TSTP Solution File: SWC412+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWC412+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n031.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 20:43:14 EDT 2023
% Result : Theorem 55.20s 8.23s
% Output : CNFRefutation 55.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 22
% Syntax : Number of formulae : 105 ( 13 unt; 0 def)
% Number of atoms : 619 ( 190 equ)
% Maximal formula atoms : 30 ( 5 avg)
% Number of connectives : 754 ( 240 ~; 233 |; 229 &)
% ( 2 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-2 aty)
% Number of variables : 377 ( 12 sgn; 180 !; 135 ?)
% 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(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f45,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ! [X16] :
( ssItem(X16)
=> ! [X17] :
( ssItem(X17)
=> ! [X18] :
( app(app(cons(X17,nil),X18),cons(X16,nil)) = X0
| app(app(cons(X16,nil),X18),cons(X17,nil)) != X1
| ~ ssList(X18) ) ) )
| ! [X13] :
( ssItem(X13)
=> ! [X14] :
( ssItem(X14)
=> ! [X15] :
( ssList(X15)
=> app(app(cons(X13,nil),cons(X14,nil)),X15) != X1 ) ) )
| ? [X10] :
( ? [X11] :
( ? [X12] :
( app(app(cons(X10,nil),X12),cons(X11,nil)) = X3
& app(app(cons(X11,nil),X12),cons(X10,nil)) != X2
& ssList(X12) )
& ssItem(X11) )
& ssItem(X10) ) )
& ( ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> app(app(cons(X7,nil),cons(X8,nil)),X9) != X1 ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(cons(X4,nil),cons(X5,nil)),X6) = X3
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) ) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ! [X16] :
( ssItem(X16)
=> ! [X17] :
( ssItem(X17)
=> ! [X18] :
( app(app(cons(X17,nil),X18),cons(X16,nil)) = X0
| app(app(cons(X16,nil),X18),cons(X17,nil)) != X1
| ~ ssList(X18) ) ) )
| ! [X13] :
( ssItem(X13)
=> ! [X14] :
( ssItem(X14)
=> ! [X15] :
( ssList(X15)
=> app(app(cons(X13,nil),cons(X14,nil)),X15) != X1 ) ) )
| ? [X10] :
( ? [X11] :
( ? [X12] :
( app(app(cons(X10,nil),X12),cons(X11,nil)) = X3
& app(app(cons(X11,nil),X12),cons(X10,nil)) != X2
& ssList(X12) )
& ssItem(X11) )
& ssItem(X10) ) )
& ( ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> app(app(cons(X7,nil),cons(X8,nil)),X9) != X1 ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(cons(X4,nil),cons(X5,nil)),X6) = X3
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) ) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssItem(X5)
=> ! [X6] :
( app(app(cons(X5,nil),X6),cons(X4,nil)) = X0
| app(app(cons(X4,nil),X6),cons(X5,nil)) != X1
| ~ ssList(X6) ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> app(app(cons(X7,nil),cons(X8,nil)),X9) != X1 ) ) )
| ? [X10] :
( ? [X11] :
( ? [X12] :
( app(app(cons(X10,nil),X12),cons(X11,nil)) = X3
& app(app(cons(X11,nil),X12),cons(X10,nil)) != X2
& ssList(X12) )
& ssItem(X11) )
& ssItem(X10) ) )
& ( ! [X13] :
( ssItem(X13)
=> ! [X14] :
( ssItem(X14)
=> ! [X15] :
( ssList(X15)
=> app(app(cons(X13,nil),cons(X14,nil)),X15) != X1 ) ) )
| ? [X16] :
( ? [X17] :
( ? [X18] :
( app(app(cons(X16,nil),cons(X17,nil)),X18) = X3
& ssList(X18) )
& ssItem(X17) )
& ssItem(X16) ) ) )
| X0 != X2
| X1 != X3
| ~ ssList(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(f158,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(cons(X5,nil),X6),cons(X4,nil)) != X0
& app(app(cons(X4,nil),X6),cons(X5,nil)) = X1
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(cons(X7,nil),cons(X8,nil)),X9) = X1
& ssList(X9) )
& ssItem(X8) )
& ssItem(X7) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( app(app(cons(X10,nil),X12),cons(X11,nil)) != X3
| app(app(cons(X11,nil),X12),cons(X10,nil)) = X2
| ~ ssList(X12) )
| ~ ssItem(X11) )
| ~ ssItem(X10) ) )
| ( ? [X13] :
( ? [X14] :
( ? [X15] :
( app(app(cons(X13,nil),cons(X14,nil)),X15) = X1
& ssList(X15) )
& ssItem(X14) )
& ssItem(X13) )
& ! [X16] :
( ! [X17] :
( ! [X18] :
( app(app(cons(X16,nil),cons(X17,nil)),X18) != X3
| ~ ssList(X18) )
| ~ ssItem(X17) )
| ~ ssItem(X16) ) ) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f232,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(cons(X5,nil),X6),cons(X4,nil)) != X0
& app(app(cons(X4,nil),X6),cons(X5,nil)) = X1
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
| ~ sP6(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f233,plain,
! [X1,X0,X3,X2] :
( ( sP6(X0,X1)
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(cons(X7,nil),cons(X8,nil)),X9) = X1
& ssList(X9) )
& ssItem(X8) )
& ssItem(X7) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( app(app(cons(X10,nil),X12),cons(X11,nil)) != X3
| app(app(cons(X11,nil),X12),cons(X10,nil)) = X2
| ~ ssList(X12) )
| ~ ssItem(X11) )
| ~ ssItem(X10) ) )
| ~ sP7(X1,X0,X3,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f234,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( sP7(X1,X0,X3,X2)
| ( ? [X13] :
( ? [X14] :
( ? [X15] :
( app(app(cons(X13,nil),cons(X14,nil)),X15) = X1
& ssList(X15) )
& ssItem(X14) )
& ssItem(X13) )
& ! [X16] :
( ! [X17] :
( ! [X18] :
( app(app(cons(X16,nil),cons(X17,nil)),X18) != X3
| ~ ssList(X18) )
| ~ ssItem(X17) )
| ~ ssItem(X16) ) ) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f222,f233,f232]) ).
fof(f248,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(f249,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,[],[f248]) ).
fof(f250,plain,
! [X0,X1] :
( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
=> ( app(X1,sK13(X0,X1)) = X0
& ssList(sK13(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f251,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ( app(X1,sK13(X0,X1)) = X0
& ssList(sK13(X0,X1)) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f249,f250]) ).
fof(f346,plain,
! [X1,X0,X3,X2] :
( ( sP6(X0,X1)
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(cons(X7,nil),cons(X8,nil)),X9) = X1
& ssList(X9) )
& ssItem(X8) )
& ssItem(X7) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( app(app(cons(X10,nil),X12),cons(X11,nil)) != X3
| app(app(cons(X11,nil),X12),cons(X10,nil)) = X2
| ~ ssList(X12) )
| ~ ssItem(X11) )
| ~ ssItem(X10) ) )
| ~ sP7(X1,X0,X3,X2) ),
inference(nnf_transformation,[],[f233]) ).
fof(f347,plain,
! [X0,X1,X2,X3] :
( ( sP6(X1,X0)
& ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(cons(X4,nil),cons(X5,nil)),X6) = X0
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ! [X7] :
( ! [X8] :
( ! [X9] :
( app(app(cons(X7,nil),X9),cons(X8,nil)) != X2
| app(app(cons(X8,nil),X9),cons(X7,nil)) = X3
| ~ ssList(X9) )
| ~ ssItem(X8) )
| ~ ssItem(X7) ) )
| ~ sP7(X0,X1,X2,X3) ),
inference(rectify,[],[f346]) ).
fof(f348,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(cons(X4,nil),cons(X5,nil)),X6) = X0
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
=> ( ? [X5] :
( ? [X6] :
( app(app(cons(sK55(X0),nil),cons(X5,nil)),X6) = X0
& ssList(X6) )
& ssItem(X5) )
& ssItem(sK55(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f349,plain,
! [X0] :
( ? [X5] :
( ? [X6] :
( app(app(cons(sK55(X0),nil),cons(X5,nil)),X6) = X0
& ssList(X6) )
& ssItem(X5) )
=> ( ? [X6] :
( app(app(cons(sK55(X0),nil),cons(sK56(X0),nil)),X6) = X0
& ssList(X6) )
& ssItem(sK56(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f350,plain,
! [X0] :
( ? [X6] :
( app(app(cons(sK55(X0),nil),cons(sK56(X0),nil)),X6) = X0
& ssList(X6) )
=> ( app(app(cons(sK55(X0),nil),cons(sK56(X0),nil)),sK57(X0)) = X0
& ssList(sK57(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f351,plain,
! [X0,X1,X2,X3] :
( ( sP6(X1,X0)
& app(app(cons(sK55(X0),nil),cons(sK56(X0),nil)),sK57(X0)) = X0
& ssList(sK57(X0))
& ssItem(sK56(X0))
& ssItem(sK55(X0))
& ! [X7] :
( ! [X8] :
( ! [X9] :
( app(app(cons(X7,nil),X9),cons(X8,nil)) != X2
| app(app(cons(X8,nil),X9),cons(X7,nil)) = X3
| ~ ssList(X9) )
| ~ ssItem(X8) )
| ~ ssItem(X7) ) )
| ~ sP7(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK55,sK56,sK57])],[f347,f350,f349,f348]) ).
fof(f352,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(cons(X5,nil),X6),cons(X4,nil)) != X0
& app(app(cons(X4,nil),X6),cons(X5,nil)) = X1
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
| ~ sP6(X0,X1) ),
inference(nnf_transformation,[],[f232]) ).
fof(f353,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( app(app(cons(X3,nil),X4),cons(X2,nil)) != X0
& app(app(cons(X2,nil),X4),cons(X3,nil)) = X1
& ssList(X4) )
& ssItem(X3) )
& ssItem(X2) )
| ~ sP6(X0,X1) ),
inference(rectify,[],[f352]) ).
fof(f354,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( app(app(cons(X3,nil),X4),cons(X2,nil)) != X0
& app(app(cons(X2,nil),X4),cons(X3,nil)) = X1
& ssList(X4) )
& ssItem(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( app(app(cons(X3,nil),X4),cons(sK58(X0,X1),nil)) != X0
& app(app(cons(sK58(X0,X1),nil),X4),cons(X3,nil)) = X1
& ssList(X4) )
& ssItem(X3) )
& ssItem(sK58(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f355,plain,
! [X0,X1] :
( ? [X3] :
( ? [X4] :
( app(app(cons(X3,nil),X4),cons(sK58(X0,X1),nil)) != X0
& app(app(cons(sK58(X0,X1),nil),X4),cons(X3,nil)) = X1
& ssList(X4) )
& ssItem(X3) )
=> ( ? [X4] :
( app(app(cons(sK59(X0,X1),nil),X4),cons(sK58(X0,X1),nil)) != X0
& app(app(cons(sK58(X0,X1),nil),X4),cons(sK59(X0,X1),nil)) = X1
& ssList(X4) )
& ssItem(sK59(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f356,plain,
! [X0,X1] :
( ? [X4] :
( app(app(cons(sK59(X0,X1),nil),X4),cons(sK58(X0,X1),nil)) != X0
& app(app(cons(sK58(X0,X1),nil),X4),cons(sK59(X0,X1),nil)) = X1
& ssList(X4) )
=> ( app(app(cons(sK59(X0,X1),nil),sK60(X0,X1)),cons(sK58(X0,X1),nil)) != X0
& app(app(cons(sK58(X0,X1),nil),sK60(X0,X1)),cons(sK59(X0,X1),nil)) = X1
& ssList(sK60(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f357,plain,
! [X0,X1] :
( ( app(app(cons(sK59(X0,X1),nil),sK60(X0,X1)),cons(sK58(X0,X1),nil)) != X0
& app(app(cons(sK58(X0,X1),nil),sK60(X0,X1)),cons(sK59(X0,X1),nil)) = X1
& ssList(sK60(X0,X1))
& ssItem(sK59(X0,X1))
& ssItem(sK58(X0,X1)) )
| ~ sP6(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK58,sK59,sK60])],[f353,f356,f355,f354]) ).
fof(f358,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( sP7(X1,X0,X3,X2)
| ( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(cons(X4,nil),cons(X5,nil)),X6) = X1
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ! [X7] :
( ! [X8] :
( ! [X9] :
( app(app(cons(X7,nil),cons(X8,nil)),X9) != X3
| ~ ssList(X9) )
| ~ ssItem(X8) )
| ~ ssItem(X7) ) ) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(rectify,[],[f234]) ).
fof(f359,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( sP7(X1,X0,X3,X2)
| ( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(cons(X4,nil),cons(X5,nil)),X6) = X1
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ! [X7] :
( ! [X8] :
( ! [X9] :
( app(app(cons(X7,nil),cons(X8,nil)),X9) != X3
| ~ ssList(X9) )
| ~ ssItem(X8) )
| ~ ssItem(X7) ) ) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( sP7(X1,sK61,X3,X2)
| ( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(cons(X4,nil),cons(X5,nil)),X6) = X1
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ! [X7] :
( ! [X8] :
( ! [X9] :
( app(app(cons(X7,nil),cons(X8,nil)),X9) != X3
| ~ ssList(X9) )
| ~ ssItem(X8) )
| ~ ssItem(X7) ) ) )
& sK61 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK61) ) ),
introduced(choice_axiom,[]) ).
fof(f360,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( sP7(X1,sK61,X3,X2)
| ( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(cons(X4,nil),cons(X5,nil)),X6) = X1
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ! [X7] :
( ! [X8] :
( ! [X9] :
( app(app(cons(X7,nil),cons(X8,nil)),X9) != X3
| ~ ssList(X9) )
| ~ ssItem(X8) )
| ~ ssItem(X7) ) ) )
& sK61 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( sP7(sK62,sK61,X3,X2)
| ( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(cons(X4,nil),cons(X5,nil)),X6) = sK62
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ! [X7] :
( ! [X8] :
( ! [X9] :
( app(app(cons(X7,nil),cons(X8,nil)),X9) != X3
| ~ ssList(X9) )
| ~ ssItem(X8) )
| ~ ssItem(X7) ) ) )
& sK61 = X2
& sK62 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK62) ) ),
introduced(choice_axiom,[]) ).
fof(f361,plain,
( ? [X2] :
( ? [X3] :
( ( sP7(sK62,sK61,X3,X2)
| ( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(cons(X4,nil),cons(X5,nil)),X6) = sK62
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ! [X7] :
( ! [X8] :
( ! [X9] :
( app(app(cons(X7,nil),cons(X8,nil)),X9) != X3
| ~ ssList(X9) )
| ~ ssItem(X8) )
| ~ ssItem(X7) ) ) )
& sK61 = X2
& sK62 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( sP7(sK62,sK61,X3,sK63)
| ( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(cons(X4,nil),cons(X5,nil)),X6) = sK62
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ! [X7] :
( ! [X8] :
( ! [X9] :
( app(app(cons(X7,nil),cons(X8,nil)),X9) != X3
| ~ ssList(X9) )
| ~ ssItem(X8) )
| ~ ssItem(X7) ) ) )
& sK61 = sK63
& sK62 = X3
& ssList(X3) )
& ssList(sK63) ) ),
introduced(choice_axiom,[]) ).
fof(f362,plain,
( ? [X3] :
( ( sP7(sK62,sK61,X3,sK63)
| ( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(cons(X4,nil),cons(X5,nil)),X6) = sK62
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ! [X7] :
( ! [X8] :
( ! [X9] :
( app(app(cons(X7,nil),cons(X8,nil)),X9) != X3
| ~ ssList(X9) )
| ~ ssItem(X8) )
| ~ ssItem(X7) ) ) )
& sK61 = sK63
& sK62 = X3
& ssList(X3) )
=> ( ( sP7(sK62,sK61,sK64,sK63)
| ( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(cons(X4,nil),cons(X5,nil)),X6) = sK62
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ! [X7] :
( ! [X8] :
( ! [X9] :
( app(app(cons(X7,nil),cons(X8,nil)),X9) != sK64
| ~ ssList(X9) )
| ~ ssItem(X8) )
| ~ ssItem(X7) ) ) )
& sK61 = sK63
& sK62 = sK64
& ssList(sK64) ) ),
introduced(choice_axiom,[]) ).
fof(f363,plain,
( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(cons(X4,nil),cons(X5,nil)),X6) = sK62
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
=> ( ? [X5] :
( ? [X6] :
( sK62 = app(app(cons(sK65,nil),cons(X5,nil)),X6)
& ssList(X6) )
& ssItem(X5) )
& ssItem(sK65) ) ),
introduced(choice_axiom,[]) ).
fof(f364,plain,
( ? [X5] :
( ? [X6] :
( sK62 = app(app(cons(sK65,nil),cons(X5,nil)),X6)
& ssList(X6) )
& ssItem(X5) )
=> ( ? [X6] :
( sK62 = app(app(cons(sK65,nil),cons(sK66,nil)),X6)
& ssList(X6) )
& ssItem(sK66) ) ),
introduced(choice_axiom,[]) ).
fof(f365,plain,
( ? [X6] :
( sK62 = app(app(cons(sK65,nil),cons(sK66,nil)),X6)
& ssList(X6) )
=> ( sK62 = app(app(cons(sK65,nil),cons(sK66,nil)),sK67)
& ssList(sK67) ) ),
introduced(choice_axiom,[]) ).
fof(f366,plain,
( ( sP7(sK62,sK61,sK64,sK63)
| ( sK62 = app(app(cons(sK65,nil),cons(sK66,nil)),sK67)
& ssList(sK67)
& ssItem(sK66)
& ssItem(sK65)
& ! [X7] :
( ! [X8] :
( ! [X9] :
( app(app(cons(X7,nil),cons(X8,nil)),X9) != sK64
| ~ ssList(X9) )
| ~ ssItem(X8) )
| ~ ssItem(X7) ) ) )
& sK61 = sK63
& sK62 = sK64
& ssList(sK64)
& ssList(sK63)
& ssList(sK62)
& ssList(sK61) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK61,sK62,sK63,sK64,sK65,sK66,sK67])],[f358,f365,f364,f363,f362,f361,f360,f359]) ).
fof(f380,plain,
! [X0,X1] :
( app(X1,sK13(X0,X1)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f251]) ).
fof(f459,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f498,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f566,plain,
! [X2,X3,X0,X1,X8,X9,X7] :
( app(app(cons(X7,nil),X9),cons(X8,nil)) != X2
| app(app(cons(X8,nil),X9),cons(X7,nil)) = X3
| ~ ssList(X9)
| ~ ssItem(X8)
| ~ ssItem(X7)
| ~ sP7(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f351]) ).
fof(f570,plain,
! [X2,X3,X0,X1] :
( app(app(cons(sK55(X0),nil),cons(sK56(X0),nil)),sK57(X0)) = X0
| ~ sP7(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f351]) ).
fof(f571,plain,
! [X2,X3,X0,X1] :
( sP6(X1,X0)
| ~ sP7(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f351]) ).
fof(f572,plain,
! [X0,X1] :
( ssItem(sK58(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f357]) ).
fof(f573,plain,
! [X0,X1] :
( ssItem(sK59(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f357]) ).
fof(f574,plain,
! [X0,X1] :
( ssList(sK60(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f357]) ).
fof(f575,plain,
! [X0,X1] :
( app(app(cons(sK58(X0,X1),nil),sK60(X0,X1)),cons(sK59(X0,X1),nil)) = X1
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f357]) ).
fof(f576,plain,
! [X0,X1] :
( app(app(cons(sK59(X0,X1),nil),sK60(X0,X1)),cons(sK58(X0,X1),nil)) != X0
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f357]) ).
fof(f577,plain,
ssList(sK61),
inference(cnf_transformation,[],[f366]) ).
fof(f581,plain,
sK62 = sK64,
inference(cnf_transformation,[],[f366]) ).
fof(f582,plain,
sK61 = sK63,
inference(cnf_transformation,[],[f366]) ).
fof(f583,plain,
! [X8,X9,X7] :
( sP7(sK62,sK61,sK64,sK63)
| app(app(cons(X7,nil),cons(X8,nil)),X9) != sK64
| ~ ssList(X9)
| ~ ssItem(X8)
| ~ ssItem(X7) ),
inference(cnf_transformation,[],[f366]) ).
fof(f584,plain,
( sP7(sK62,sK61,sK64,sK63)
| ssItem(sK65) ),
inference(cnf_transformation,[],[f366]) ).
fof(f585,plain,
( sP7(sK62,sK61,sK64,sK63)
| ssItem(sK66) ),
inference(cnf_transformation,[],[f366]) ).
fof(f586,plain,
( sP7(sK62,sK61,sK64,sK63)
| ssList(sK67) ),
inference(cnf_transformation,[],[f366]) ).
fof(f587,plain,
( sP7(sK62,sK61,sK64,sK63)
| sK62 = app(app(cons(sK65,nil),cons(sK66,nil)),sK67) ),
inference(cnf_transformation,[],[f366]) ).
fof(f588,plain,
( sP7(sK64,sK63,sK64,sK63)
| sK64 = app(app(cons(sK65,nil),cons(sK66,nil)),sK67) ),
inference(definition_unfolding,[],[f587,f581,f582,f581]) ).
fof(f589,plain,
( sP7(sK64,sK63,sK64,sK63)
| ssList(sK67) ),
inference(definition_unfolding,[],[f586,f581,f582]) ).
fof(f590,plain,
( sP7(sK64,sK63,sK64,sK63)
| ssItem(sK66) ),
inference(definition_unfolding,[],[f585,f581,f582]) ).
fof(f591,plain,
( sP7(sK64,sK63,sK64,sK63)
| ssItem(sK65) ),
inference(definition_unfolding,[],[f584,f581,f582]) ).
fof(f592,plain,
! [X8,X9,X7] :
( sP7(sK64,sK63,sK64,sK63)
| app(app(cons(X7,nil),cons(X8,nil)),X9) != sK64
| ~ ssList(X9)
| ~ ssItem(X8)
| ~ ssItem(X7) ),
inference(definition_unfolding,[],[f583,f581,f582]) ).
fof(f594,plain,
ssList(sK63),
inference(definition_unfolding,[],[f577,f582]) ).
fof(f622,plain,
! [X3,X0,X1,X8,X9,X7] :
( app(app(cons(X8,nil),X9),cons(X7,nil)) = X3
| ~ ssList(X9)
| ~ ssItem(X8)
| ~ ssItem(X7)
| ~ sP7(X0,X1,app(app(cons(X7,nil),X9),cons(X8,nil)),X3) ),
inference(equality_resolution,[],[f566]) ).
cnf(c_62,plain,
( ~ frontsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X1,sK13(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f380]) ).
cnf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f459]) ).
cnf(c_180,plain,
( ~ ssList(X0)
| frontsegP(X0,nil) ),
inference(cnf_transformation,[],[f498]) ).
cnf(c_246,plain,
( ~ sP7(X0,X1,X2,X3)
| sP6(X1,X0) ),
inference(cnf_transformation,[],[f571]) ).
cnf(c_247,plain,
( ~ sP7(X0,X1,X2,X3)
| app(app(cons(sK55(X0),nil),cons(sK56(X0),nil)),sK57(X0)) = X0 ),
inference(cnf_transformation,[],[f570]) ).
cnf(c_251,plain,
( ~ sP7(X0,X1,app(app(cons(X2,nil),X3),cons(X4,nil)),X5)
| ~ ssItem(X2)
| ~ ssItem(X4)
| ~ ssList(X3)
| app(app(cons(X4,nil),X3),cons(X2,nil)) = X5 ),
inference(cnf_transformation,[],[f622]) ).
cnf(c_252,plain,
( app(app(cons(sK59(X0,X1),nil),sK60(X0,X1)),cons(sK58(X0,X1),nil)) != X0
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f576]) ).
cnf(c_253,plain,
( ~ sP6(X0,X1)
| app(app(cons(sK58(X0,X1),nil),sK60(X0,X1)),cons(sK59(X0,X1),nil)) = X1 ),
inference(cnf_transformation,[],[f575]) ).
cnf(c_254,plain,
( ~ sP6(X0,X1)
| ssList(sK60(X0,X1)) ),
inference(cnf_transformation,[],[f574]) ).
cnf(c_255,plain,
( ~ sP6(X0,X1)
| ssItem(sK59(X0,X1)) ),
inference(cnf_transformation,[],[f573]) ).
cnf(c_256,plain,
( ~ sP6(X0,X1)
| ssItem(sK58(X0,X1)) ),
inference(cnf_transformation,[],[f572]) ).
cnf(c_257,negated_conjecture,
( app(app(cons(sK65,nil),cons(sK66,nil)),sK67) = sK64
| sP7(sK64,sK63,sK64,sK63) ),
inference(cnf_transformation,[],[f588]) ).
cnf(c_258,negated_conjecture,
( sP7(sK64,sK63,sK64,sK63)
| ssList(sK67) ),
inference(cnf_transformation,[],[f589]) ).
cnf(c_259,negated_conjecture,
( sP7(sK64,sK63,sK64,sK63)
| ssItem(sK66) ),
inference(cnf_transformation,[],[f590]) ).
cnf(c_260,negated_conjecture,
( sP7(sK64,sK63,sK64,sK63)
| ssItem(sK65) ),
inference(cnf_transformation,[],[f591]) ).
cnf(c_261,negated_conjecture,
( app(app(cons(X0,nil),cons(X1,nil)),X2) != sK64
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sP7(sK64,sK63,sK64,sK63) ),
inference(cnf_transformation,[],[f592]) ).
cnf(c_265,negated_conjecture,
ssList(sK63),
inference(cnf_transformation,[],[f594]) ).
cnf(c_456,plain,
X0 = X0,
theory(equality) ).
cnf(c_482,plain,
( X0 != X1
| X2 != X3
| X4 != X5
| X6 != X7
| ~ sP7(X1,X3,X5,X7)
| sP7(X0,X2,X4,X6) ),
theory(equality) ).
cnf(c_549,plain,
( ~ sP7(sK64,sK63,sK64,sK63)
| sP6(sK63,sK64) ),
inference(instantiation,[status(thm)],[c_246]) ).
cnf(c_555,plain,
( ~ sP7(sK64,sK63,sK64,sK63)
| app(app(cons(sK55(sK64),nil),cons(sK56(sK64),nil)),sK57(sK64)) = sK64 ),
inference(instantiation,[status(thm)],[c_247]) ).
cnf(c_598,plain,
( X0 != sK64
| X1 != sK63
| X2 != sK64
| X3 != sK63
| ~ sP7(sK64,sK63,sK64,sK63)
| sP7(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_482]) ).
cnf(c_697,plain,
( ~ ssItem(sK65)
| ~ ssItem(sK66)
| ~ ssList(sK67)
| sP7(sK64,sK63,sK64,sK63) ),
inference(resolution,[status(thm)],[c_261,c_257]) ).
cnf(c_747,plain,
sP7(sK64,sK63,sK64,sK63),
inference(global_subsumption_just,[status(thm)],[c_697,c_260,c_259,c_258,c_697]) ).
cnf(c_773,plain,
( ~ sP6(sK63,sK64)
| app(app(cons(sK58(sK63,sK64),nil),sK60(sK63,sK64)),cons(sK59(sK63,sK64),nil)) = sK64 ),
inference(instantiation,[status(thm)],[c_253]) ).
cnf(c_774,plain,
( app(app(cons(sK59(sK63,sK64),nil),sK60(sK63,sK64)),cons(sK58(sK63,sK64),nil)) != sK63
| ~ sP6(sK63,sK64) ),
inference(instantiation,[status(thm)],[c_252]) ).
cnf(c_775,plain,
( ~ sP6(sK63,sK64)
| ssItem(sK58(sK63,sK64)) ),
inference(instantiation,[status(thm)],[c_256]) ).
cnf(c_776,plain,
( ~ sP6(sK63,sK64)
| ssItem(sK59(sK63,sK64)) ),
inference(instantiation,[status(thm)],[c_255]) ).
cnf(c_777,plain,
( ~ sP6(sK63,sK64)
| ssList(sK60(sK63,sK64)) ),
inference(instantiation,[status(thm)],[c_254]) ).
cnf(c_833,plain,
sK63 = sK63,
inference(instantiation,[status(thm)],[c_456]) ).
cnf(c_1723,plain,
( app(app(cons(sK58(sK63,sK64),nil),sK60(sK63,sK64)),cons(sK59(sK63,sK64),nil)) != sK64
| X0 != sK64
| X1 != sK63
| X2 != sK63
| ~ sP7(sK64,sK63,sK64,sK63)
| sP7(X0,X1,app(app(cons(sK58(sK63,sK64),nil),sK60(sK63,sK64)),cons(sK59(sK63,sK64),nil)),X2) ),
inference(instantiation,[status(thm)],[c_598]) ).
cnf(c_2556,plain,
( ~ ssList(sK63)
| frontsegP(sK63,nil) ),
inference(instantiation,[status(thm)],[c_180]) ).
cnf(c_7259,plain,
( app(app(cons(sK58(sK63,sK64),nil),sK60(sK63,sK64)),cons(sK59(sK63,sK64),nil)) != sK64
| app(app(cons(sK55(sK64),nil),cons(sK56(sK64),nil)),sK57(sK64)) != sK64
| X0 != sK63
| X1 != sK63
| ~ sP7(sK64,sK63,sK64,sK63)
| sP7(app(app(cons(sK55(sK64),nil),cons(sK56(sK64),nil)),sK57(sK64)),X0,app(app(cons(sK58(sK63,sK64),nil),sK60(sK63,sK64)),cons(sK59(sK63,sK64),nil)),X1) ),
inference(instantiation,[status(thm)],[c_1723]) ).
cnf(c_13371,plain,
( ~ sP7(app(app(cons(sK55(sK64),nil),cons(sK56(sK64),nil)),sK57(sK64)),X0,app(app(cons(sK58(sK63,sK64),nil),sK60(sK63,sK64)),cons(sK59(sK63,sK64),nil)),X1)
| ~ ssItem(sK59(sK63,sK64))
| ~ ssItem(sK58(sK63,sK64))
| ~ ssList(sK60(sK63,sK64))
| app(app(cons(sK59(sK63,sK64),nil),sK60(sK63,sK64)),cons(sK58(sK63,sK64),nil)) = X1 ),
inference(instantiation,[status(thm)],[c_251]) ).
cnf(c_24073,plain,
( ~ sP7(app(app(cons(sK55(sK64),nil),cons(sK56(sK64),nil)),sK57(sK64)),X0,app(app(cons(sK58(sK63,sK64),nil),sK60(sK63,sK64)),cons(sK59(sK63,sK64),nil)),sK63)
| ~ ssItem(sK59(sK63,sK64))
| ~ ssItem(sK58(sK63,sK64))
| ~ ssList(sK60(sK63,sK64))
| app(app(cons(sK59(sK63,sK64),nil),sK60(sK63,sK64)),cons(sK58(sK63,sK64),nil)) = sK63 ),
inference(instantiation,[status(thm)],[c_13371]) ).
cnf(c_26640,plain,
( app(app(cons(sK58(sK63,sK64),nil),sK60(sK63,sK64)),cons(sK59(sK63,sK64),nil)) != sK64
| app(app(cons(sK55(sK64),nil),cons(sK56(sK64),nil)),sK57(sK64)) != sK64
| X0 != sK63
| sK63 != sK63
| ~ sP7(sK64,sK63,sK64,sK63)
| sP7(app(app(cons(sK55(sK64),nil),cons(sK56(sK64),nil)),sK57(sK64)),X0,app(app(cons(sK58(sK63,sK64),nil),sK60(sK63,sK64)),cons(sK59(sK63,sK64),nil)),sK63) ),
inference(instantiation,[status(thm)],[c_7259]) ).
cnf(c_39906,plain,
( X0 != sK64
| X1 != sK63
| X2 != sK64
| X3 != sK63
| sP7(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c_482,c_747]) ).
cnf(c_39918,plain,
( X0 != sK63
| X1 != sK64
| X2 != sK63
| X3 != sK64
| sP6(X0,X1) ),
inference(resolution,[status(thm)],[c_39906,c_246]) ).
cnf(c_40122,plain,
X0 != sK63,
inference(global_subsumption_just,[status(thm)],[c_39918,c_549,c_555,c_747,c_777,c_776,c_775,c_774,c_773,c_833,c_24073,c_26640]) ).
cnf(c_40148,plain,
( ~ frontsegP(sK63,X0)
| ~ ssList(X0)
| ~ ssList(sK63) ),
inference(resolution,[status(thm)],[c_40122,c_62]) ).
cnf(c_40149,plain,
( ~ frontsegP(sK63,nil)
| ~ ssList(nil)
| ~ ssList(sK63) ),
inference(instantiation,[status(thm)],[c_40148]) ).
cnf(c_40150,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_40149,c_2556,c_141,c_265]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC412+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n031.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 : Mon Aug 28 15:30:10 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 55.20/8.23 % SZS status Started for theBenchmark.p
% 55.20/8.23 % SZS status Theorem for theBenchmark.p
% 55.20/8.23
% 55.20/8.23 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 55.20/8.23
% 55.20/8.23 ------ iProver source info
% 55.20/8.23
% 55.20/8.23 git: date: 2023-05-31 18:12:56 +0000
% 55.20/8.23 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 55.20/8.23 git: non_committed_changes: false
% 55.20/8.23 git: last_make_outside_of_git: false
% 55.20/8.23
% 55.20/8.23 ------ Parsing...
% 55.20/8.23 ------ Clausification by vclausify_rel & Parsing by iProver...
% 55.20/8.23
% 55.20/8.23 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 1 0s sf_e
% 55.20/8.23
% 55.20/8.23 ------ Preprocessing...
% 55.20/8.23
% 55.20/8.23 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 55.20/8.23 ------ Proving...
% 55.20/8.23 ------ Problem Properties
% 55.20/8.23
% 55.20/8.23
% 55.20/8.23 clauses 211
% 55.20/8.23 conjectures 7
% 55.20/8.23 EPR 68
% 55.20/8.23 Horn 137
% 55.20/8.23 unary 18
% 55.20/8.23 binary 62
% 55.20/8.23 lits 691
% 55.20/8.23 lits eq 86
% 55.20/8.23 fd_pure 0
% 55.20/8.23 fd_pseudo 0
% 55.20/8.23 fd_cond 21
% 55.20/8.23 fd_pseudo_cond 17
% 55.20/8.23 AC symbols 0
% 55.20/8.23
% 55.20/8.23 ------ Input Options Time Limit: Unbounded
% 55.20/8.23
% 55.20/8.23
% 55.20/8.23 ------
% 55.20/8.23 Current options:
% 55.20/8.23 ------
% 55.20/8.23
% 55.20/8.23
% 55.20/8.23
% 55.20/8.23
% 55.20/8.23 ------ Proving...
% 55.20/8.23
% 55.20/8.23
% 55.20/8.23 % SZS status Theorem for theBenchmark.p
% 55.20/8.23
% 55.20/8.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 55.20/8.23
% 55.20/8.23
%------------------------------------------------------------------------------