TSTP Solution File: SWC308+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWC308+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n020.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 : Mon Jun 24 16:24:24 EDT 2024
% Result : Theorem 40.59s 6.23s
% Output : CNFRefutation 40.59s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f595)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f41,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( frontsegP(X1,X0)
& frontsegP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X3
& nil != X2 )
| ? [X8] :
( ? [X9] :
( app(cons(X8,nil),X9) = X3
& app(X9,cons(X8,nil)) != X2
& ssList(X9) )
& ssItem(X8) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( neq(nil,X1)
& ? [X7] :
( neq(nil,X1)
& hd(X1) = X7
& cons(X7,nil) = X6
& ssItem(X7) )
& app(X5,X6) = X4
& tl(X1) = X5
& ssList(X6) )
& ssList(X5) )
& X0 = X4
& ssList(X4) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X3
& nil != X2 )
| ? [X8] :
( ? [X9] :
( app(cons(X8,nil),X9) = X3
& app(X9,cons(X8,nil)) != X2
& ssList(X9) )
& ssItem(X8) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( neq(nil,X1)
& ? [X7] :
( neq(nil,X1)
& hd(X1) = X7
& cons(X7,nil) = X6
& ssItem(X7) )
& app(X5,X6) = X4
& tl(X1) = X5
& ssList(X6) )
& ssList(X5) )
& X0 = X4
& ssList(X4) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X3
& nil != X2 )
| ? [X4] :
( ? [X5] :
( app(cons(X4,nil),X5) = X3
& app(X5,cons(X4,nil)) != X2
& ssList(X5) )
& ssItem(X4) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( neq(nil,X1)
& ? [X9] :
( neq(nil,X1)
& hd(X1) = X9
& cons(X9,nil) = X8
& ssItem(X9) )
& app(X7,X8) = X6
& tl(X1) = X7
& ssList(X8) )
& ssList(X7) )
& X0 = X6
& ssList(X6) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f127,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f128,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f127]) ).
fof(f130,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f131,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f130]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f152,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f153,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f152]) ).
fof(f193,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f194,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f193]) ).
fof(f199,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f202,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X3
| nil = X2 )
& ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != X3
| app(X5,cons(X4,nil)) = X2
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,X1)
| ! [X9] :
( ~ neq(nil,X1)
| hd(X1) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(X1) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| X0 != X6
| ~ ssList(X6) )
& neq(X1,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f223,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X3
| nil = X2 )
& ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != X3
| app(X5,cons(X4,nil)) = X2
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,X1)
| ! [X9] :
( ~ neq(nil,X1)
| hd(X1) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(X1) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| X0 != X6
| ~ ssList(X6) )
& neq(X1,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f222]) ).
fof(f246,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,[],[f102]) ).
fof(f247,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,[],[f246]) ).
fof(f248,plain,
! [X0,X1] :
( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
=> ( app(X1,sK11(X0,X1)) = X0
& ssList(sK11(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f249,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ( app(X1,sK11(X0,X1)) = X0
& ssList(sK11(X0,X1)) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f247,f248]) ).
fof(f317,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f119]) ).
fof(f344,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X3
| nil = X2 )
& ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != X3
| app(X5,cons(X4,nil)) = X2
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,X1)
| ! [X9] :
( ~ neq(nil,X1)
| hd(X1) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(X1) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| X0 != X6
| ~ ssList(X6) )
& neq(X1,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X3
| nil = X2 )
& ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != X3
| app(X5,cons(X4,nil)) = X2
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,X1)
| ! [X9] :
( ~ neq(nil,X1)
| hd(X1) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(X1) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| sK53 != X6
| ~ ssList(X6) )
& neq(X1,nil)
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK53) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X3
| nil = X2 )
& ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != X3
| app(X5,cons(X4,nil)) = X2
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,X1)
| ! [X9] :
( ~ neq(nil,X1)
| hd(X1) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(X1) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| sK53 != X6
| ~ ssList(X6) )
& neq(X1,nil)
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( nil != X3
| nil = X2 )
& ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != X3
| app(X5,cons(X4,nil)) = X2
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,sK54)
| ! [X9] :
( ~ neq(nil,sK54)
| hd(sK54) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(sK54) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| sK53 != X6
| ~ ssList(X6) )
& neq(sK54,nil)
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK54) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
( ? [X2] :
( ? [X3] :
( ( nil != X3
| nil = X2 )
& ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != X3
| app(X5,cons(X4,nil)) = X2
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,sK54)
| ! [X9] :
( ~ neq(nil,sK54)
| hd(sK54) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(sK54) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| sK53 != X6
| ~ ssList(X6) )
& neq(sK54,nil)
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( nil != X3
| nil = sK55 )
& ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != X3
| app(X5,cons(X4,nil)) = sK55
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,sK54)
| ! [X9] :
( ~ neq(nil,sK54)
| hd(sK54) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(sK54) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| sK53 != X6
| ~ ssList(X6) )
& neq(sK54,nil)
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
& ssList(sK55) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
( ? [X3] :
( ( nil != X3
| nil = sK55 )
& ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != X3
| app(X5,cons(X4,nil)) = sK55
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,sK54)
| ! [X9] :
( ~ neq(nil,sK54)
| hd(sK54) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(sK54) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| sK53 != X6
| ~ ssList(X6) )
& neq(sK54,nil)
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
=> ( ( nil != sK56
| nil = sK55 )
& ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != sK56
| app(X5,cons(X4,nil)) = sK55
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,sK54)
| ! [X9] :
( ~ neq(nil,sK54)
| hd(sK54) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(sK54) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| sK53 != X6
| ~ ssList(X6) )
& neq(sK54,nil)
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
( ( nil != sK56
| nil = sK55 )
& ! [X4] :
( ! [X5] :
( app(cons(X4,nil),X5) != sK56
| app(X5,cons(X4,nil)) = sK55
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,sK54)
| ! [X9] :
( ~ neq(nil,sK54)
| hd(sK54) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(sK54) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| sK53 != X6
| ~ ssList(X6) )
& neq(sK54,nil)
& sK53 = sK55
& sK54 = sK56
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56])],[f223,f347,f346,f345,f344]) ).
fof(f363,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f249]) ).
fof(f439,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f317]) ).
fof(f440,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f441,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f449,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f451,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f453,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f474,plain,
! [X0,X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f526,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f194]) ).
fof(f529,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f199]) ).
fof(f534,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f202]) ).
fof(f549,plain,
ssList(sK54),
inference(cnf_transformation,[],[f348]) ).
fof(f552,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f348]) ).
fof(f554,plain,
neq(sK54,nil),
inference(cnf_transformation,[],[f348]) ).
fof(f556,plain,
! [X4,X5] :
( app(cons(X4,nil),X5) != sK56
| app(X5,cons(X4,nil)) = sK55
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f348]) ).
fof(f559,plain,
neq(sK56,nil),
inference(definition_unfolding,[],[f554,f552]) ).
fof(f560,plain,
ssList(sK56),
inference(definition_unfolding,[],[f549,f552]) ).
fof(f565,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(equality_resolution,[],[f363]) ).
cnf(c_61,plain,
( ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| frontsegP(app(X0,X1),X0) ),
inference(cnf_transformation,[],[f565]) ).
cnf(c_138,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f439]) ).
cnf(c_139,plain,
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f595]) ).
cnf(c_140,plain,
( ~ ssItem(X0)
| ~ ssList(X1)
| ssList(cons(X0,X1)) ),
inference(cnf_transformation,[],[f440]) ).
cnf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f441]) ).
cnf(c_149,plain,
( ~ ssList(X0)
| X0 = nil
| ssItem(hd(X0)) ),
inference(cnf_transformation,[],[f449]) ).
cnf(c_151,plain,
( ~ ssList(X0)
| X0 = nil
| ssList(tl(X0)) ),
inference(cnf_transformation,[],[f451]) ).
cnf(c_153,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f453]) ).
cnf(c_174,plain,
( ~ frontsegP(X0,X1)
| ~ frontsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f474]) ).
cnf(c_224,plain,
( ~ ssList(X0)
| cons(hd(X0),tl(X0)) = X0
| X0 = nil ),
inference(cnf_transformation,[],[f526]) ).
cnf(c_227,plain,
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) = cons(X0,X1) ),
inference(cnf_transformation,[],[f529]) ).
cnf(c_232,plain,
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f534]) ).
cnf(c_247,negated_conjecture,
( app(cons(X0,nil),X1) != sK56
| ~ ssItem(X0)
| ~ ssList(X1)
| app(X1,cons(X0,nil)) = sK55 ),
inference(cnf_transformation,[],[f556]) ).
cnf(c_248,negated_conjecture,
( app(tl(sK56),cons(hd(sK56),nil)) != sK55
| ~ ssList(app(tl(sK56),cons(hd(sK56),nil)))
| ~ ssList(cons(hd(sK56),nil))
| ~ neq(nil,sK56)
| ~ ssItem(hd(sK56))
| ~ ssList(tl(sK56)) ),
inference(cnf_transformation,[],[f600]) ).
cnf(c_249,negated_conjecture,
neq(sK56,nil),
inference(cnf_transformation,[],[f559]) ).
cnf(c_252,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f560]) ).
cnf(c_376,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| frontsegP(app(X0,X1),X0) ),
inference(global_subsumption_just,[status(thm)],[c_61,c_153,c_61]) ).
cnf(c_805,plain,
( app(tl(sK56),cons(hd(sK56),nil)) != sK55
| ~ ssList(cons(hd(sK56),nil))
| ~ neq(nil,sK56)
| ~ ssItem(hd(sK56))
| ~ ssList(tl(sK56)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_248,c_153]) ).
cnf(c_1951,plain,
( app(tl(sK56),cons(hd(sK56),nil)) != sK55
| X0 != nil
| X1 != sK56
| ~ ssList(cons(hd(sK56),nil))
| ~ ssItem(hd(sK56))
| ~ ssList(tl(sK56))
| ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1 ),
inference(resolution_lifted,[status(thm)],[c_138,c_805]) ).
cnf(c_1952,plain,
( app(tl(sK56),cons(hd(sK56),nil)) != sK55
| ~ ssList(cons(hd(sK56),nil))
| ~ ssItem(hd(sK56))
| ~ ssList(tl(sK56))
| ~ ssList(nil)
| ~ ssList(sK56)
| nil = sK56 ),
inference(unflattening,[status(thm)],[c_1951]) ).
cnf(c_1953,plain,
( app(tl(sK56),cons(hd(sK56),nil)) != sK55
| ~ ssList(cons(hd(sK56),nil))
| ~ ssItem(hd(sK56))
| ~ ssList(tl(sK56))
| nil = sK56 ),
inference(global_subsumption_just,[status(thm)],[c_1952,c_252,c_141,c_1952]) ).
cnf(c_1974,plain,
( X0 != nil
| X0 != sK56
| ~ ssList(X0) ),
inference(resolution_lifted,[status(thm)],[c_139,c_249]) ).
cnf(c_1975,plain,
( nil != sK56
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_1974]) ).
cnf(c_1976,plain,
nil != sK56,
inference(global_subsumption_just,[status(thm)],[c_1975,c_141,c_1975]) ).
cnf(c_1981,plain,
( app(tl(sK56),cons(hd(sK56),nil)) != sK55
| ~ ssList(cons(hd(sK56),nil))
| ~ ssItem(hd(sK56))
| ~ ssList(tl(sK56)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1953,c_1976]) ).
cnf(c_6381,plain,
( app(tl(sK56),cons(hd(sK56),nil)) != sK55
| ~ ssList(cons(hd(sK56),nil))
| ~ ssItem(hd(sK56))
| ~ ssList(tl(sK56)) ),
inference(subtyping,[status(esa)],[c_1981]) ).
cnf(c_6382,plain,
nil != sK56,
inference(subtyping,[status(esa)],[c_1976]) ).
cnf(c_6389,plain,
( ~ ssList(X0_13)
| ~ ssList(X1_13)
| frontsegP(app(X0_13,X1_13),X0_13) ),
inference(subtyping,[status(esa)],[c_376]) ).
cnf(c_6396,negated_conjecture,
ssList(sK56),
inference(subtyping,[status(esa)],[c_252]) ).
cnf(c_6397,negated_conjecture,
( app(cons(X0_14,nil),X0_13) != sK56
| ~ ssItem(X0_14)
| ~ ssList(X0_13)
| app(X0_13,cons(X0_14,nil)) = sK55 ),
inference(subtyping,[status(esa)],[c_247]) ).
cnf(c_6409,plain,
( ~ ssList(X0_13)
| app(X0_13,nil) = X0_13 ),
inference(subtyping,[status(esa)],[c_232]) ).
cnf(c_6413,plain,
( ~ ssItem(X0_14)
| ~ ssList(X0_13)
| app(cons(X0_14,nil),X0_13) = cons(X0_14,X0_13) ),
inference(subtyping,[status(esa)],[c_227]) ).
cnf(c_6416,plain,
( ~ ssList(X0_13)
| cons(hd(X0_13),tl(X0_13)) = X0_13
| X0_13 = nil ),
inference(subtyping,[status(esa)],[c_224]) ).
cnf(c_6455,plain,
( ~ frontsegP(X0_13,X1_13)
| ~ frontsegP(X1_13,X0_13)
| ~ ssList(X0_13)
| ~ ssList(X1_13)
| X0_13 = X1_13 ),
inference(subtyping,[status(esa)],[c_174]) ).
cnf(c_6478,plain,
( ~ ssList(X0_13)
| X0_13 = nil
| ssList(tl(X0_13)) ),
inference(subtyping,[status(esa)],[c_151]) ).
cnf(c_6480,plain,
( ~ ssList(X0_13)
| X0_13 = nil
| ssItem(hd(X0_13)) ),
inference(subtyping,[status(esa)],[c_149]) ).
cnf(c_6489,plain,
( ~ ssItem(X0_14)
| ~ ssList(X0_13)
| ssList(cons(X0_14,X0_13)) ),
inference(subtyping,[status(esa)],[c_140]) ).
cnf(c_6566,negated_conjecture,
( app(cons(X0_14,nil),X0_13) != sK56
| ~ ssItem(X0_14)
| ~ ssList(X0_13)
| app(X0_13,cons(X0_14,nil)) = sK55 ),
inference(demodulation,[status(thm)],[c_6397]) ).
cnf(c_6567,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_6396]) ).
cnf(c_6570,plain,
X0_13 = X0_13,
theory(equality) ).
cnf(c_6572,plain,
( X0_13 != X1_13
| X2_13 != X1_13
| X2_13 = X0_13 ),
theory(equality) ).
cnf(c_6599,plain,
nil = nil,
inference(instantiation,[status(thm)],[c_6570]) ).
cnf(c_9515,plain,
( nil != X0_13
| sK56 != X0_13
| nil = sK56 ),
inference(instantiation,[status(thm)],[c_6572]) ).
cnf(c_9516,plain,
( nil != nil
| sK56 != nil
| nil = sK56 ),
inference(instantiation,[status(thm)],[c_9515]) ).
cnf(c_9653,plain,
( ~ frontsegP(X0_13,sK56)
| ~ frontsegP(sK56,X0_13)
| ~ ssList(X0_13)
| ~ ssList(sK56)
| sK56 = X0_13 ),
inference(instantiation,[status(thm)],[c_6455]) ).
cnf(c_10418,plain,
( ~ ssList(sK56)
| cons(hd(sK56),tl(sK56)) = sK56
| sK56 = nil ),
inference(instantiation,[status(thm)],[c_6416]) ).
cnf(c_10424,plain,
( ~ ssList(sK56)
| sK56 = nil
| ssItem(hd(sK56)) ),
inference(instantiation,[status(thm)],[c_6480]) ).
cnf(c_10425,plain,
( ~ ssList(sK56)
| sK56 = nil
| ssList(tl(sK56)) ),
inference(instantiation,[status(thm)],[c_6478]) ).
cnf(c_10449,plain,
( ~ frontsegP(sK56,sK56)
| ~ ssList(sK56)
| sK56 = sK56 ),
inference(instantiation,[status(thm)],[c_9653]) ).
cnf(c_10958,plain,
( ~ ssItem(hd(sK56))
| ~ ssList(nil)
| ssList(cons(hd(sK56),nil)) ),
inference(instantiation,[status(thm)],[c_6489]) ).
cnf(c_11075,plain,
app(sK56,nil) = sK56,
inference(superposition,[status(thm)],[c_6567,c_6409]) ).
cnf(c_11821,plain,
( ~ ssList(nil)
| ~ ssList(sK56)
| frontsegP(sK56,sK56) ),
inference(superposition,[status(thm)],[c_11075,c_6389]) ).
cnf(c_12296,plain,
( app(cons(X0_14,nil),X0_13) != X1_13
| sK56 != X1_13
| app(cons(X0_14,nil),X0_13) = sK56 ),
inference(instantiation,[status(thm)],[c_6572]) ).
cnf(c_12407,plain,
( X0_13 != X1_13
| sK56 != X1_13
| sK56 = X0_13 ),
inference(instantiation,[status(thm)],[c_6572]) ).
cnf(c_13088,plain,
( X0_13 != sK56
| sK56 != sK56
| sK56 = X0_13 ),
inference(instantiation,[status(thm)],[c_12407]) ).
cnf(c_16685,plain,
( cons(hd(sK56),tl(sK56)) != sK56
| sK56 != sK56
| sK56 = cons(hd(sK56),tl(sK56)) ),
inference(instantiation,[status(thm)],[c_13088]) ).
cnf(c_21286,plain,
( app(cons(X0_14,nil),X0_13) != cons(hd(sK56),tl(sK56))
| sK56 != cons(hd(sK56),tl(sK56))
| app(cons(X0_14,nil),X0_13) = sK56 ),
inference(instantiation,[status(thm)],[c_12296]) ).
cnf(c_26616,plain,
( app(cons(hd(sK56),nil),tl(sK56)) != cons(hd(sK56),tl(sK56))
| sK56 != cons(hd(sK56),tl(sK56))
| app(cons(hd(sK56),nil),tl(sK56)) = sK56 ),
inference(instantiation,[status(thm)],[c_21286]) ).
cnf(c_31396,plain,
( ~ ssItem(hd(sK56))
| ~ ssList(tl(sK56))
| app(cons(hd(sK56),nil),tl(sK56)) = cons(hd(sK56),tl(sK56)) ),
inference(instantiation,[status(thm)],[c_6413]) ).
cnf(c_51056,plain,
( app(cons(hd(sK56),nil),tl(sK56)) != sK56
| ~ ssItem(hd(sK56))
| ~ ssList(tl(sK56))
| app(tl(sK56),cons(hd(sK56),nil)) = sK55 ),
inference(instantiation,[status(thm)],[c_6566]) ).
cnf(c_51057,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_51056,c_31396,c_26616,c_16685,c_11821,c_10958,c_10449,c_10418,c_10424,c_10425,c_9516,c_6382,c_6381,c_6599,c_141,c_252]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC308+1 : TPTP v8.2.0. Released v2.4.0.
% 0.03/0.12 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 20 03:39:24 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 40.59/6.23 % SZS status Started for theBenchmark.p
% 40.59/6.23 % SZS status Theorem for theBenchmark.p
% 40.59/6.23
% 40.59/6.23 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 40.59/6.23
% 40.59/6.23 ------ iProver source info
% 40.59/6.23
% 40.59/6.23 git: date: 2024-06-12 09:56:46 +0000
% 40.59/6.23 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 40.59/6.23 git: non_committed_changes: false
% 40.59/6.23
% 40.59/6.23 ------ Parsing...
% 40.59/6.23 ------ Clausification by vclausify_rel & Parsing by iProver...
% 40.59/6.23
% 40.59/6.23 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e
% 40.59/6.23
% 40.59/6.23 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 40.59/6.23
% 40.59/6.23 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 40.59/6.23 ------ Proving...
% 40.59/6.23 ------ Problem Properties
% 40.59/6.23
% 40.59/6.23
% 40.59/6.23 clauses 185
% 40.59/6.23 conjectures 3
% 40.59/6.23 EPR 52
% 40.59/6.23 Horn 117
% 40.59/6.23 unary 19
% 40.59/6.23 binary 40
% 40.59/6.23 lits 629
% 40.59/6.23 lits eq 82
% 40.59/6.23 fd_pure 0
% 40.59/6.23 fd_pseudo 0
% 40.59/6.23 fd_cond 21
% 40.59/6.23 fd_pseudo_cond 14
% 40.59/6.23 AC symbols 0
% 40.59/6.23
% 40.59/6.23 ------ Input Options Time Limit: Unbounded
% 40.59/6.23
% 40.59/6.23
% 40.59/6.23 ------
% 40.59/6.23 Current options:
% 40.59/6.23 ------
% 40.59/6.23
% 40.59/6.23
% 40.59/6.23
% 40.59/6.23
% 40.59/6.23 ------ Proving...
% 40.59/6.23
% 40.59/6.23
% 40.59/6.23 % SZS status Theorem for theBenchmark.p
% 40.59/6.23
% 40.59/6.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 40.59/6.23
% 40.59/6.24
%------------------------------------------------------------------------------