TSTP Solution File: SWC310+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWC310+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% 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 : Thu Aug 31 20:42:26 EDT 2023
% Result : Theorem 17.13s 3.13s
% Output : CNFRefutation 17.13s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f607)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
fof(f25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax75) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax76) ).
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(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ? [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) )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( app(X5,cons(X4,nil)) != X2
| app(cons(X4,nil),X5) != X3
| ~ ssList(X5) ) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ? [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) )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( app(X5,cons(X4,nil)) != X2
| app(cons(X4,nil),X5) != X3
| ~ ssList(X5) ) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ? [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) )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ! [X8] :
( ssItem(X8)
=> ! [X9] :
( app(X9,cons(X8,nil)) != X2
| app(cons(X8,nil),X9) != X3
| ~ ssList(X9) ) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(rectify,[],[f97]) ).
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(f129,plain,
! [X0] :
( ! [X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f187,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f75]) ).
fof(f188,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f187]) ).
fof(f189,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f76]) ).
fof(f190,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f189]) ).
fof(f199,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [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) )
| ( nil != X0
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ? [X8] :
( ? [X9] :
( app(X9,cons(X8,nil)) = X2
& app(cons(X8,nil),X9) = X3
& ssList(X9) )
& ssItem(X8) ) )
& ( nil != X3
| nil = X2 )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f316,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f119]) ).
fof(f335,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
=> ( hd(X0) = sK51(X0)
& ssItem(sK51(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f336,plain,
! [X0] :
( ( hd(X0) = sK51(X0)
& ssItem(sK51(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK51])],[f188,f335]) ).
fof(f337,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
=> ( tl(X0) = sK52(X0)
& ssList(sK52(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f338,plain,
! [X0] :
( ( tl(X0) = sK52(X0)
& ssList(sK52(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f190,f337]) ).
fof(f343,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [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) )
| ( nil != X0
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ? [X8] :
( ? [X9] :
( app(X9,cons(X8,nil)) = X2
& app(cons(X8,nil),X9) = X3
& ssList(X9) )
& ssItem(X8) ) )
& ( nil != X3
| nil = X2 )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [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) )
| sK53 != X4
| ~ ssList(X4) )
& neq(X1,nil) )
| ( nil != sK53
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ? [X8] :
( ? [X9] :
( app(X9,cons(X8,nil)) = X2
& app(cons(X8,nil),X9) = X3
& ssList(X9) )
& ssItem(X8) ) )
& ( nil != X3
| nil = X2 )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK53) ) ),
introduced(choice_axiom,[]) ).
fof(f344,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [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) )
| sK53 != X4
| ~ ssList(X4) )
& neq(X1,nil) )
| ( nil != sK53
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ? [X8] :
( ? [X9] :
( app(X9,cons(X8,nil)) = X2
& app(cons(X8,nil),X9) = X3
& ssList(X9) )
& ssItem(X8) ) )
& ( nil != X3
| nil = X2 )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,sK54)
| ! [X7] :
( ~ neq(nil,sK54)
| hd(sK54) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(sK54) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| sK53 != X4
| ~ ssList(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( ~ neq(X3,nil)
| ? [X8] :
( ? [X9] :
( app(X9,cons(X8,nil)) = X2
& app(cons(X8,nil),X9) = X3
& ssList(X9) )
& ssItem(X8) ) )
& ( nil != X3
| nil = X2 )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK54) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,sK54)
| ! [X7] :
( ~ neq(nil,sK54)
| hd(sK54) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(sK54) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| sK53 != X4
| ~ ssList(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( ~ neq(X3,nil)
| ? [X8] :
( ? [X9] :
( app(X9,cons(X8,nil)) = X2
& app(cons(X8,nil),X9) = X3
& ssList(X9) )
& ssItem(X8) ) )
& ( nil != X3
| nil = X2 )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,sK54)
| ! [X7] :
( ~ neq(nil,sK54)
| hd(sK54) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(sK54) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| sK53 != X4
| ~ ssList(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( ~ neq(X3,nil)
| ? [X8] :
( ? [X9] :
( app(X9,cons(X8,nil)) = sK55
& app(cons(X8,nil),X9) = X3
& ssList(X9) )
& ssItem(X8) ) )
& ( nil != X3
| nil = sK55 )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
& ssList(sK55) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,sK54)
| ! [X7] :
( ~ neq(nil,sK54)
| hd(sK54) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(sK54) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| sK53 != X4
| ~ ssList(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( ~ neq(X3,nil)
| ? [X8] :
( ? [X9] :
( app(X9,cons(X8,nil)) = sK55
& app(cons(X8,nil),X9) = X3
& ssList(X9) )
& ssItem(X8) ) )
& ( nil != X3
| nil = sK55 )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
=> ( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,sK54)
| ! [X7] :
( ~ neq(nil,sK54)
| hd(sK54) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(sK54) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| sK53 != X4
| ~ ssList(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( ~ neq(sK56,nil)
| ? [X8] :
( ? [X9] :
( app(X9,cons(X8,nil)) = sK55
& app(cons(X8,nil),X9) = sK56
& ssList(X9) )
& ssItem(X8) ) )
& ( nil != sK56
| nil = sK55 )
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
( ? [X8] :
( ? [X9] :
( app(X9,cons(X8,nil)) = sK55
& app(cons(X8,nil),X9) = sK56
& ssList(X9) )
& ssItem(X8) )
=> ( ? [X9] :
( sK55 = app(X9,cons(sK57,nil))
& sK56 = app(cons(sK57,nil),X9)
& ssList(X9) )
& ssItem(sK57) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
( ? [X9] :
( sK55 = app(X9,cons(sK57,nil))
& sK56 = app(cons(sK57,nil),X9)
& ssList(X9) )
=> ( sK55 = app(sK58,cons(sK57,nil))
& sK56 = app(cons(sK57,nil),sK58)
& ssList(sK58) ) ),
introduced(choice_axiom,[]) ).
fof(f349,plain,
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,sK54)
| ! [X7] :
( ~ neq(nil,sK54)
| hd(sK54) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(sK54) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| sK53 != X4
| ~ ssList(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( ~ neq(sK56,nil)
| ( sK55 = app(sK58,cons(sK57,nil))
& sK56 = app(cons(sK57,nil),sK58)
& ssList(sK58)
& ssItem(sK57) ) )
& ( nil != sK56
| nil = sK55 )
& sK53 = sK55
& sK54 = sK56
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58])],[f222,f348,f347,f346,f345,f344,f343]) ).
fof(f440,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f316]) ).
fof(f441,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f442,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f451,plain,
! [X0,X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f453,plain,
! [X0,X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f454,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f523,plain,
! [X0] :
( hd(X0) = sK51(X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f525,plain,
! [X0] :
( tl(X0) = sK52(X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f338]) ).
fof(f530,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f199]) ).
fof(f550,plain,
ssList(sK54),
inference(cnf_transformation,[],[f349]) ).
fof(f553,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f349]) ).
fof(f554,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f349]) ).
fof(f555,plain,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f349]) ).
fof(f556,plain,
( ~ neq(sK56,nil)
| ssItem(sK57) ),
inference(cnf_transformation,[],[f349]) ).
fof(f557,plain,
( ~ neq(sK56,nil)
| ssList(sK58) ),
inference(cnf_transformation,[],[f349]) ).
fof(f558,plain,
( ~ neq(sK56,nil)
| sK56 = app(cons(sK57,nil),sK58) ),
inference(cnf_transformation,[],[f349]) ).
fof(f559,plain,
( ~ neq(sK56,nil)
| sK55 = app(sK58,cons(sK57,nil)) ),
inference(cnf_transformation,[],[f349]) ).
fof(f560,plain,
( neq(sK54,nil)
| nil = sK54 ),
inference(cnf_transformation,[],[f349]) ).
fof(f561,plain,
( neq(sK54,nil)
| nil != sK53 ),
inference(cnf_transformation,[],[f349]) ).
fof(f566,plain,
( neq(sK56,nil)
| nil != sK55 ),
inference(definition_unfolding,[],[f561,f553,f554]) ).
fof(f567,plain,
( neq(sK56,nil)
| nil = sK56 ),
inference(definition_unfolding,[],[f560,f553,f553]) ).
fof(f568,plain,
ssList(sK56),
inference(definition_unfolding,[],[f550,f553]) ).
cnf(c_138,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f440]) ).
cnf(c_139,plain,
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f607]) ).
cnf(c_140,plain,
( ~ ssItem(X0)
| ~ ssList(X1)
| ssList(cons(X0,X1)) ),
inference(cnf_transformation,[],[f441]) ).
cnf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f442]) ).
cnf(c_150,plain,
( ~ ssItem(X0)
| ~ ssList(X1)
| hd(cons(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f451]) ).
cnf(c_152,plain,
( ~ ssItem(X0)
| ~ ssList(X1)
| tl(cons(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f453]) ).
cnf(c_153,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f454]) ).
cnf(c_219,plain,
( ~ ssList(X0)
| hd(X0) = sK51(X0)
| X0 = nil ),
inference(cnf_transformation,[],[f523]) ).
cnf(c_221,plain,
( ~ ssList(X0)
| tl(X0) = sK52(X0)
| X0 = nil ),
inference(cnf_transformation,[],[f525]) ).
cnf(c_227,plain,
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) = cons(X0,X1) ),
inference(cnf_transformation,[],[f530]) ).
cnf(c_246,negated_conjecture,
( app(tl(sK56),cons(hd(sK56),nil)) != sK55
| 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,[],[f612]) ).
cnf(c_247,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))
| nil = sK56 ),
inference(cnf_transformation,[],[f613]) ).
cnf(c_248,negated_conjecture,
( nil != sK55
| neq(sK56,nil) ),
inference(cnf_transformation,[],[f566]) ).
cnf(c_249,negated_conjecture,
( nil = sK56
| neq(sK56,nil) ),
inference(cnf_transformation,[],[f567]) ).
cnf(c_250,negated_conjecture,
( ~ neq(sK56,nil)
| app(sK58,cons(sK57,nil)) = sK55 ),
inference(cnf_transformation,[],[f559]) ).
cnf(c_251,negated_conjecture,
( ~ neq(sK56,nil)
| app(cons(sK57,nil),sK58) = sK56 ),
inference(cnf_transformation,[],[f558]) ).
cnf(c_252,negated_conjecture,
( ~ neq(sK56,nil)
| ssList(sK58) ),
inference(cnf_transformation,[],[f557]) ).
cnf(c_253,negated_conjecture,
( ~ neq(sK56,nil)
| ssItem(sK57) ),
inference(cnf_transformation,[],[f556]) ).
cnf(c_254,negated_conjecture,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f555]) ).
cnf(c_257,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f568]) ).
cnf(c_365,negated_conjecture,
ssItem(sK57),
inference(global_subsumption_just,[status(thm)],[c_253,c_253,c_249,c_248,c_254]) ).
cnf(c_367,negated_conjecture,
ssList(sK58),
inference(global_subsumption_just,[status(thm)],[c_252,c_252,c_249,c_248,c_254]) ).
cnf(c_375,negated_conjecture,
neq(sK56,nil),
inference(global_subsumption_just,[status(thm)],[c_249,c_249,c_248,c_254]) ).
cnf(c_377,negated_conjecture,
neq(sK56,nil),
inference(global_subsumption_just,[status(thm)],[c_248,c_375]) ).
cnf(c_385,negated_conjecture,
app(cons(sK57,nil),sK58) = sK56,
inference(global_subsumption_just,[status(thm)],[c_251,c_249,c_248,c_254,c_251]) ).
cnf(c_387,negated_conjecture,
app(sK58,cons(sK57,nil)) = sK55,
inference(global_subsumption_just,[status(thm)],[c_250,c_249,c_248,c_254,c_250]) ).
cnf(c_395,plain,
( ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil))
| ~ ssList(app(tl(sK56),cons(hd(sK56),nil)))
| app(tl(sK56),cons(hd(sK56),nil)) != sK55 ),
inference(global_subsumption_just,[status(thm)],[c_247,c_254,c_247,c_246]) ).
cnf(c_396,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(renaming,[status(thm)],[c_395]) ).
cnf(c_833,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_396,c_153]) ).
cnf(c_2611,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_833]) ).
cnf(c_2612,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_2611]) ).
cnf(c_2613,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_2612,c_257,c_141,c_2612]) ).
cnf(c_2634,plain,
( X0 != nil
| X0 != sK56
| ~ ssList(X0) ),
inference(resolution_lifted,[status(thm)],[c_139,c_377]) ).
cnf(c_2635,plain,
( nil != sK56
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_2634]) ).
cnf(c_2636,plain,
nil != sK56,
inference(global_subsumption_just,[status(thm)],[c_2635,c_141,c_2635]) ).
cnf(c_2641,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_2613,c_2636]) ).
cnf(c_7645,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_2641]) ).
cnf(c_7646,plain,
nil != sK56,
inference(subtyping,[status(esa)],[c_2636]) ).
cnf(c_7655,negated_conjecture,
app(sK58,cons(sK57,nil)) = sK55,
inference(subtyping,[status(esa)],[c_387]) ).
cnf(c_7656,negated_conjecture,
app(cons(sK57,nil),sK58) = sK56,
inference(subtyping,[status(esa)],[c_385]) ).
cnf(c_7661,negated_conjecture,
ssList(sK58),
inference(subtyping,[status(esa)],[c_367]) ).
cnf(c_7662,negated_conjecture,
ssItem(sK57),
inference(subtyping,[status(esa)],[c_365]) ).
cnf(c_7664,negated_conjecture,
ssList(sK56),
inference(subtyping,[status(esa)],[c_257]) ).
cnf(c_7680,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_7686,plain,
( ~ ssList(X0_13)
| tl(X0_13) = sK52(X0_13)
| X0_13 = nil ),
inference(subtyping,[status(esa)],[c_221]) ).
cnf(c_7688,plain,
( ~ ssList(X0_13)
| hd(X0_13) = sK51(X0_13)
| X0_13 = nil ),
inference(subtyping,[status(esa)],[c_219]) ).
cnf(c_7744,plain,
( ~ ssItem(X0_14)
| ~ ssList(X0_13)
| tl(cons(X0_14,X0_13)) = X0_13 ),
inference(subtyping,[status(esa)],[c_152]) ).
cnf(c_7746,plain,
( ~ ssItem(X0_14)
| ~ ssList(X0_13)
| hd(cons(X0_14,X0_13)) = X0_14 ),
inference(subtyping,[status(esa)],[c_150]) ).
cnf(c_7755,plain,
ssList(nil),
inference(subtyping,[status(esa)],[c_141]) ).
cnf(c_7756,plain,
( ~ ssItem(X0_14)
| ~ ssList(X0_13)
| ssList(cons(X0_14,X0_13)) ),
inference(subtyping,[status(esa)],[c_140]) ).
cnf(c_10755,plain,
( ~ ssList(X0_13)
| app(cons(sK57,nil),X0_13) = cons(sK57,X0_13) ),
inference(superposition,[status(thm)],[c_7662,c_7680]) ).
cnf(c_10836,plain,
( tl(sK56) = sK52(sK56)
| nil = sK56 ),
inference(superposition,[status(thm)],[c_7664,c_7686]) ).
cnf(c_10841,plain,
tl(sK56) = sK52(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_10836,c_7646]) ).
cnf(c_10879,plain,
( ~ ssList(X0_13)
| tl(cons(sK57,X0_13)) = X0_13 ),
inference(superposition,[status(thm)],[c_7662,c_7744]) ).
cnf(c_11208,plain,
app(cons(sK57,nil),sK58) = cons(sK57,sK58),
inference(superposition,[status(thm)],[c_7661,c_10755]) ).
cnf(c_11216,plain,
cons(sK57,sK58) = sK56,
inference(demodulation,[status(thm)],[c_11208,c_7656]) ).
cnf(c_12586,plain,
tl(cons(sK57,sK58)) = sK58,
inference(superposition,[status(thm)],[c_7661,c_10879]) ).
cnf(c_12602,plain,
sK52(sK56) = sK58,
inference(demodulation,[status(thm)],[c_12586,c_10841,c_11216]) ).
cnf(c_18942,plain,
( ~ ssList(X0_13)
| app(cons(sK57,nil),X0_13) = cons(sK57,X0_13) ),
inference(superposition,[status(thm)],[c_7662,c_7680]) ).
cnf(c_19023,plain,
( tl(sK56) = sK52(sK56)
| nil = sK56 ),
inference(superposition,[status(thm)],[c_7664,c_7686]) ).
cnf(c_19028,plain,
tl(sK56) = sK52(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_19023,c_7646]) ).
cnf(c_19029,plain,
tl(sK56) = sK58,
inference(demodulation,[status(thm)],[c_19028,c_12602]) ).
cnf(c_19039,plain,
( hd(sK56) = sK51(sK56)
| nil = sK56 ),
inference(superposition,[status(thm)],[c_7664,c_7688]) ).
cnf(c_19044,plain,
hd(sK56) = sK51(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_19039,c_7646]) ).
cnf(c_19085,plain,
( ~ ssList(X0_13)
| hd(cons(sK57,X0_13)) = sK57 ),
inference(superposition,[status(thm)],[c_7662,c_7746]) ).
cnf(c_19139,plain,
( app(sK58,cons(hd(sK56),nil)) != sK55
| ~ ssList(cons(hd(sK56),nil))
| ~ ssItem(hd(sK56))
| ~ ssList(tl(sK56)) ),
inference(superposition,[status(thm)],[c_19029,c_7645]) ).
cnf(c_19141,plain,
( app(sK58,cons(sK51(sK56),nil)) != sK55
| ~ ssList(cons(sK51(sK56),nil))
| ~ ssItem(sK51(sK56))
| ~ ssList(sK58) ),
inference(demodulation,[status(thm)],[c_19139,c_19044,c_19029]) ).
cnf(c_19142,plain,
( app(sK58,cons(sK51(sK56),nil)) != sK55
| ~ ssList(cons(sK51(sK56),nil))
| ~ ssItem(sK51(sK56)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19141,c_7661]) ).
cnf(c_19394,plain,
app(cons(sK57,nil),sK58) = cons(sK57,sK58),
inference(superposition,[status(thm)],[c_7661,c_18942]) ).
cnf(c_19402,plain,
cons(sK57,sK58) = sK56,
inference(demodulation,[status(thm)],[c_19394,c_7656]) ).
cnf(c_20764,plain,
hd(cons(sK57,sK58)) = sK57,
inference(superposition,[status(thm)],[c_7661,c_19085]) ).
cnf(c_20781,plain,
sK51(sK56) = sK57,
inference(demodulation,[status(thm)],[c_20764,c_19044,c_19402]) ).
cnf(c_21352,plain,
( sK55 != sK55
| ~ ssList(cons(sK57,nil))
| ~ ssItem(sK57) ),
inference(demodulation,[status(thm)],[c_19142,c_7655,c_20781]) ).
cnf(c_21353,plain,
( ~ ssList(cons(sK57,nil))
| ~ ssItem(sK57) ),
inference(equality_resolution_simp,[status(thm)],[c_21352]) ).
cnf(c_21356,plain,
( ~ ssItem(sK57)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_7756,c_21353]) ).
cnf(c_21357,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_21356,c_7755,c_7662]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC310+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.12 % Command : run_iprover %s %d THM
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 28 19:03:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.45 Running first-order theorem proving
% 0.20/0.45 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 17.13/3.13 % SZS status Started for theBenchmark.p
% 17.13/3.13 % SZS status Theorem for theBenchmark.p
% 17.13/3.13
% 17.13/3.13 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 17.13/3.13
% 17.13/3.13 ------ iProver source info
% 17.13/3.13
% 17.13/3.13 git: date: 2023-05-31 18:12:56 +0000
% 17.13/3.13 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 17.13/3.13 git: non_committed_changes: false
% 17.13/3.13 git: last_make_outside_of_git: false
% 17.13/3.13
% 17.13/3.13 ------ Parsing...
% 17.13/3.13 ------ Clausification by vclausify_rel & Parsing by iProver...
% 17.13/3.13
% 17.13/3.13 ------ 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
% 17.13/3.13
% 17.13/3.13 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 17.13/3.13
% 17.13/3.13 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.13/3.13 ------ Proving...
% 17.13/3.13 ------ Problem Properties
% 17.13/3.13
% 17.13/3.13
% 17.13/3.13 clauses 188
% 17.13/3.13 conjectures 6
% 17.13/3.13 EPR 54
% 17.13/3.13 Horn 120
% 17.13/3.13 unary 23
% 17.13/3.13 binary 40
% 17.13/3.13 lits 629
% 17.13/3.13 lits eq 82
% 17.13/3.13 fd_pure 0
% 17.13/3.13 fd_pseudo 0
% 17.13/3.13 fd_cond 21
% 17.13/3.13 fd_pseudo_cond 14
% 17.13/3.13 AC symbols 0
% 17.13/3.13
% 17.13/3.13 ------ Input Options Time Limit: Unbounded
% 17.13/3.13
% 17.13/3.13
% 17.13/3.13 ------
% 17.13/3.13 Current options:
% 17.13/3.13 ------
% 17.13/3.13
% 17.13/3.13
% 17.13/3.13
% 17.13/3.13
% 17.13/3.13 ------ Proving...
% 17.13/3.13
% 17.13/3.13
% 17.13/3.13 % SZS status Theorem for theBenchmark.p
% 17.13/3.13
% 17.13/3.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.13/3.13
% 17.13/3.13
%------------------------------------------------------------------------------