TSTP Solution File: SWC247+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWC247+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n005.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 20:41:59 EDT 2023
% Result : Theorem 273.60s 36.34s
% Output : CNFRefutation 273.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of formulae : 134 ( 18 unt; 0 def)
% Number of atoms : 737 ( 188 equ)
% Maximal formula atoms : 46 ( 5 avg)
% Number of connectives : 997 ( 394 ~; 366 |; 195 &)
% ( 4 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 282 ( 0 sgn; 141 !; 57 ?)
% 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(f20,axiom,
! [X0] :
( ssList(X0)
=> ( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
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(f82,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> app(app(X0,X1),X2) = app(X0,app(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax82) ).
fof(f93,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( lt(X0,X1)
<=> ( leq(X0,X1)
& X0 != X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax93) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ! [X8] :
( ssItem(X8)
=> ( leq(X5,X8)
| ~ lt(X5,X8)
| ~ memberP(X7,X8)
| ~ memberP(X6,X8) ) )
& app(app(X6,cons(X5,nil)),X7) = X0
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| ? [X4] :
( totalorderedP(X4)
& segmentP(X4,X2)
& frontsegP(X3,X4)
& neq(X2,X4)
& ssList(X4) )
| nil = X0
| ~ totalorderedP(X2)
| ~ frontsegP(X3,X2)
| 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)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ! [X8] :
( ssItem(X8)
=> ( leq(X5,X8)
| ~ lt(X5,X8)
| ~ memberP(X7,X8)
| ~ memberP(X6,X8) ) )
& app(app(X6,cons(X5,nil)),X7) = X0
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| ? [X4] :
( totalorderedP(X4)
& segmentP(X4,X2)
& frontsegP(X3,X4)
& neq(X2,X4)
& ssList(X4) )
| nil = X0
| ~ totalorderedP(X2)
| ~ frontsegP(X3,X2)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ssItem(X7)
=> ( leq(X4,X7)
| ~ lt(X4,X7)
| ~ memberP(X6,X7)
| ~ memberP(X5,X7) ) )
& app(app(X5,cons(X4,nil)),X6) = X0
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| ? [X8] :
( totalorderedP(X8)
& segmentP(X8,X2)
& frontsegP(X3,X8)
& neq(X2,X8)
& ssList(X8) )
| nil = X0
| ~ totalorderedP(X2)
| ~ frontsegP(X3,X2)
| X0 != X2
| X1 != 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(f124,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f125,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f124]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f135,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f173,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f199,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f200,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f217,plain,
! [X0] :
( ! [X1] :
( ( lt(X0,X1)
<=> ( leq(X0,X1)
& X0 != X1 ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f93]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ? [X7] :
( ~ leq(X4,X7)
& lt(X4,X7)
& memberP(X6,X7)
& memberP(X5,X7)
& ssItem(X7) )
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X8] :
( ~ totalorderedP(X8)
| ~ segmentP(X8,X2)
| ~ frontsegP(X3,X8)
| ~ neq(X2,X8)
| ~ ssList(X8) )
& nil != X0
& totalorderedP(X2)
& frontsegP(X3,X2)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f223,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ? [X7] :
( ~ leq(X4,X7)
& lt(X4,X7)
& memberP(X6,X7)
& memberP(X5,X7)
& ssItem(X7) )
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X8] :
( ~ totalorderedP(X8)
| ~ segmentP(X8,X2)
| ~ frontsegP(X3,X8)
| ~ neq(X2,X8)
| ~ ssList(X8) )
& nil != X0
& totalorderedP(X2)
& frontsegP(X3,X2)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f222]) ).
fof(f317,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f119]) ).
fof(f318,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
=> ( ? [X2] :
( cons(X2,sK49(X0)) = X0
& ssItem(X2) )
& ssList(sK49(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f319,plain,
! [X0] :
( ? [X2] :
( cons(X2,sK49(X0)) = X0
& ssItem(X2) )
=> ( cons(sK50(X0),sK49(X0)) = X0
& ssItem(sK50(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f320,plain,
! [X0] :
( ( cons(sK50(X0),sK49(X0)) = X0
& ssItem(sK50(X0))
& ssList(sK49(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK49,sK50])],[f125,f319,f318]) ).
fof(f342,plain,
! [X0] :
( ! [X1] :
( ( ( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1 )
& ( ( leq(X0,X1)
& X0 != X1 )
| ~ lt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f217]) ).
fof(f343,plain,
! [X0] :
( ! [X1] :
( ( ( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1 )
& ( ( leq(X0,X1)
& X0 != X1 )
| ~ lt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f342]) ).
fof(f344,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ? [X7] :
( ~ leq(X4,X7)
& lt(X4,X7)
& memberP(X6,X7)
& memberP(X5,X7)
& ssItem(X7) )
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X8] :
( ~ totalorderedP(X8)
| ~ segmentP(X8,X2)
| ~ frontsegP(X3,X8)
| ~ neq(X2,X8)
| ~ ssList(X8) )
& nil != X0
& totalorderedP(X2)
& frontsegP(X3,X2)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ? [X7] :
( ~ leq(X4,X7)
& lt(X4,X7)
& memberP(X6,X7)
& memberP(X5,X7)
& ssItem(X7) )
| app(app(X5,cons(X4,nil)),X6) != sK53
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X8] :
( ~ totalorderedP(X8)
| ~ segmentP(X8,X2)
| ~ frontsegP(X3,X8)
| ~ neq(X2,X8)
| ~ ssList(X8) )
& nil != sK53
& totalorderedP(X2)
& frontsegP(X3,X2)
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK53) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ? [X7] :
( ~ leq(X4,X7)
& lt(X4,X7)
& memberP(X6,X7)
& memberP(X5,X7)
& ssItem(X7) )
| app(app(X5,cons(X4,nil)),X6) != sK53
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X8] :
( ~ totalorderedP(X8)
| ~ segmentP(X8,X2)
| ~ frontsegP(X3,X8)
| ~ neq(X2,X8)
| ~ ssList(X8) )
& nil != sK53
& totalorderedP(X2)
& frontsegP(X3,X2)
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ? [X7] :
( ~ leq(X4,X7)
& lt(X4,X7)
& memberP(X6,X7)
& memberP(X5,X7)
& ssItem(X7) )
| app(app(X5,cons(X4,nil)),X6) != sK53
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X8] :
( ~ totalorderedP(X8)
| ~ segmentP(X8,X2)
| ~ frontsegP(X3,X8)
| ~ neq(X2,X8)
| ~ ssList(X8) )
& nil != sK53
& totalorderedP(X2)
& frontsegP(X3,X2)
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK54) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ? [X7] :
( ~ leq(X4,X7)
& lt(X4,X7)
& memberP(X6,X7)
& memberP(X5,X7)
& ssItem(X7) )
| app(app(X5,cons(X4,nil)),X6) != sK53
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X8] :
( ~ totalorderedP(X8)
| ~ segmentP(X8,X2)
| ~ frontsegP(X3,X8)
| ~ neq(X2,X8)
| ~ ssList(X8) )
& nil != sK53
& totalorderedP(X2)
& frontsegP(X3,X2)
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ? [X7] :
( ~ leq(X4,X7)
& lt(X4,X7)
& memberP(X6,X7)
& memberP(X5,X7)
& ssItem(X7) )
| app(app(X5,cons(X4,nil)),X6) != sK53
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X8] :
( ~ totalorderedP(X8)
| ~ segmentP(X8,sK55)
| ~ frontsegP(X3,X8)
| ~ neq(sK55,X8)
| ~ ssList(X8) )
& nil != sK53
& totalorderedP(sK55)
& frontsegP(X3,sK55)
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
& ssList(sK55) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
( ? [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ? [X7] :
( ~ leq(X4,X7)
& lt(X4,X7)
& memberP(X6,X7)
& memberP(X5,X7)
& ssItem(X7) )
| app(app(X5,cons(X4,nil)),X6) != sK53
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X8] :
( ~ totalorderedP(X8)
| ~ segmentP(X8,sK55)
| ~ frontsegP(X3,X8)
| ~ neq(sK55,X8)
| ~ ssList(X8) )
& nil != sK53
& totalorderedP(sK55)
& frontsegP(X3,sK55)
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
=> ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ? [X7] :
( ~ leq(X4,X7)
& lt(X4,X7)
& memberP(X6,X7)
& memberP(X5,X7)
& ssItem(X7) )
| app(app(X5,cons(X4,nil)),X6) != sK53
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X8] :
( ~ totalorderedP(X8)
| ~ segmentP(X8,sK55)
| ~ frontsegP(sK56,X8)
| ~ neq(sK55,X8)
| ~ ssList(X8) )
& nil != sK53
& totalorderedP(sK55)
& frontsegP(sK56,sK55)
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
! [X4,X5,X6] :
( ? [X7] :
( ~ leq(X4,X7)
& lt(X4,X7)
& memberP(X6,X7)
& memberP(X5,X7)
& ssItem(X7) )
=> ( ~ leq(X4,sK57(X4,X5,X6))
& lt(X4,sK57(X4,X5,X6))
& memberP(X6,sK57(X4,X5,X6))
& memberP(X5,sK57(X4,X5,X6))
& ssItem(sK57(X4,X5,X6)) ) ),
introduced(choice_axiom,[]) ).
fof(f349,plain,
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ( ~ leq(X4,sK57(X4,X5,X6))
& lt(X4,sK57(X4,X5,X6))
& memberP(X6,sK57(X4,X5,X6))
& memberP(X5,sK57(X4,X5,X6))
& ssItem(sK57(X4,X5,X6)) )
| app(app(X5,cons(X4,nil)),X6) != sK53
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X8] :
( ~ totalorderedP(X8)
| ~ segmentP(X8,sK55)
| ~ frontsegP(sK56,X8)
| ~ neq(sK55,X8)
| ~ ssList(X8) )
& nil != sK53
& totalorderedP(sK55)
& frontsegP(sK56,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])],[f223,f348,f347,f346,f345,f344]) ).
fof(f440,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f317]) ).
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(f446,plain,
! [X0] :
( ssList(sK49(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f320]) ).
fof(f447,plain,
! [X0] :
( ssItem(sK50(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f320]) ).
fof(f448,plain,
! [X0] :
( cons(sK50(X0),sK49(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f320]) ).
fof(f454,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f456,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f493,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f173]) ).
fof(f530,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f199]) ).
fof(f531,plain,
! [X2,X0,X1] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f200]) ).
fof(f545,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f343]) ).
fof(f549,plain,
ssList(sK53),
inference(cnf_transformation,[],[f349]) ).
fof(f554,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f349]) ).
fof(f555,plain,
frontsegP(sK56,sK55),
inference(cnf_transformation,[],[f349]) ).
fof(f556,plain,
totalorderedP(sK55),
inference(cnf_transformation,[],[f349]) ).
fof(f557,plain,
nil != sK53,
inference(cnf_transformation,[],[f349]) ).
fof(f558,plain,
! [X8] :
( ~ totalorderedP(X8)
| ~ segmentP(X8,sK55)
| ~ frontsegP(sK56,X8)
| ~ neq(sK55,X8)
| ~ ssList(X8) ),
inference(cnf_transformation,[],[f349]) ).
fof(f559,plain,
! [X6,X4,X5] :
( ssItem(sK57(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK53
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f349]) ).
fof(f562,plain,
! [X6,X4,X5] :
( lt(X4,sK57(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK53
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f349]) ).
fof(f563,plain,
! [X6,X4,X5] :
( ~ leq(X4,sK57(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK53
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f349]) ).
fof(f564,plain,
! [X6,X4,X5] :
( ~ leq(X4,sK57(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK55
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f563,f554]) ).
fof(f565,plain,
! [X6,X4,X5] :
( lt(X4,sK57(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK55
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f562,f554]) ).
fof(f568,plain,
! [X6,X4,X5] :
( ssItem(sK57(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK55
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f559,f554]) ).
fof(f569,plain,
nil != sK55,
inference(definition_unfolding,[],[f557,f554]) ).
fof(f571,plain,
ssList(sK55),
inference(definition_unfolding,[],[f549,f554]) ).
cnf(c_138,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f440]) ).
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_145,plain,
( ~ ssList(X0)
| cons(sK50(X0),sK49(X0)) = X0
| X0 = nil ),
inference(cnf_transformation,[],[f448]) ).
cnf(c_146,plain,
( ~ ssList(X0)
| X0 = nil
| ssItem(sK50(X0)) ),
inference(cnf_transformation,[],[f447]) ).
cnf(c_147,plain,
( ~ ssList(X0)
| X0 = nil
| ssList(sK49(X0)) ),
inference(cnf_transformation,[],[f446]) ).
cnf(c_153,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f454]) ).
cnf(c_155,plain,
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f456]) ).
cnf(c_192,plain,
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[],[f493]) ).
cnf(c_227,plain,
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) = cons(X0,X1) ),
inference(cnf_transformation,[],[f530]) ).
cnf(c_228,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X0,X1),X2) = app(X0,app(X1,X2)) ),
inference(cnf_transformation,[],[f531]) ).
cnf(c_242,plain,
( ~ lt(X0,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| leq(X0,X1) ),
inference(cnf_transformation,[],[f545]) ).
cnf(c_246,negated_conjecture,
( app(app(X0,cons(X1,nil)),X2) != sK55
| ~ leq(X1,sK57(X1,X0,X2))
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2) ),
inference(cnf_transformation,[],[f564]) ).
cnf(c_247,negated_conjecture,
( app(app(X0,cons(X1,nil)),X2) != sK55
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| lt(X1,sK57(X1,X0,X2)) ),
inference(cnf_transformation,[],[f565]) ).
cnf(c_250,negated_conjecture,
( app(app(X0,cons(X1,nil)),X2) != sK55
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ssItem(sK57(X1,X0,X2)) ),
inference(cnf_transformation,[],[f568]) ).
cnf(c_251,negated_conjecture,
( ~ neq(sK55,X0)
| ~ frontsegP(sK56,X0)
| ~ segmentP(X0,sK55)
| ~ ssList(X0)
| ~ totalorderedP(X0) ),
inference(cnf_transformation,[],[f558]) ).
cnf(c_252,negated_conjecture,
nil != sK55,
inference(cnf_transformation,[],[f569]) ).
cnf(c_253,negated_conjecture,
totalorderedP(sK55),
inference(cnf_transformation,[],[f556]) ).
cnf(c_254,negated_conjecture,
frontsegP(sK56,sK55),
inference(cnf_transformation,[],[f555]) ).
cnf(c_258,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f571]) ).
cnf(c_2001,plain,
( X0 != sK55
| X1 != X2
| ~ frontsegP(sK56,X2)
| ~ segmentP(X2,sK55)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ totalorderedP(X2)
| X0 = X1 ),
inference(resolution_lifted,[status(thm)],[c_138,c_251]) ).
cnf(c_2002,plain,
( ~ frontsegP(sK56,X0)
| ~ segmentP(X0,sK55)
| ~ ssList(X0)
| ~ totalorderedP(X0)
| ~ ssList(sK55)
| sK55 = X0 ),
inference(unflattening,[status(thm)],[c_2001]) ).
cnf(c_2004,plain,
( ~ totalorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sK55)
| ~ frontsegP(sK56,X0)
| sK55 = X0 ),
inference(global_subsumption_just,[status(thm)],[c_2002,c_258,c_2002]) ).
cnf(c_2005,plain,
( ~ frontsegP(sK56,X0)
| ~ segmentP(X0,sK55)
| ~ ssList(X0)
| ~ totalorderedP(X0)
| sK55 = X0 ),
inference(renaming,[status(thm)],[c_2004]) ).
cnf(c_6471,plain,
( ~ frontsegP(sK56,X0_13)
| ~ segmentP(X0_13,sK55)
| ~ ssList(X0_13)
| ~ totalorderedP(X0_13)
| sK55 = X0_13 ),
inference(subtyping,[status(esa)],[c_2005]) ).
cnf(c_6488,negated_conjecture,
nil != sK55,
inference(subtyping,[status(esa)],[c_252]) ).
cnf(c_6489,negated_conjecture,
( app(app(X0_13,cons(X0_14,nil)),X1_13) != sK55
| ~ ssItem(X0_14)
| ~ ssList(X0_13)
| ~ ssList(X1_13)
| ssItem(sK57(X0_14,X0_13,X1_13)) ),
inference(subtyping,[status(esa)],[c_250]) ).
cnf(c_6492,negated_conjecture,
( app(app(X0_13,cons(X0_14,nil)),X1_13) != sK55
| ~ ssItem(X0_14)
| ~ ssList(X0_13)
| ~ ssList(X1_13)
| lt(X0_14,sK57(X0_14,X0_13,X1_13)) ),
inference(subtyping,[status(esa)],[c_247]) ).
cnf(c_6493,negated_conjecture,
( app(app(X0_13,cons(X0_14,nil)),X1_13) != sK55
| ~ leq(X0_14,sK57(X0_14,X0_13,X1_13))
| ~ ssItem(X0_14)
| ~ ssList(X0_13)
| ~ ssList(X1_13) ),
inference(subtyping,[status(esa)],[c_246]) ).
cnf(c_6496,plain,
( ~ lt(X0_14,X1_14)
| ~ ssItem(X0_14)
| ~ ssItem(X1_14)
| leq(X0_14,X1_14) ),
inference(subtyping,[status(esa)],[c_242]) ).
cnf(c_6508,plain,
( ~ ssList(X0_13)
| ~ ssList(X1_13)
| ~ ssList(X2_13)
| app(app(X0_13,X1_13),X2_13) = app(X0_13,app(X1_13,X2_13)) ),
inference(subtyping,[status(esa)],[c_228]) ).
cnf(c_6509,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_6535,plain,
( ~ ssList(X0_13)
| segmentP(X0_13,X0_13) ),
inference(subtyping,[status(esa)],[c_192]) ).
cnf(c_6570,plain,
( ~ ssList(X0_13)
| app(nil,X0_13) = X0_13 ),
inference(subtyping,[status(esa)],[c_155]) ).
cnf(c_6572,plain,
( ~ ssList(X0_13)
| ~ ssList(X1_13)
| ssList(app(X0_13,X1_13)) ),
inference(subtyping,[status(esa)],[c_153]) ).
cnf(c_6578,plain,
( ~ ssList(X0_13)
| X0_13 = nil
| ssList(sK49(X0_13)) ),
inference(subtyping,[status(esa)],[c_147]) ).
cnf(c_6579,plain,
( ~ ssList(X0_13)
| X0_13 = nil
| ssItem(sK50(X0_13)) ),
inference(subtyping,[status(esa)],[c_146]) ).
cnf(c_6580,plain,
( ~ ssList(X0_13)
| cons(sK50(X0_13),sK49(X0_13)) = X0_13
| X0_13 = nil ),
inference(subtyping,[status(esa)],[c_145]) ).
cnf(c_6585,plain,
( ~ ssItem(X0_14)
| ~ ssList(X0_13)
| ssList(cons(X0_14,X0_13)) ),
inference(subtyping,[status(esa)],[c_140]) ).
cnf(c_6663,plain,
X0_13 = X0_13,
theory(equality) ).
cnf(c_6665,plain,
( X0_13 != X1_13
| X2_13 != X1_13
| X2_13 = X0_13 ),
theory(equality) ).
cnf(c_6692,plain,
nil = nil,
inference(instantiation,[status(thm)],[c_6663]) ).
cnf(c_9690,plain,
( ~ ssList(sK55)
| segmentP(sK55,sK55) ),
inference(instantiation,[status(thm)],[c_6535]) ).
cnf(c_9691,plain,
( ~ frontsegP(sK56,sK55)
| ~ segmentP(sK55,sK55)
| ~ ssList(sK55)
| ~ totalorderedP(sK55)
| sK55 = sK55 ),
inference(instantiation,[status(thm)],[c_6471]) ).
cnf(c_9747,plain,
( nil != X0_13
| sK55 != X0_13
| nil = sK55 ),
inference(instantiation,[status(thm)],[c_6665]) ).
cnf(c_9748,plain,
( nil != nil
| sK55 != nil
| nil = sK55 ),
inference(instantiation,[status(thm)],[c_9747]) ).
cnf(c_9758,plain,
( ~ ssList(X0_13)
| ~ ssList(X1_13)
| app(nil,app(X0_13,X1_13)) = app(X0_13,X1_13) ),
inference(superposition,[status(thm)],[c_6572,c_6570]) ).
cnf(c_10153,plain,
( ~ ssList(sK55)
| cons(sK50(sK55),sK49(sK55)) = sK55
| sK55 = nil ),
inference(instantiation,[status(thm)],[c_6580]) ).
cnf(c_10158,plain,
( ~ ssList(sK55)
| sK55 = nil
| ssItem(sK50(sK55)) ),
inference(instantiation,[status(thm)],[c_6579]) ).
cnf(c_10159,plain,
( ~ ssList(sK55)
| sK55 = nil
| ssList(sK49(sK55)) ),
inference(instantiation,[status(thm)],[c_6578]) ).
cnf(c_10185,plain,
( X0_13 != X1_13
| sK55 != X1_13
| sK55 = X0_13 ),
inference(instantiation,[status(thm)],[c_6665]) ).
cnf(c_12934,plain,
( X0_13 != sK55
| sK55 != sK55
| sK55 = X0_13 ),
inference(instantiation,[status(thm)],[c_10185]) ).
cnf(c_21123,plain,
( cons(sK50(sK55),sK49(sK55)) != sK55
| sK55 != sK55
| sK55 = cons(sK50(sK55),sK49(sK55)) ),
inference(instantiation,[status(thm)],[c_12934]) ).
cnf(c_29607,plain,
( X0_13 != cons(sK50(sK55),sK49(sK55))
| sK55 != cons(sK50(sK55),sK49(sK55))
| sK55 = X0_13 ),
inference(instantiation,[status(thm)],[c_10185]) ).
cnf(c_39484,plain,
( app(cons(sK50(sK55),nil),sK49(sK55)) != cons(sK50(sK55),sK49(sK55))
| sK55 != cons(sK50(sK55),sK49(sK55))
| sK55 = app(cons(sK50(sK55),nil),sK49(sK55)) ),
inference(instantiation,[status(thm)],[c_29607]) ).
cnf(c_39485,plain,
( ~ ssItem(sK50(sK55))
| ~ ssList(sK49(sK55))
| app(cons(sK50(sK55),nil),sK49(sK55)) = cons(sK50(sK55),sK49(sK55)) ),
inference(instantiation,[status(thm)],[c_6509]) ).
cnf(c_92185,plain,
( X0_13 != X1_13
| sK55 != X1_13
| sK55 = X0_13 ),
inference(instantiation,[status(thm)],[c_6665]) ).
cnf(c_137288,plain,
( X0_13 != app(cons(sK50(sK55),nil),sK49(sK55))
| sK55 != app(cons(sK50(sK55),nil),sK49(sK55))
| sK55 = X0_13 ),
inference(instantiation,[status(thm)],[c_92185]) ).
cnf(c_139529,plain,
( app(nil,app(cons(sK50(sK55),nil),sK49(sK55))) != app(cons(sK50(sK55),nil),sK49(sK55))
| sK55 != app(cons(sK50(sK55),nil),sK49(sK55))
| sK55 = app(nil,app(cons(sK50(sK55),nil),sK49(sK55))) ),
inference(instantiation,[status(thm)],[c_137288]) ).
cnf(c_139530,plain,
( ~ ssList(cons(sK50(sK55),nil))
| ~ ssList(sK49(sK55))
| app(nil,app(cons(sK50(sK55),nil),sK49(sK55))) = app(cons(sK50(sK55),nil),sK49(sK55)) ),
inference(instantiation,[status(thm)],[c_9758]) ).
cnf(c_200395,plain,
( ~ ssItem(sK50(sK55))
| ~ ssList(nil)
| ssList(cons(sK50(sK55),nil)) ),
inference(instantiation,[status(thm)],[c_6585]) ).
cnf(c_204772,plain,
( app(app(X0_13,cons(X0_14,nil)),X1_13) != X2_13
| sK55 != X2_13
| app(app(X0_13,cons(X0_14,nil)),X1_13) = sK55 ),
inference(instantiation,[status(thm)],[c_6665]) ).
cnf(c_213518,plain,
( ~ ssList(cons(X0_14,nil))
| ~ ssList(X0_13)
| ~ ssList(X1_13)
| app(app(X0_13,cons(X0_14,nil)),X1_13) = app(X0_13,app(cons(X0_14,nil),X1_13)) ),
inference(instantiation,[status(thm)],[c_6508]) ).
cnf(c_285812,plain,
( app(app(X0_13,cons(X0_14,nil)),X1_13) != app(nil,app(cons(sK50(sK55),nil),sK49(sK55)))
| sK55 != app(nil,app(cons(sK50(sK55),nil),sK49(sK55)))
| app(app(X0_13,cons(X0_14,nil)),X1_13) = sK55 ),
inference(instantiation,[status(thm)],[c_204772]) ).
cnf(c_290132,plain,
( app(app(nil,cons(sK50(sK55),nil)),sK49(sK55)) != app(nil,app(cons(sK50(sK55),nil),sK49(sK55)))
| sK55 != app(nil,app(cons(sK50(sK55),nil),sK49(sK55)))
| app(app(nil,cons(sK50(sK55),nil)),sK49(sK55)) = sK55 ),
inference(instantiation,[status(thm)],[c_285812]) ).
cnf(c_290133,plain,
( ~ ssList(cons(sK50(sK55),nil))
| ~ ssList(sK49(sK55))
| ~ ssList(nil)
| app(app(nil,cons(sK50(sK55),nil)),sK49(sK55)) = app(nil,app(cons(sK50(sK55),nil),sK49(sK55))) ),
inference(instantiation,[status(thm)],[c_213518]) ).
cnf(c_295226,plain,
( app(app(nil,cons(sK50(sK55),nil)),sK49(sK55)) != sK55
| ~ leq(sK50(sK55),sK57(sK50(sK55),nil,sK49(sK55)))
| ~ ssItem(sK50(sK55))
| ~ ssList(sK49(sK55))
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_6493]) ).
cnf(c_295227,plain,
( app(app(nil,cons(sK50(sK55),nil)),sK49(sK55)) != sK55
| ~ ssItem(sK50(sK55))
| ~ ssList(sK49(sK55))
| ~ ssList(nil)
| lt(sK50(sK55),sK57(sK50(sK55),nil,sK49(sK55))) ),
inference(instantiation,[status(thm)],[c_6492]) ).
cnf(c_295230,plain,
( app(app(nil,cons(sK50(sK55),nil)),sK49(sK55)) != sK55
| ~ ssItem(sK50(sK55))
| ~ ssList(sK49(sK55))
| ~ ssList(nil)
| ssItem(sK57(sK50(sK55),nil,sK49(sK55))) ),
inference(instantiation,[status(thm)],[c_6489]) ).
cnf(c_298940,plain,
( ~ lt(sK50(sK55),sK57(sK50(sK55),nil,sK49(sK55)))
| ~ ssItem(sK57(sK50(sK55),nil,sK49(sK55)))
| ~ ssItem(sK50(sK55))
| leq(sK50(sK55),sK57(sK50(sK55),nil,sK49(sK55))) ),
inference(instantiation,[status(thm)],[c_6496]) ).
cnf(c_298941,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_298940,c_295226,c_295227,c_295230,c_290133,c_290132,c_200395,c_139530,c_139529,c_39485,c_39484,c_21123,c_10153,c_10158,c_10159,c_9748,c_9691,c_9690,c_6488,c_6692,c_254,c_141,c_253,c_258]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWC247+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.11 % Command : run_iprover %s %d THM
% 0.10/0.32 % Computer : n005.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 : Mon Aug 28 17:19:23 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.17/0.44 Running first-order theorem proving
% 0.17/0.44 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 273.60/36.34 % SZS status Started for theBenchmark.p
% 273.60/36.34 % SZS status Theorem for theBenchmark.p
% 273.60/36.34
% 273.60/36.34 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 273.60/36.34
% 273.60/36.34 ------ iProver source info
% 273.60/36.34
% 273.60/36.34 git: date: 2023-05-31 18:12:56 +0000
% 273.60/36.34 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 273.60/36.34 git: non_committed_changes: false
% 273.60/36.34 git: last_make_outside_of_git: false
% 273.60/36.34
% 273.60/36.34 ------ Parsing...
% 273.60/36.34 ------ Clausification by vclausify_rel & Parsing by iProver...
% 273.60/36.34
% 273.60/36.34 ------ 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
% 273.60/36.34
% 273.60/36.34 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 273.60/36.34
% 273.60/36.34 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 273.60/36.34 ------ Proving...
% 273.60/36.34 ------ Problem Properties
% 273.60/36.34
% 273.60/36.34
% 273.60/36.34 clauses 191
% 273.60/36.34 conjectures 10
% 273.60/36.34 EPR 55
% 273.60/36.34 Horn 123
% 273.60/36.34 unary 21
% 273.60/36.34 binary 40
% 273.60/36.34 lits 653
% 273.60/36.34 lits eq 85
% 273.60/36.34 fd_pure 0
% 273.60/36.34 fd_pseudo 0
% 273.60/36.34 fd_cond 22
% 273.60/36.34 fd_pseudo_cond 14
% 273.60/36.34 AC symbols 0
% 273.60/36.34
% 273.60/36.34 ------ Input Options Time Limit: Unbounded
% 273.60/36.34
% 273.60/36.34
% 273.60/36.34 ------
% 273.60/36.34 Current options:
% 273.60/36.34 ------
% 273.60/36.34
% 273.60/36.34
% 273.60/36.34
% 273.60/36.34
% 273.60/36.34 ------ Proving...
% 273.60/36.34
% 273.60/36.34
% 273.60/36.34 % SZS status Theorem for theBenchmark.p
% 273.60/36.34
% 273.60/36.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 273.60/36.34
% 273.60/36.35
%------------------------------------------------------------------------------