580,f581,f582,f584,f635,f586,f585,f636,f590,f589,f588,f637,f593,f592,f640,f596,f595,f598,f600,f599,f601,f602,f603,f604,f605,f606,f607,f608,f609,f386,f387,f388,f389,f396,f397,f398,f399,f400,f401,f402,f403,f404,f610,f611,f390,f391,f392,f612,f617,f619,f647,f648,f649,f490,f501,f513,f525,f537,f548,f559,f655,f405,f406,f407,f408,f460,f461,f462,f463,f464,f465,f484,f485,f486,f487,f494,f495,f496,f497,f498,f505,f506,f507,f508,f509,f517,f518,f519,f520,f521,f529,f530,f531,f532,f533,f541,f542,f543,f544,f545,f552,f553,f554,f555,f556,f641,f646,f650,f409,f410,f411,f412,f413,f414,f415,f481,f491,f502,f514,f526,f538,f539,f549,f550,f668,f669,f670,f671,f672,f673,f674,f675,f382,f676,f448,f456,f466,f682,f707,f708,f687,f688,f689,f690,f691,f692,f693,f694,f695,f696,f697,f698,f699,f700,f701,f702,f703,f704,f705,f706,f683,f684,f467,f710,f735,f736,f715,f716,f717,f718,f719,f720,f721,f722,f723,f724,f725,f726,f727,f728,f729,f730,f731,f732,f733,f734,f711,f712,f478,f489,f500,f511,f512,f523,f524,f535,f536,f547,f558,f383,f384,f385,f444,f452,f468,f739,f740,f469,f471,f472,f741,f742,f474,f476,f743,f744,f560,f562,f564,f566,f764,f765,f576,f766,f767,f762,f763,f393,f784,f780,f782,f786,f658]) ).
fof(f658,plain,
( sP0(sK20,sK21)
| nil = sK20 ),
inference(forward_demodulation,[],[f657,f391]) ).
fof(f657,plain,
( sP0(sK22,sK21)
| nil = sK20 ),
inference(forward_demodulation,[],[f656,f390]) ).
fof(f656,plain,
( nil = sK20
| sP0(sK22,sK23) ),
inference(forward_demodulation,[],[f395,f391]) ).
fof(f786,plain,
~ sP0(sK20,sK21),
inference(duplicate_literal_removal,[],[f785]) ).
fof(f785,plain,
( ~ sP0(sK20,sK21)
| ~ sP0(sK20,sK21) ),
inference(resolution,[],[f782,f385]) ).
fof(f782,plain,
! [X0] :
( ~ frontsegP(sK20,sK19(X0,sK21))
| ~ sP0(X0,sK21) ),
inference(subsumption_resolution,[],[f781,f382]) ).
fof(f781,plain,
! [X0] :
( ~ frontsegP(sK20,sK19(X0,sK21))
| ~ ssList(sK19(X0,sK21))
| ~ sP0(X0,sK21) ),
inference(subsumption_resolution,[],[f776,f383]) ).
fof(f776,plain,
! [X0] :
( ~ frontsegP(sK20,sK19(X0,sK21))
| ~ neq(sK19(X0,sK21),nil)
| ~ ssList(sK19(X0,sK21))
| ~ sP0(X0,sK21) ),
inference(resolution,[],[f393,f384]) ).
fof(f784,plain,
! [X0] :
( ~ frontsegP(sK20,sK19(sK21,X0))
| ~ sP0(sK21,X0) ),
inference(subsumption_resolution,[],[f783,f382]) ).
fof(f783,plain,
! [X0] :
( ~ frontsegP(sK20,sK19(sK21,X0))
| ~ ssList(sK19(sK21,X0))
| ~ sP0(sK21,X0) ),
inference(subsumption_resolution,[],[f777,f383]) ).
fof(f777,plain,
! [X0] :
( ~ frontsegP(sK20,sK19(sK21,X0))
| ~ neq(sK19(sK21,X0),nil)
| ~ ssList(sK19(sK21,X0))
| ~ sP0(sK21,X0) ),
inference(resolution,[],[f393,f385]) ).
fof(f763,plain,
! [X0] :
( ~ sP0(nil,X0)
| nil = sK19(nil,X0) ),
inference(subsumption_resolution,[],[f759,f382]) ).
fof(f759,plain,
! [X0] :
( nil = sK19(nil,X0)
| ~ ssList(sK19(nil,X0))
| ~ sP0(nil,X0) ),
inference(resolution,[],[f564,f385]) ).
fof(f762,plain,
! [X0] :
( ~ sP0(X0,nil)
| nil = sK19(X0,nil) ),
inference(subsumption_resolution,[],[f758,f382]) ).
fof(f758,plain,
! [X0] :
( nil = sK19(X0,nil)
| ~ ssList(sK19(X0,nil))
| ~ sP0(X0,nil) ),
inference(resolution,[],[f564,f384]) ).
fof(f767,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X1,X0) = app(app(X1,X0),nil) ),
inference(resolution,[],[f576,f466]) ).
fof(f766,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X1,X0) = app(nil,app(X1,X0)) ),
inference(resolution,[],[f576,f467]) ).
fof(f576,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f186]) ).
fof(f186,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f765,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) = app(cons(X0,X1),nil) ),
inference(resolution,[],[f566,f466]) ).
fof(f764,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) = app(nil,cons(X0,X1)) ),
inference(resolution,[],[f566,f467]) ).
fof(f566,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f179]) ).
fof(f179,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
fof(f564,plain,
! [X0] :
( ~ frontsegP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f744,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| sK27(X0) = app(sK27(X0),nil) ),
inference(resolution,[],[f476,f466]) ).
fof(f743,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| sK27(X0) = app(nil,sK27(X0)) ),
inference(resolution,[],[f476,f467]) ).
fof(f742,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| tl(X0) = app(tl(X0),nil) ),
inference(resolution,[],[f472,f466]) ).
fof(f741,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| tl(X0) = app(nil,tl(X0)) ),
inference(resolution,[],[f472,f467]) ).
fof(f740,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| sK24(X0) = app(sK24(X0),nil) ),
inference(resolution,[],[f468,f466]) ).
fof(f739,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| sK24(X0) = app(nil,sK24(X0)) ),
inference(resolution,[],[f468,f467]) ).
fof(f712,plain,
sK21 = app(nil,sK21),
inference(resolution,[],[f467,f387]) ).
fof(f711,plain,
sK20 = app(nil,sK20),
inference(resolution,[],[f467,f386]) ).
fof(f734,plain,
! [X0] :
( sK62(X0) = app(nil,sK62(X0))
| sP17(X0) ),
inference(resolution,[],[f467,f556]) ).
fof(f733,plain,
! [X0] :
( sK61(X0) = app(nil,sK61(X0))
| sP17(X0) ),
inference(resolution,[],[f467,f555]) ).
fof(f732,plain,
! [X0] :
( sK60(X0) = app(nil,sK60(X0))
| sP17(X0) ),
inference(resolution,[],[f467,f554]) ).
fof(f731,plain,
! [X0] :
( sK57(X0) = app(nil,sK57(X0))
| sP15(X0) ),
inference(resolution,[],[f467,f545]) ).
fof(f730,plain,
! [X0] :
( sK56(X0) = app(nil,sK56(X0))
| sP15(X0) ),
inference(resolution,[],[f467,f544]) ).
fof(f729,plain,
! [X0] :
( sK55(X0) = app(nil,sK55(X0))
| sP15(X0) ),
inference(resolution,[],[f467,f543]) ).
fof(f728,plain,
! [X0] :
( sK52(X0) = app(nil,sK52(X0))
| sP13(X0) ),
inference(resolution,[],[f467,f533]) ).
fof(f727,plain,
! [X0] :
( sK51(X0) = app(nil,sK51(X0))
| sP13(X0) ),
inference(resolution,[],[f467,f532]) ).
fof(f726,plain,
! [X0] :
( sK50(X0) = app(nil,sK50(X0))
| sP13(X0) ),
inference(resolution,[],[f467,f531]) ).
fof(f725,plain,
! [X0] :
( sK47(X0) = app(nil,sK47(X0))
| sP11(X0) ),
inference(resolution,[],[f467,f521]) ).
fof(f724,plain,
! [X0] :
( sK46(X0) = app(nil,sK46(X0))
| sP11(X0) ),
inference(resolution,[],[f467,f520]) ).
fof(f723,plain,
! [X0] :
( sK45(X0) = app(nil,sK45(X0))
| sP11(X0) ),
inference(resolution,[],[f467,f519]) ).
fof(f722,plain,
! [X0] :
( sK42(X0) = app(nil,sK42(X0))
| sP9(X0) ),
inference(resolution,[],[f467,f509]) ).
fof(f721,plain,
! [X0] :
( sK41(X0) = app(nil,sK41(X0))
| sP9(X0) ),
inference(resolution,[],[f467,f508]) ).
fof(f720,plain,
! [X0] :
( sK40(X0) = app(nil,sK40(X0))
| sP9(X0) ),
inference(resolution,[],[f467,f507]) ).
fof(f719,plain,
! [X0] :
( sK37(X0) = app(nil,sK37(X0))
| sP7(X0) ),
inference(resolution,[],[f467,f498]) ).
fof(f718,plain,
! [X0] :
( sK36(X0) = app(nil,sK36(X0))
| sP7(X0) ),
inference(resolution,[],[f467,f497]) ).
fof(f717,plain,
! [X0] :
( sK35(X0) = app(nil,sK35(X0))
| sP7(X0) ),
inference(resolution,[],[f467,f496]) ).
fof(f716,plain,
! [X0] :
( sK32(X0) = app(nil,sK32(X0))
| sP5(X0) ),
inference(resolution,[],[f467,f487]) ).
fof(f715,plain,
! [X0] :
( sK31(X0) = app(nil,sK31(X0))
| sP5(X0) ),
inference(resolution,[],[f467,f486]) ).
fof(f736,plain,
sK21 = app(nil,sK21),
inference(forward_demodulation,[],[f714,f390]) ).
fof(f714,plain,
sK23 = app(nil,sK23),
inference(resolution,[],[f467,f389]) ).
fof(f735,plain,
sK20 = app(nil,sK20),
inference(forward_demodulation,[],[f713,f391]) ).
fof(f713,plain,
sK22 = app(nil,sK22),
inference(resolution,[],[f467,f388]) ).
fof(f710,plain,
! [X0,X1] :
( sK19(X0,X1) = app(nil,sK19(X0,X1))
| ~ sP0(X0,X1) ),
inference(resolution,[],[f467,f382]) ).
fof(f684,plain,
sK21 = app(sK21,nil),
inference(resolution,[],[f466,f387]) ).
fof(f683,plain,
sK20 = app(sK20,nil),
inference(resolution,[],[f466,f386]) ).
fof(f706,plain,
! [X0] :
( sK62(X0) = app(sK62(X0),nil)
| sP17(X0) ),
inference(resolution,[],[f466,f556]) ).
fof(f705,plain,
! [X0] :
( sK61(X0) = app(sK61(X0),nil)
| sP17(X0) ),
inference(resolution,[],[f466,f555]) ).
fof(f704,plain,
! [X0] :
( sK60(X0) = app(sK60(X0),nil)
| sP17(X0) ),
inference(resolution,[],[f466,f554]) ).
fof(f703,plain,
! [X0] :
( sK57(X0) = app(sK57(X0),nil)
| sP15(X0) ),
inference(resolution,[],[f466,f545]) ).
fof(f702,plain,
! [X0] :
( sK56(X0) = app(sK56(X0),nil)
| sP15(X0) ),
inference(resolution,[],[f466,f544]) ).
fof(f701,plain,
! [X0] :
( sK55(X0) = app(sK55(X0),nil)
| sP15(X0) ),
inference(resolution,[],[f466,f543]) ).
fof(f700,plain,
! [X0] :
( sK52(X0) = app(sK52(X0),nil)
| sP13(X0) ),
inference(resolution,[],[f466,f533]) ).
fof(f699,plain,
! [X0] :
( sK51(X0) = app(sK51(X0),nil)
| sP13(X0) ),
inference(resolution,[],[f466,f532]) ).
fof(f698,plain,
! [X0] :
( sK50(X0) = app(sK50(X0),nil)
| sP13(X0) ),
inference(resolution,[],[f466,f531]) ).
fof(f697,plain,
! [X0] :
( sK47(X0) = app(sK47(X0),nil)
| sP11(X0) ),
inference(resolution,[],[f466,f521]) ).
fof(f696,plain,
! [X0] :
( sK46(X0) = app(sK46(X0),nil)
| sP11(X0) ),
inference(resolution,[],[f466,f520]) ).
fof(f695,plain,
! [X0] :
( sK45(X0) = app(sK45(X0),nil)
| sP11(X0) ),
inference(resolution,[],[f466,f519]) ).
fof(f694,plain,
! [X0] :
( sK42(X0) = app(sK42(X0),nil)
| sP9(X0) ),
inference(resolution,[],[f466,f509]) ).
fof(f693,plain,
! [X0] :
( sK41(X0) = app(sK41(X0),nil)
| sP9(X0) ),
inference(resolution,[],[f466,f508]) ).
fof(f692,plain,
! [X0] :
( sK40(X0) = app(sK40(X0),nil)
| sP9(X0) ),
inference(resolution,[],[f466,f507]) ).
fof(f691,plain,
! [X0] :
( sK37(X0) = app(sK37(X0),nil)
| sP7(X0) ),
inference(resolution,[],[f466,f498]) ).
fof(f690,plain,
! [X0] :
( sK36(X0) = app(sK36(X0),nil)
| sP7(X0) ),
inference(resolution,[],[f466,f497]) ).
fof(f689,plain,
! [X0] :
( sK35(X0) = app(sK35(X0),nil)
| sP7(X0) ),
inference(resolution,[],[f466,f496]) ).
fof(f688,plain,
! [X0] :
( sK32(X0) = app(sK32(X0),nil)
| sP5(X0) ),
inference(resolution,[],[f466,f487]) ).
fof(f687,plain,
! [X0] :
( sK31(X0) = app(sK31(X0),nil)
| sP5(X0) ),
inference(resolution,[],[f466,f486]) ).
fof(f708,plain,
sK21 = app(sK21,nil),
inference(forward_demodulation,[],[f686,f390]) ).
fof(f686,plain,
sK23 = app(sK23,nil),
inference(resolution,[],[f466,f389]) ).
fof(f707,plain,
sK20 = app(sK20,nil),
inference(forward_demodulation,[],[f685,f391]) ).
fof(f685,plain,
sK22 = app(sK22,nil),
inference(resolution,[],[f466,f388]) ).
fof(f682,plain,
! [X0,X1] :
( sK19(X0,X1) = app(sK19(X0,X1),nil)
| ~ sP0(X0,X1) ),
inference(resolution,[],[f466,f382]) ).
fof(f676,plain,
! [X0] :
( ~ sP17(X0)
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f550,f559]) ).
fof(f675,plain,
! [X0] :
( sP17(X0)
| ~ strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f549,f559]) ).
fof(f674,plain,
! [X0] :
( ~ sP15(X0)
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f539,f548]) ).
fof(f673,plain,
! [X0] :
( sP15(X0)
| ~ totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f538,f548]) ).
fof(f672,plain,
! [X0] :
( sP13(X0)
| ~ cyclefreeP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f526,f537]) ).
fof(f671,plain,
! [X0] :
( sP11(X0)
| ~ strictorderP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f514,f525]) ).
fof(f670,plain,
! [X0] :
( sP9(X0)
| ~ totalorderP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f502,f513]) ).
fof(f669,plain,
! [X0] :
( sP7(X0)
| ~ duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f491,f501]) ).
fof(f668,plain,
! [X0] :
( sP5(X0)
| ~ equalelemsP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f481,f490]) ).
fof(f650,plain,
nil = app(nil,nil),
inference(global_subsumption,[],[f385,f384,f383,f382,f395,f394,f393,f392,f391,f390,f389,f388,f387,f386,f396,f397,f398,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f422,f421,f424,f646,f426,f425,f429,f428,f645,f430,f431,f432,f433,f434,f437,f644,f435,f643,f439,f438,f442,f441,f447,f617,f445,f444,f448,f450,f449,f455,f619,f453,f452,f456,f459,f458,f457,f460,f461,f462,f463,f464,f465,f466,f467,f470,f469,f468,f471,f472,f473,f475,f474,f477,f476,f621,f479,f478,f481,f489,f488,f487,f486,f485,f484,f622,f490,f491,f500,f499,f498,f497,f496,f495,f494,f642,f501,f502,f512,f511,f510,f509,f508,f507,f506,f505,f625,f513,f514,f524,f523,f522,f521,f520,f519,f518,f517,f626,f525,f526,f536,f535,f534,f533,f532,f531,f530,f529,f627,f537,f539,f538,f547,f546,f545,f544,f543,f542,f541,f628,f548,f550,f549,f558,f557,f556,f555,f554,f553,f552,f629,f559,f630,f647,f560,f631,f648,f562,f632,f649,f564,f566,f567,f568,f569,f570,f571,f633,f574,f573,f572,f576,f577,f578,f579,f580,f581,f582,f584,f641,f635,f586,f585,f636,f590,f589,f588,f637,f593,f592,f640]) ).
fof(f641,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f634]) ).
fof(f634,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f583]) ).
fof(f583,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f363]) ).
fof(f363,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f199]) ).
fof(f199,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
fof(f655,plain,
( sP0(sK20,sK21)
| nil = sK21 ),
inference(forward_demodulation,[],[f654,f391]) ).
fof(f654,plain,
( sP0(sK22,sK21)
| nil = sK21 ),
inference(forward_demodulation,[],[f653,f390]) ).
fof(f653,plain,
( nil = sK21
| sP0(sK22,sK23) ),
inference(forward_demodulation,[],[f394,f390]) ).
fof(f612,plain,
sK69 != sK70,
inference(cnf_transformation,[],[f381]) ).
fof(f381,plain,
( sK69 != sK70
& ssItem(sK70)
& ssItem(sK69) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK69,sK70])],[f2,f380,f379]) ).
fof(f379,plain,
( ? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) )
=> ( ? [X1] :
( sK69 != X1
& ssItem(X1) )
& ssItem(sK69) ) ),
introduced(choice_axiom,[]) ).
fof(f380,plain,
( ? [X1] :
( sK69 != X1
& ssItem(X1) )
=> ( sK69 != sK70
& ssItem(sK70) ) ),
introduced(choice_axiom,[]) ).
fof(f2,axiom,
? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f611,plain,
ssItem(sK70),
inference(cnf_transformation,[],[f381]) ).
fof(f610,plain,
ssItem(sK69),
inference(cnf_transformation,[],[f381]) ).
fof(f609,plain,
! [X2,X3,X0,X1] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f223]) ).
fof(f223,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f222]) ).
fof(f222,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( segmentP(X0,X1)
=> segmentP(app(app(X2,X0),X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax56) ).
fof(f608,plain,
! [X2,X0,X1] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f221]) ).
fof(f221,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f220]) ).
fof(f220,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( frontsegP(X1,X2)
& frontsegP(X0,X1) )
=> frontsegP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax40) ).
fof(f607,plain,
! [X2,X0,X1] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f219]) ).
fof(f219,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f218]) ).
fof(f218,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( rearsegP(X1,X2)
& rearsegP(X0,X1) )
=> rearsegP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax47) ).
fof(f606,plain,
! [X2,X0,X1] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f217]) ).
fof(f217,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f216]) ).
fof(f216,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X1,X2)
& segmentP(X0,X1) )
=> segmentP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).
fof(f605,plain,
! [X2,X0,X1] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f215]) ).
fof(f215,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f214]) ).
fof(f214,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f80]) ).
fof(f80,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X1,X2) = app(X1,X0)
=> X0 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax80) ).
fof(f604,plain,
! [X2,X0,X1] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f213]) ).
fof(f213,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f212]) ).
fof(f212,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f79]) ).
fof(f79,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X2,X1) = app(X0,X1)
=> X0 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax79) ).
fof(f603,plain,
! [X2,X0,X1] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f211]) ).
fof(f211,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f210]) ).
fof(f210,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X0,X1)
=> frontsegP(app(X0,X2),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax43) ).
fof(f602,plain,
! [X2,X0,X1] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f209]) ).
fof(f209,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f208]) ).
fof(f208,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X0,X1)
=> rearsegP(app(X2,X0),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax50) ).
fof(f601,plain,
! [X2,X0,X1] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f207]) ).
fof(f207,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f82,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> app(app(X0,X1),X2) = app(X0,app(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax82) ).
fof(f599,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f206]) ).
fof(f206,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( X0 = X1
& X2 = X3 )
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3) )
| ~ ssItem(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f205]) ).
fof(f205,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( X0 = X1
& X2 = X3 )
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3) )
| ~ ssItem(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ( cons(X2,X0) = cons(X3,X1)
=> ( X0 = X1
& X2 = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax19) ).
fof(f600,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f206]) ).
fof(f598,plain,
! [X2,X0,X1] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f204]) ).
fof(f204,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax27) ).
fof(f595,plain,
! [X0,X1] :
( nil = X1
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f378]) ).
fof(f378,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f377]) ).
fof(f377,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f203]) ).
fof(f203,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax83) ).
fof(f596,plain,
! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f378]) ).
fof(f640,plain,
( nil = app(nil,nil)
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f639]) ).
fof(f639,plain,
( nil = app(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f638]) ).
fof(f638,plain,
! [X1] :
( nil = app(nil,X1)
| nil != X1
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f597]) ).
fof(f597,plain,
! [X0,X1] :
( nil = app(X0,X1)
| nil != X0
| nil != X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f378]) ).
fof(f592,plain,
! [X0,X1] :
( ssList(sK68(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f376]) ).
fof(f376,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ( app(X1,sK68(X0,X1)) = X0
& ssList(sK68(X0,X1)) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK68])],[f374,f375]) ).
fof(f375,plain,
! [X0,X1] :
( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
=> ( app(X1,sK68(X0,X1)) = X0
& ssList(sK68(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f374,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f373]) ).
fof(f373,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ? [X2] :
( app(X1,X2) = X0
& ssList(X2) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f202]) ).
fof(f202,plain,
! [X0] :
( ! [X1] :
( ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
fof(f593,plain,
! [X0,X1] :
( app(X1,sK68(X0,X1)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f376]) ).
fof(f637,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(equality_resolution,[],[f594]) ).
fof(f594,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f376]) ).
fof(f588,plain,
! [X0,X1] :
( ssList(sK66(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f372]) ).
fof(f372,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(app(sK66(X0,X1),X1),sK67(X0,X1)) = X0
& ssList(sK67(X0,X1))
& ssList(sK66(X0,X1)) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK66,sK67])],[f369,f371,f370]) ).
fof(f370,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(app(sK66(X0,X1),X1),X5) = X0
& ssList(X5) )
& ssList(sK66(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f371,plain,
! [X0,X1] :
( ? [X5] :
( app(app(sK66(X0,X1),X1),X5) = X0
& ssList(X5) )
=> ( app(app(sK66(X0,X1),X1),sK67(X0,X1)) = X0
& ssList(sK67(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f369,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f368]) ).
fof(f368,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f201]) ).
fof(f201,plain,
! [X0] :
( ! [X1] :
( ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).
fof(f589,plain,
! [X0,X1] :
( ssList(sK67(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f372]) ).
fof(f590,plain,
! [X0,X1] :
( app(app(sK66(X0,X1),X1),sK67(X0,X1)) = X0
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f372]) ).
fof(f636,plain,
! [X2,X3,X1] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) ),
inference(equality_resolution,[],[f591]) ).
fof(f591,plain,
! [X2,X3,X0,X1] :
( segmentP(X0,X1)
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f372]) ).
fof(f585,plain,
! [X0,X1] :
( ssList(sK65(X0,X1))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f367]) ).
fof(f367,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ( app(sK65(X0,X1),X1) = X0
& ssList(sK65(X0,X1)) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK65])],[f365,f366]) ).
fof(f366,plain,
! [X0,X1] :
( ? [X3] :
( app(X3,X1) = X0
& ssList(X3) )
=> ( app(sK65(X0,X1),X1) = X0
& ssList(sK65(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f365,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ? [X3] :
( app(X3,X1) = X0
& ssList(X3) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f364]) ).
fof(f364,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ? [X2] :
( app(X2,X1) = X0
& ssList(X2) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f200]) ).
fof(f200,plain,
! [X0] :
( ! [X1] :
( ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
fof(f586,plain,
! [X0,X1] :
( app(sK65(X0,X1),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f367]) ).
fof(f635,plain,
! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X2,X1)) ),
inference(equality_resolution,[],[f587]) ).
fof(f587,plain,
! [X2,X0,X1] :
( rearsegP(X0,X1)
| app(X2,X1) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f367]) ).
fof(f584,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f363]) ).
fof(f582,plain,
! [X0,X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f198,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f197]) ).
fof(f197,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( frontsegP(X1,X0)
& frontsegP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax41) ).
fof(f581,plain,
! [X0,X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f196]) ).
fof(f196,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f195]) ).
fof(f195,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( segmentP(X1,X0)
& segmentP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax54) ).
fof(f580,plain,
! [X0,X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f194]) ).
fof(f194,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f193]) ).
fof(f193,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( rearsegP(X1,X0)
& rearsegP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax48) ).
fof(f579,plain,
! [X0,X1] :
( X0 = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1)
| nil = X0
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f192]) ).
fof(f192,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1)
| nil = X0
| nil = X1
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f191]) ).
fof(f191,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1)
| nil = X0
| nil = X1
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f77]) ).
fof(f77,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( tl(X0) = tl(X1)
& hd(X0) = hd(X1)
& nil != X0
& nil != X1 )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax77) ).
fof(f578,plain,
! [X0,X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f190]) ).
fof(f190,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f189]) ).
fof(f189,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f86]) ).
fof(f86,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> tl(app(X0,X1)) = app(tl(X0),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax86) ).
fof(f577,plain,
! [X0,X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f188]) ).
fof(f188,plain,
! [X0] :
( ! [X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f187]) ).
fof(f187,plain,
! [X0] :
( ! [X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f85,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> hd(X0) = hd(app(X0,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax85) ).
fof(f572,plain,
! [X0,X1] :
( ssList(sK63(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f362]) ).
fof(f362,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(sK63(X0,X1),cons(X1,sK64(X0,X1))) = X0
& ssList(sK64(X0,X1))
& ssList(sK63(X0,X1)) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK63,sK64])],[f359,f361,f360]) ).
fof(f360,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(sK63(X0,X1),cons(X1,X5)) = X0
& ssList(X5) )
& ssList(sK63(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f361,plain,
! [X0,X1] :
( ? [X5] :
( app(sK63(X0,X1),cons(X1,X5)) = X0
& ssList(X5) )
=> ( app(sK63(X0,X1),cons(X1,sK64(X0,X1))) = X0
& ssList(sK64(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f359,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f358]) ).
fof(f358,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f185]) ).
fof(f185,plain,
! [X0] :
( ! [X1] :
( ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f573,plain,
! [X0,X1] :
( ssList(sK64(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f362]) ).
fof(f574,plain,
! [X0,X1] :
( app(sK63(X0,X1),cons(X1,sK64(X0,X1))) = X0
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f362]) ).
fof(f633,plain,
! [X2,X3,X1] :
( memberP(app(X2,cons(X1,X3)),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(app(X2,cons(X1,X3))) ),
inference(equality_resolution,[],[f575]) ).
fof(f575,plain,
! [X2,X3,X0,X1] :
( memberP(X0,X1)
| app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f362]) ).
fof(f571,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f184]) ).
fof(f184,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax81) ).
fof(f570,plain,
! [X0,X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f183]) ).
fof(f183,plain,
! [X0] :
( ! [X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
fof(f569,plain,
! [X0,X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f182]) ).
fof(f182,plain,
! [X0] :
( ! [X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).
fof(f568,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f181]) ).
fof(f181,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
fof(f567,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f180]) ).
fof(f180,plain,
! [X0] :
( ! [X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
fof(f780,plain,
~ frontsegP(sK20,sK21),
inference(subsumption_resolution,[],[f779,f387]) ).
fof(f779,plain,
( ~ frontsegP(sK20,sK21)
| ~ ssList(sK21) ),
inference(subsumption_resolution,[],[f778,f392]) ).
fof(f778,plain,
( ~ frontsegP(sK20,sK21)
| ~ neq(sK21,nil)
| ~ ssList(sK21) ),
inference(duplicate_literal_removal,[],[f774]) ).
fof(f774,plain,
( ~ frontsegP(sK20,sK21)
| ~ neq(sK21,nil)
| ~ ssList(sK21)
| ~ ssList(sK21) ),
inference(resolution,[],[f393,f462]) ).
fof(f788,plain,
~ spl71_2,
inference(avatar_contradiction_clause,[],[f787]) ).
fof(f787,plain,
( $false
| ~ spl71_2 ),
inference(subsumption_resolution,[],[f786,f666]) ).
fof(f666,plain,
( sP0(sK20,sK21)
| ~ spl71_2 ),
inference(avatar_component_clause,[],[f664]) ).
fof(f664,plain,
( spl71_2
<=> sP0(sK20,sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_2])]) ).
fof(f667,plain,
( spl71_1
| spl71_2 ),
inference(avatar_split_clause,[],[f655,f664,f660]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWC023+1 : TPTP v8.2.0. Released v2.4.0.
% 0.10/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n025.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 : Sun May 19 03:08:53 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % (16801)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (16804)WARNING: value z3 for option sas not known
% 0.14/0.37 % (16803)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (16805)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (16802)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (16804)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37 % (16807)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.37 % (16806)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.37 % (16808)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 % (16804)First to succeed.
% 0.14/0.39 TRYING [2]
% 0.14/0.39 TRYING [2]
% 0.14/0.39 TRYING [3]
% 0.14/0.40 TRYING [3]
% 0.14/0.40 % (16804)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-16801"
% 0.14/0.40 % (16804)Refutation found. Thanks to Tanya!
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.41 % (16804)------------------------------
% 0.14/0.41 % (16804)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.41 % (16804)Termination reason: Refutation
% 0.14/0.41
% 0.14/0.41 % (16804)Memory used [KB]: 1439
% 0.14/0.41 % (16804)Time elapsed: 0.032 s
% 0.14/0.41 % (16804)Instructions burned: 59 (million)
% 0.14/0.41 % (16801)Success in time 0.044 s
%------------------------------------------------------------------------------