TSTP Solution File: SWC003+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWC003+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n004.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 : Fri May 3 03:10:49 EDT 2024
% Result : Theorem 3.95s 1.13s
% Output : CNFRefutation 3.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 16
% Syntax : Number of formulae : 98 ( 22 unt; 0 def)
% Number of atoms : 560 ( 176 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 723 ( 261 ~; 247 |; 176 &)
% ( 4 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 282 ( 24 sgn 140 !; 69 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
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(f39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( ? [X10] :
( geq(X10,X7)
& memberP(X3,X10)
& X7 != X10
& ssItem(X10) )
| app(X8,X9) != X2
| app(app(X8,cons(X7,nil)),X9) != X3 ) ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( neq(X5,nil)
& app(X4,X6) = X0
& app(app(X4,X5),X6) = X1
& ssList(X6) )
& ssList(X5) )
& ssList(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( ? [X10] :
( geq(X10,X7)
& memberP(X3,X10)
& X7 != X10
& ssItem(X10) )
| app(X8,X9) != X2
| app(app(X8,cons(X7,nil)),X9) != X3 ) ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( neq(X5,nil)
& app(X4,X6) = X0
& app(app(X4,X5),X6) = X1
& ssList(X6) )
& ssList(X5) )
& 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)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( ? [X7] :
( geq(X7,X4)
& memberP(X3,X7)
& X4 != X7
& ssItem(X7) )
| app(X5,X6) != X2
| app(app(X5,cons(X4,nil)),X6) != X3 ) ) ) )
| ? [X8] :
( ? [X9] :
( ? [X10] :
( neq(X9,nil)
& app(X8,X10) = X0
& app(app(X8,X9),X10) = X1
& ssList(X10) )
& ssList(X9) )
& ssList(X8) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f101,plain,
! [X0] :
( ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f4]) ).
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(f202,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ~ geq(X7,X4)
| ~ memberP(X3,X7)
| X4 = X7
| ~ ssItem(X7) )
& app(X5,X6) = X2
& app(app(X5,cons(X4,nil)),X6) = X3
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ neq(X9,nil)
| app(X8,X10) != X0
| app(app(X8,X9),X10) != X1
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
& 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] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ~ geq(X7,X4)
| ~ memberP(X3,X7)
| X4 = X7
| ~ ssItem(X7) )
& app(X5,X6) = X2
& app(app(X5,cons(X4,nil)),X6) = X3
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ neq(X9,nil)
| app(X8,X10) != X0
| app(app(X8,X9),X10) != X1
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f222]) ).
fof(f233,plain,
! [X3,X2,X0,X1] :
( ( ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ~ geq(X7,X4)
| ~ memberP(X3,X7)
| X4 = X7
| ~ ssItem(X7) )
& app(X5,X6) = X2
& app(app(X5,cons(X4,nil)),X6) = X3
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ neq(X9,nil)
| app(X8,X10) != X0
| app(app(X8,X9),X10) != X1
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
& neq(X1,nil) )
| ~ sP6(X3,X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f234,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP6(X3,X2,X0,X1) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f223,f233]) ).
fof(f244,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,[],[f101]) ).
fof(f245,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f244]) ).
fof(f246,plain,
! [X0] :
( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
=> ( cons(sK11(X0),nil) = X0
& ssItem(sK11(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f247,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ( cons(sK11(X0),nil) = X0
& ssItem(sK11(X0)) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f245,f246]) ).
fof(f319,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f119]) ).
fof(f346,plain,
! [X3,X2,X0,X1] :
( ( ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ~ geq(X7,X4)
| ~ memberP(X3,X7)
| X4 = X7
| ~ ssItem(X7) )
& app(X5,X6) = X2
& app(app(X5,cons(X4,nil)),X6) = X3
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ neq(X9,nil)
| app(X8,X10) != X0
| app(app(X8,X9),X10) != X1
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
& neq(X1,nil) )
| ~ sP6(X3,X2,X0,X1) ),
inference(nnf_transformation,[],[f233]) ).
fof(f347,plain,
! [X0,X1,X2,X3] :
( ( ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ~ geq(X7,X4)
| ~ memberP(X0,X7)
| X4 = X7
| ~ ssItem(X7) )
& app(X5,X6) = X1
& app(app(X5,cons(X4,nil)),X6) = X0
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ neq(X9,nil)
| app(X8,X10) != X2
| app(app(X8,X9),X10) != X3
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
& neq(X3,nil) )
| ~ sP6(X0,X1,X2,X3) ),
inference(rectify,[],[f346]) ).
fof(f348,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ~ geq(X7,X4)
| ~ memberP(X0,X7)
| X4 = X7
| ~ ssItem(X7) )
& app(X5,X6) = X1
& app(app(X5,cons(X4,nil)),X6) = X0
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
=> ( ? [X5] :
( ? [X6] :
( ! [X7] :
( ~ geq(X7,sK54(X0,X1))
| ~ memberP(X0,X7)
| sK54(X0,X1) = X7
| ~ ssItem(X7) )
& app(X5,X6) = X1
& app(app(X5,cons(sK54(X0,X1),nil)),X6) = X0
& ssList(X6) )
& ssList(X5) )
& ssItem(sK54(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f349,plain,
! [X0,X1] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ~ geq(X7,sK54(X0,X1))
| ~ memberP(X0,X7)
| sK54(X0,X1) = X7
| ~ ssItem(X7) )
& app(X5,X6) = X1
& app(app(X5,cons(sK54(X0,X1),nil)),X6) = X0
& ssList(X6) )
& ssList(X5) )
=> ( ? [X6] :
( ! [X7] :
( ~ geq(X7,sK54(X0,X1))
| ~ memberP(X0,X7)
| sK54(X0,X1) = X7
| ~ ssItem(X7) )
& app(sK55(X0,X1),X6) = X1
& app(app(sK55(X0,X1),cons(sK54(X0,X1),nil)),X6) = X0
& ssList(X6) )
& ssList(sK55(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f350,plain,
! [X0,X1] :
( ? [X6] :
( ! [X7] :
( ~ geq(X7,sK54(X0,X1))
| ~ memberP(X0,X7)
| sK54(X0,X1) = X7
| ~ ssItem(X7) )
& app(sK55(X0,X1),X6) = X1
& app(app(sK55(X0,X1),cons(sK54(X0,X1),nil)),X6) = X0
& ssList(X6) )
=> ( ! [X7] :
( ~ geq(X7,sK54(X0,X1))
| ~ memberP(X0,X7)
| sK54(X0,X1) = X7
| ~ ssItem(X7) )
& app(sK55(X0,X1),sK56(X0,X1)) = X1
& app(app(sK55(X0,X1),cons(sK54(X0,X1),nil)),sK56(X0,X1)) = X0
& ssList(sK56(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f351,plain,
! [X0,X1,X2,X3] :
( ( ! [X7] :
( ~ geq(X7,sK54(X0,X1))
| ~ memberP(X0,X7)
| sK54(X0,X1) = X7
| ~ ssItem(X7) )
& app(sK55(X0,X1),sK56(X0,X1)) = X1
& app(app(sK55(X0,X1),cons(sK54(X0,X1),nil)),sK56(X0,X1)) = X0
& ssList(sK56(X0,X1))
& ssList(sK55(X0,X1))
& ssItem(sK54(X0,X1))
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ neq(X9,nil)
| app(X8,X10) != X2
| app(app(X8,X9),X10) != X3
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
& neq(X3,nil) )
| ~ sP6(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54,sK55,sK56])],[f347,f350,f349,f348]) ).
fof(f352,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP6(X3,X2,X0,X1) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP6(X3,X2,sK57,X1) )
& sK57 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK57) ) ),
introduced(choice_axiom,[]) ).
fof(f353,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP6(X3,X2,sK57,X1) )
& sK57 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(sK58,nil) )
| sP6(X3,X2,sK57,sK58) )
& sK57 = X2
& sK58 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK58) ) ),
introduced(choice_axiom,[]) ).
fof(f354,plain,
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(sK58,nil) )
| sP6(X3,X2,sK57,sK58) )
& sK57 = X2
& sK58 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(sK58,nil) )
| sP6(X3,sK59,sK57,sK58) )
& sK57 = sK59
& sK58 = X3
& ssList(X3) )
& ssList(sK59) ) ),
introduced(choice_axiom,[]) ).
fof(f355,plain,
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(sK58,nil) )
| sP6(X3,sK59,sK57,sK58) )
& sK57 = sK59
& sK58 = X3
& ssList(X3) )
=> ( ( ( ~ neq(sK60,nil)
& neq(sK58,nil) )
| sP6(sK60,sK59,sK57,sK58) )
& sK57 = sK59
& sK58 = sK60
& ssList(sK60) ) ),
introduced(choice_axiom,[]) ).
fof(f356,plain,
( ( ( ~ neq(sK60,nil)
& neq(sK58,nil) )
| sP6(sK60,sK59,sK57,sK58) )
& sK57 = sK59
& sK58 = sK60
& ssList(sK60)
& ssList(sK59)
& ssList(sK58)
& ssList(sK57) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK57,sK58,sK59,sK60])],[f234,f355,f354,f353,f352]) ).
fof(f368,plain,
! [X0,X1] :
( singletonP(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f247]) ).
fof(f447,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f448,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f449,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f480,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f39]) ).
fof(f542,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f202]) ).
fof(f557,plain,
! [X2,X3,X10,X0,X1,X8,X9] :
( ~ neq(X9,nil)
| app(X8,X10) != X2
| app(app(X8,X9),X10) != X3
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f351]) ).
fof(f558,plain,
! [X2,X3,X0,X1] :
( ssItem(sK54(X0,X1))
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f351]) ).
fof(f559,plain,
! [X2,X3,X0,X1] :
( ssList(sK55(X0,X1))
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f351]) ).
fof(f560,plain,
! [X2,X3,X0,X1] :
( ssList(sK56(X0,X1))
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f351]) ).
fof(f561,plain,
! [X2,X3,X0,X1] :
( app(app(sK55(X0,X1),cons(sK54(X0,X1),nil)),sK56(X0,X1)) = X0
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f351]) ).
fof(f562,plain,
! [X2,X3,X0,X1] :
( app(sK55(X0,X1),sK56(X0,X1)) = X1
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f351]) ).
fof(f568,plain,
sK58 = sK60,
inference(cnf_transformation,[],[f356]) ).
fof(f569,plain,
sK57 = sK59,
inference(cnf_transformation,[],[f356]) ).
fof(f570,plain,
( neq(sK58,nil)
| sP6(sK60,sK59,sK57,sK58) ),
inference(cnf_transformation,[],[f356]) ).
fof(f571,plain,
( ~ neq(sK60,nil)
| sP6(sK60,sK59,sK57,sK58) ),
inference(cnf_transformation,[],[f356]) ).
fof(f572,plain,
( ~ neq(sK60,nil)
| sP6(sK60,sK59,sK59,sK60) ),
inference(definition_unfolding,[],[f571,f569,f568]) ).
fof(f573,plain,
( neq(sK60,nil)
| sP6(sK60,sK59,sK59,sK60) ),
inference(definition_unfolding,[],[f570,f568,f569,f568]) ).
fof(f578,plain,
! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(equality_resolution,[],[f368]) ).
fof(f603,plain,
! [X3,X10,X0,X1,X8,X9] :
( ~ neq(X9,nil)
| app(app(X8,X9),X10) != X3
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ sP6(X0,X1,app(X8,X10),X3) ),
inference(equality_resolution,[],[f557]) ).
fof(f604,plain,
! [X10,X0,X1,X8,X9] :
( ~ neq(X9,nil)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ sP6(X0,X1,app(X8,X10),app(app(X8,X9),X10)) ),
inference(equality_resolution,[],[f603]) ).
cnf(c_58,plain,
( ~ ssList(cons(X0,nil))
| ~ ssItem(X0)
| singletonP(cons(X0,nil)) ),
inference(cnf_transformation,[],[f578]) ).
cnf(c_138,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f447]) ).
cnf(c_140,plain,
( ~ ssItem(X0)
| ~ ssList(X1)
| ssList(cons(X0,X1)) ),
inference(cnf_transformation,[],[f448]) ).
cnf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f449]) ).
cnf(c_172,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f480]) ).
cnf(c_232,plain,
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f542]) ).
cnf(c_247,plain,
( ~ sP6(X0,X1,X2,X3)
| app(sK55(X0,X1),sK56(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f562]) ).
cnf(c_248,plain,
( ~ sP6(X0,X1,X2,X3)
| app(app(sK55(X0,X1),cons(sK54(X0,X1),nil)),sK56(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f561]) ).
cnf(c_249,plain,
( ~ sP6(X0,X1,X2,X3)
| ssList(sK56(X0,X1)) ),
inference(cnf_transformation,[],[f560]) ).
cnf(c_250,plain,
( ~ sP6(X0,X1,X2,X3)
| ssList(sK55(X0,X1)) ),
inference(cnf_transformation,[],[f559]) ).
cnf(c_251,plain,
( ~ sP6(X0,X1,X2,X3)
| ssItem(sK54(X0,X1)) ),
inference(cnf_transformation,[],[f558]) ).
cnf(c_252,plain,
( ~ sP6(X0,X1,app(X2,X3),app(app(X2,X4),X3))
| ~ neq(X4,nil)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f604]) ).
cnf(c_254,negated_conjecture,
( ~ neq(sK60,nil)
| sP6(sK60,sK59,sK59,sK60) ),
inference(cnf_transformation,[],[f572]) ).
cnf(c_255,negated_conjecture,
( sP6(sK60,sK59,sK59,sK60)
| neq(sK60,nil) ),
inference(cnf_transformation,[],[f573]) ).
cnf(c_378,negated_conjecture,
sP6(sK60,sK59,sK59,sK60),
inference(global_subsumption_just,[status(thm)],[c_255,c_255,c_254]) ).
cnf(c_380,negated_conjecture,
sP6(sK60,sK59,sK59,sK60),
inference(global_subsumption_just,[status(thm)],[c_254,c_378]) ).
cnf(c_3298,plain,
( X0 != sK60
| X1 != sK59
| X2 != sK59
| X3 != sK60
| ssItem(sK54(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_251,c_380]) ).
cnf(c_3299,plain,
ssItem(sK54(sK60,sK59)),
inference(unflattening,[status(thm)],[c_3298]) ).
cnf(c_3303,plain,
( X0 != sK60
| X1 != sK59
| X2 != sK59
| X3 != sK60
| ssList(sK55(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_250,c_380]) ).
cnf(c_3304,plain,
ssList(sK55(sK60,sK59)),
inference(unflattening,[status(thm)],[c_3303]) ).
cnf(c_3308,plain,
( X0 != sK60
| X1 != sK59
| X2 != sK59
| X3 != sK60
| ssList(sK56(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_249,c_380]) ).
cnf(c_3309,plain,
ssList(sK56(sK60,sK59)),
inference(unflattening,[status(thm)],[c_3308]) ).
cnf(c_3313,plain,
( X0 != sK60
| X1 != sK59
| X2 != sK59
| X3 != sK60
| app(app(sK55(X0,X1),cons(sK54(X0,X1),nil)),sK56(X0,X1)) = X0 ),
inference(resolution_lifted,[status(thm)],[c_248,c_380]) ).
cnf(c_3314,plain,
app(app(sK55(sK60,sK59),cons(sK54(sK60,sK59),nil)),sK56(sK60,sK59)) = sK60,
inference(unflattening,[status(thm)],[c_3313]) ).
cnf(c_3318,plain,
( X0 != sK60
| X1 != sK59
| X2 != sK59
| X3 != sK60
| app(sK55(X0,X1),sK56(X0,X1)) = X1 ),
inference(resolution_lifted,[status(thm)],[c_247,c_380]) ).
cnf(c_3319,plain,
app(sK55(sK60,sK59),sK56(sK60,sK59)) = sK59,
inference(unflattening,[status(thm)],[c_3318]) ).
cnf(c_3338,plain,
( app(app(X0,X1),X2) != sK60
| app(X0,X2) != sK59
| X3 != sK60
| X4 != sK59
| ~ neq(X1,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(resolution_lifted,[status(thm)],[c_252,c_380]) ).
cnf(c_3339,plain,
( app(app(X0,X1),X2) != sK60
| app(X0,X2) != sK59
| ~ neq(X1,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(unflattening,[status(thm)],[c_3338]) ).
cnf(c_3382,plain,
( app(app(X0,X1),X2) != sK60
| app(X0,X2) != sK59
| X1 != X3
| X4 != nil
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| X3 = X4 ),
inference(resolution_lifted,[status(thm)],[c_138,c_3339]) ).
cnf(c_3383,plain,
( app(app(X0,X1),X2) != sK60
| app(X0,X2) != sK59
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(nil)
| X1 = nil ),
inference(unflattening,[status(thm)],[c_3382]) ).
cnf(c_3385,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X2) != sK59
| app(app(X0,X1),X2) != sK60
| X1 = nil ),
inference(global_subsumption_just,[status(thm)],[c_3383,c_141,c_3383]) ).
cnf(c_3386,plain,
( app(app(X0,X1),X2) != sK60
| app(X0,X2) != sK59
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| X1 = nil ),
inference(renaming,[status(thm)],[c_3385]) ).
cnf(c_12035,plain,
( app(sK55(sK60,sK59),sK56(sK60,sK59)) != sK59
| ~ ssList(cons(sK54(sK60,sK59),nil))
| ~ ssList(sK55(sK60,sK59))
| ~ ssList(sK56(sK60,sK59))
| cons(sK54(sK60,sK59),nil) = nil ),
inference(superposition,[status(thm)],[c_3314,c_3386]) ).
cnf(c_12044,plain,
( ~ ssList(cons(sK54(sK60,sK59),nil))
| cons(sK54(sK60,sK59),nil) = nil ),
inference(forward_subsumption_resolution,[status(thm)],[c_12035,c_3309,c_3304,c_3319]) ).
cnf(c_12527,plain,
app(sK55(sK60,sK59),nil) = sK55(sK60,sK59),
inference(superposition,[status(thm)],[c_3304,c_232]) ).
cnf(c_12589,plain,
( ~ ssItem(sK54(sK60,sK59))
| ~ ssList(nil)
| cons(sK54(sK60,sK59),nil) = nil ),
inference(superposition,[status(thm)],[c_140,c_12044]) ).
cnf(c_12593,plain,
cons(sK54(sK60,sK59),nil) = nil,
inference(forward_subsumption_resolution,[status(thm)],[c_12589,c_141,c_3299]) ).
cnf(c_12602,plain,
app(app(sK55(sK60,sK59),nil),sK56(sK60,sK59)) = sK60,
inference(demodulation,[status(thm)],[c_3314,c_12593]) ).
cnf(c_12603,plain,
sK60 = sK59,
inference(light_normalisation,[status(thm)],[c_12602,c_3319,c_12527]) ).
cnf(c_12615,plain,
ssItem(sK54(sK60,sK60)),
inference(demodulation,[status(thm)],[c_3299,c_12603]) ).
cnf(c_12689,plain,
cons(sK54(sK60,sK60),nil) = nil,
inference(light_normalisation,[status(thm)],[c_12593,c_12603]) ).
cnf(c_12695,plain,
( ~ ssItem(sK54(sK60,sK60))
| ~ ssList(nil)
| singletonP(cons(sK54(sK60,sK60),nil)) ),
inference(superposition,[status(thm)],[c_12689,c_58]) ).
cnf(c_12697,plain,
( ~ ssItem(sK54(sK60,sK60))
| ~ ssList(nil)
| singletonP(nil) ),
inference(light_normalisation,[status(thm)],[c_12695,c_12689]) ).
cnf(c_12698,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_12697,c_172,c_141,c_12615]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWC003+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.11 % Command : run_iprover %s %d THM
% 0.10/0.32 % Computer : n004.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Thu May 2 23:16:48 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.95/1.13 % SZS status Started for theBenchmark.p
% 3.95/1.13 % SZS status Theorem for theBenchmark.p
% 3.95/1.13
% 3.95/1.13 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.95/1.13
% 3.95/1.13 ------ iProver source info
% 3.95/1.13
% 3.95/1.13 git: date: 2024-05-02 19:28:25 +0000
% 3.95/1.13 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.95/1.13 git: non_committed_changes: false
% 3.95/1.13
% 3.95/1.13 ------ Parsing...
% 3.95/1.13 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.95/1.13
% 3.95/1.13 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 6 0s sf_e pe_s pe_e
% 3.95/1.13
% 3.95/1.13 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.95/1.13
% 3.95/1.13 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.95/1.13 ------ Proving...
% 3.95/1.13 ------ Problem Properties
% 3.95/1.13
% 3.95/1.13
% 3.95/1.13 clauses 191
% 3.95/1.13 conjectures 2
% 3.95/1.13 EPR 52
% 3.95/1.13 Horn 123
% 3.95/1.13 unary 24
% 3.95/1.13 binary 40
% 3.95/1.13 lits 640
% 3.95/1.13 lits eq 87
% 3.95/1.13 fd_pure 0
% 3.95/1.13 fd_pseudo 0
% 3.95/1.13 fd_cond 23
% 3.95/1.13 fd_pseudo_cond 14
% 3.95/1.13 AC symbols 0
% 3.95/1.13
% 3.95/1.13 ------ Schedule dynamic 5 is on
% 3.95/1.13
% 3.95/1.13 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.95/1.13
% 3.95/1.13
% 3.95/1.13 ------
% 3.95/1.13 Current options:
% 3.95/1.13 ------
% 3.95/1.13
% 3.95/1.13
% 3.95/1.13
% 3.95/1.13
% 3.95/1.13 ------ Proving...
% 3.95/1.13
% 3.95/1.13
% 3.95/1.13 % SZS status Theorem for theBenchmark.p
% 3.95/1.13
% 3.95/1.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.95/1.13
% 3.95/1.13
%------------------------------------------------------------------------------