TSTP Solution File: SWC123+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWC123+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n027.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 20:41:08 EDT 2023
% Result : Theorem 23.63s 4.23s
% Output : CNFRefutation 23.63s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f591)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).
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(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
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(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
fof(f73,axiom,
! [X0] :
( ssItem(X0)
=> equalelemsP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax73) ).
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(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( segmentP(X1,X0)
& neq(X0,nil) )
| ? [X4] :
( equalelemsP(X4)
& segmentP(X4,X2)
& frontsegP(X3,X4)
& neq(X2,X4)
& ssList(X4) )
| ~ equalelemsP(X2)
| ~ frontsegP(X3,X2)
| ~ 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)
=> ( ( segmentP(X1,X0)
& neq(X0,nil) )
| ? [X4] :
( equalelemsP(X4)
& segmentP(X4,X2)
& frontsegP(X3,X4)
& neq(X2,X4)
& ssList(X4) )
| ~ equalelemsP(X2)
| ~ frontsegP(X3,X2)
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f101,plain,
! [X0] :
( ! [X1] :
( ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f134,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f175,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f185,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f73]) ).
fof(f186,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f75]) ).
fof(f187,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f186]) ).
fof(f188,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f76]) ).
fof(f189,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f188]) ).
fof(f192,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f193,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f192]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ segmentP(X1,X0)
| ~ neq(X0,nil) )
& ! [X4] :
( ~ equalelemsP(X4)
| ~ segmentP(X4,X2)
| ~ frontsegP(X3,X4)
| ~ neq(X2,X4)
| ~ ssList(X4) )
& equalelemsP(X2)
& frontsegP(X3,X2)
& neq(X1,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ segmentP(X1,X0)
| ~ neq(X0,nil) )
& ! [X4] :
( ~ equalelemsP(X4)
| ~ segmentP(X4,X2)
| ~ frontsegP(X3,X4)
| ~ neq(X2,X4)
| ~ ssList(X4) )
& equalelemsP(X2)
& frontsegP(X3,X2)
& neq(X1,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f245,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,[],[f101]) ).
fof(f246,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,[],[f245]) ).
fof(f247,plain,
! [X0,X1] :
( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
=> ( app(X1,sK11(X0,X1)) = X0
& ssList(sK11(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f248,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ( app(X1,sK11(X0,X1)) = X0
& ssList(sK11(X0,X1)) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f246,f247]) ).
fof(f253,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f103]) ).
fof(f254,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f253]) ).
fof(f255,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(app(sK13(X0,X1),X1),X5) = X0
& ssList(X5) )
& ssList(sK13(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f256,plain,
! [X0,X1] :
( ? [X5] :
( app(app(sK13(X0,X1),X1),X5) = X0
& ssList(X5) )
=> ( app(app(sK13(X0,X1),X1),sK14(X0,X1)) = X0
& ssList(sK14(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f257,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(app(sK13(X0,X1),X1),sK14(X0,X1)) = X0
& ssList(sK14(X0,X1))
& ssList(sK13(X0,X1)) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f254,f256,f255]) ).
fof(f316,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
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])],[f187,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])],[f189,f337]) ).
fof(f343,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ segmentP(X1,X0)
| ~ neq(X0,nil) )
& ! [X4] :
( ~ equalelemsP(X4)
| ~ segmentP(X4,X2)
| ~ frontsegP(X3,X4)
| ~ neq(X2,X4)
| ~ ssList(X4) )
& equalelemsP(X2)
& frontsegP(X3,X2)
& neq(X1,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ segmentP(X1,sK53)
| ~ neq(sK53,nil) )
& ! [X4] :
( ~ equalelemsP(X4)
| ~ segmentP(X4,X2)
| ~ frontsegP(X3,X4)
| ~ neq(X2,X4)
| ~ ssList(X4) )
& equalelemsP(X2)
& frontsegP(X3,X2)
& neq(X1,nil)
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK53) ) ),
introduced(choice_axiom,[]) ).
fof(f344,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ segmentP(X1,sK53)
| ~ neq(sK53,nil) )
& ! [X4] :
( ~ equalelemsP(X4)
| ~ segmentP(X4,X2)
| ~ frontsegP(X3,X4)
| ~ neq(X2,X4)
| ~ ssList(X4) )
& equalelemsP(X2)
& frontsegP(X3,X2)
& neq(X1,nil)
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ~ segmentP(sK54,sK53)
| ~ neq(sK53,nil) )
& ! [X4] :
( ~ equalelemsP(X4)
| ~ segmentP(X4,X2)
| ~ frontsegP(X3,X4)
| ~ neq(X2,X4)
| ~ ssList(X4) )
& equalelemsP(X2)
& frontsegP(X3,X2)
& neq(sK54,nil)
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK54) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
( ? [X2] :
( ? [X3] :
( ( ~ segmentP(sK54,sK53)
| ~ neq(sK53,nil) )
& ! [X4] :
( ~ equalelemsP(X4)
| ~ segmentP(X4,X2)
| ~ frontsegP(X3,X4)
| ~ neq(X2,X4)
| ~ ssList(X4) )
& equalelemsP(X2)
& frontsegP(X3,X2)
& neq(sK54,nil)
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ~ segmentP(sK54,sK53)
| ~ neq(sK53,nil) )
& ! [X4] :
( ~ equalelemsP(X4)
| ~ segmentP(X4,sK55)
| ~ frontsegP(X3,X4)
| ~ neq(sK55,X4)
| ~ ssList(X4) )
& equalelemsP(sK55)
& frontsegP(X3,sK55)
& neq(sK54,nil)
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
& ssList(sK55) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
( ? [X3] :
( ( ~ segmentP(sK54,sK53)
| ~ neq(sK53,nil) )
& ! [X4] :
( ~ equalelemsP(X4)
| ~ segmentP(X4,sK55)
| ~ frontsegP(X3,X4)
| ~ neq(sK55,X4)
| ~ ssList(X4) )
& equalelemsP(sK55)
& frontsegP(X3,sK55)
& neq(sK54,nil)
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
=> ( ( ~ segmentP(sK54,sK53)
| ~ neq(sK53,nil) )
& ! [X4] :
( ~ equalelemsP(X4)
| ~ segmentP(X4,sK55)
| ~ frontsegP(sK56,X4)
| ~ neq(sK55,X4)
| ~ ssList(X4) )
& equalelemsP(sK55)
& frontsegP(sK56,sK55)
& neq(sK54,nil)
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
( ( ~ segmentP(sK54,sK53)
| ~ neq(sK53,nil) )
& ! [X4] :
( ~ equalelemsP(X4)
| ~ segmentP(X4,sK55)
| ~ frontsegP(sK56,X4)
| ~ neq(sK55,X4)
| ~ ssList(X4) )
& equalelemsP(sK55)
& frontsegP(sK56,sK55)
& neq(sK54,nil)
& sK53 = sK55
& sK54 = sK56
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56])],[f222,f346,f345,f344,f343]) ).
fof(f360,plain,
! [X0,X1] :
( ssList(sK11(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f248]) ).
fof(f361,plain,
! [X0,X1] :
( app(X1,sK11(X0,X1)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f248]) ).
fof(f362,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f248]) ).
fof(f369,plain,
! [X2,X3,X0,X1] :
( segmentP(X0,X1)
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f257]) ).
fof(f438,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f316]) ).
fof(f439,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f440,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f447,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f452,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f454,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f493,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f518,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f185]) ).
fof(f520,plain,
! [X0] :
( ssItem(sK51(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f521,plain,
! [X0] :
( hd(X0) = sK51(X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f522,plain,
! [X0] :
( ssList(sK52(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f338]) ).
fof(f523,plain,
! [X0] :
( tl(X0) = sK52(X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f338]) ).
fof(f525,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f193]) ).
fof(f547,plain,
ssList(sK53),
inference(cnf_transformation,[],[f347]) ).
fof(f548,plain,
ssList(sK54),
inference(cnf_transformation,[],[f347]) ).
fof(f551,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f347]) ).
fof(f552,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f347]) ).
fof(f553,plain,
neq(sK54,nil),
inference(cnf_transformation,[],[f347]) ).
fof(f554,plain,
frontsegP(sK56,sK55),
inference(cnf_transformation,[],[f347]) ).
fof(f556,plain,
! [X4] :
( ~ equalelemsP(X4)
| ~ segmentP(X4,sK55)
| ~ frontsegP(sK56,X4)
| ~ neq(sK55,X4)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f347]) ).
fof(f557,plain,
( ~ segmentP(sK54,sK53)
| ~ neq(sK53,nil) ),
inference(cnf_transformation,[],[f347]) ).
fof(f558,plain,
( ~ segmentP(sK56,sK55)
| ~ neq(sK55,nil) ),
inference(definition_unfolding,[],[f557,f551,f552,f552]) ).
fof(f559,plain,
neq(sK56,nil),
inference(definition_unfolding,[],[f553,f551]) ).
fof(f560,plain,
ssList(sK56),
inference(definition_unfolding,[],[f548,f551]) ).
fof(f561,plain,
ssList(sK55),
inference(definition_unfolding,[],[f547,f552]) ).
fof(f565,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(equality_resolution,[],[f362]) ).
fof(f567,plain,
! [X2,X3,X1] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) ),
inference(equality_resolution,[],[f369]) ).
cnf(c_61,plain,
( ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| frontsegP(app(X0,X1),X0) ),
inference(cnf_transformation,[],[f565]) ).
cnf(c_62,plain,
( ~ frontsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X1,sK11(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f361]) ).
cnf(c_63,plain,
( ~ frontsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ssList(sK11(X0,X1)) ),
inference(cnf_transformation,[],[f360]) ).
cnf(c_67,plain,
( ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| segmentP(app(app(X0,X1),X2),X1) ),
inference(cnf_transformation,[],[f567]) ).
cnf(c_138,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f438]) ).
cnf(c_139,plain,
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f591]) ).
cnf(c_140,plain,
( ~ ssItem(X0)
| ~ ssList(X1)
| ssList(cons(X0,X1)) ),
inference(cnf_transformation,[],[f439]) ).
cnf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f440]) ).
cnf(c_148,plain,
( cons(X0,X1) != nil
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(cnf_transformation,[],[f447]) ).
cnf(c_153,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f452]) ).
cnf(c_155,plain,
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f454]) ).
cnf(c_177,plain,
( ~ frontsegP(X0,X1)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| frontsegP(cons(X2,X0),cons(X2,X1)) ),
inference(cnf_transformation,[],[f593]) ).
cnf(c_194,plain,
( ~ ssList(X0)
| segmentP(X0,nil) ),
inference(cnf_transformation,[],[f493]) ).
cnf(c_217,plain,
( ~ ssItem(X0)
| equalelemsP(cons(X0,nil)) ),
inference(cnf_transformation,[],[f518]) ).
cnf(c_219,plain,
( ~ ssList(X0)
| hd(X0) = sK51(X0)
| X0 = nil ),
inference(cnf_transformation,[],[f521]) ).
cnf(c_220,plain,
( ~ ssList(X0)
| X0 = nil
| ssItem(sK51(X0)) ),
inference(cnf_transformation,[],[f520]) ).
cnf(c_221,plain,
( ~ ssList(X0)
| tl(X0) = sK52(X0)
| X0 = nil ),
inference(cnf_transformation,[],[f523]) ).
cnf(c_222,plain,
( ~ ssList(X0)
| X0 = nil
| ssList(sK52(X0)) ),
inference(cnf_transformation,[],[f522]) ).
cnf(c_224,plain,
( ~ ssList(X0)
| cons(hd(X0),tl(X0)) = X0
| X0 = nil ),
inference(cnf_transformation,[],[f525]) ).
cnf(c_246,negated_conjecture,
( ~ neq(sK55,nil)
| ~ segmentP(sK56,sK55) ),
inference(cnf_transformation,[],[f558]) ).
cnf(c_247,negated_conjecture,
( ~ neq(sK55,X0)
| ~ frontsegP(sK56,X0)
| ~ segmentP(X0,sK55)
| ~ ssList(X0)
| ~ equalelemsP(X0) ),
inference(cnf_transformation,[],[f556]) ).
cnf(c_249,negated_conjecture,
frontsegP(sK56,sK55),
inference(cnf_transformation,[],[f554]) ).
cnf(c_250,negated_conjecture,
neq(sK56,nil),
inference(cnf_transformation,[],[f559]) ).
cnf(c_253,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f560]) ).
cnf(c_254,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f561]) ).
cnf(c_377,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| frontsegP(app(X0,X1),X0) ),
inference(global_subsumption_just,[status(thm)],[c_61,c_153,c_61]) ).
cnf(c_3229,plain,
( X0 != sK55
| X1 != nil
| ~ segmentP(sK56,sK55)
| ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1 ),
inference(resolution_lifted,[status(thm)],[c_138,c_246]) ).
cnf(c_3230,plain,
( ~ segmentP(sK56,sK55)
| ~ ssList(nil)
| ~ ssList(sK55)
| sK55 = nil ),
inference(unflattening,[status(thm)],[c_3229]) ).
cnf(c_3231,plain,
( ~ segmentP(sK56,sK55)
| sK55 = nil ),
inference(global_subsumption_just,[status(thm)],[c_3230,c_254,c_141,c_3230]) ).
cnf(c_3243,plain,
( X0 != sK55
| X1 != X2
| ~ frontsegP(sK56,X2)
| ~ segmentP(X2,sK55)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ equalelemsP(X2)
| X0 = X1 ),
inference(resolution_lifted,[status(thm)],[c_138,c_247]) ).
cnf(c_3244,plain,
( ~ frontsegP(sK56,X0)
| ~ segmentP(X0,sK55)
| ~ ssList(X0)
| ~ equalelemsP(X0)
| ~ ssList(sK55)
| sK55 = X0 ),
inference(unflattening,[status(thm)],[c_3243]) ).
cnf(c_3246,plain,
( ~ equalelemsP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sK55)
| ~ frontsegP(sK56,X0)
| sK55 = X0 ),
inference(global_subsumption_just,[status(thm)],[c_3244,c_254,c_3244]) ).
cnf(c_3247,plain,
( ~ frontsegP(sK56,X0)
| ~ segmentP(X0,sK55)
| ~ ssList(X0)
| ~ equalelemsP(X0)
| sK55 = X0 ),
inference(renaming,[status(thm)],[c_3246]) ).
cnf(c_3269,plain,
( X0 != nil
| X0 != sK56
| ~ ssList(X0) ),
inference(resolution_lifted,[status(thm)],[c_139,c_250]) ).
cnf(c_3270,plain,
( nil != sK56
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_3269]) ).
cnf(c_3271,plain,
nil != sK56,
inference(global_subsumption_just,[status(thm)],[c_3270,c_141,c_3270]) ).
cnf(c_12538,plain,
app(nil,sK55) = sK55,
inference(superposition,[status(thm)],[c_254,c_155]) ).
cnf(c_13825,plain,
( hd(sK56) = sK51(sK56)
| nil = sK56 ),
inference(superposition,[status(thm)],[c_253,c_219]) ).
cnf(c_13829,plain,
hd(sK56) = sK51(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_13825,c_3271]) ).
cnf(c_14000,plain,
( tl(sK56) = sK52(sK56)
| nil = sK56 ),
inference(superposition,[status(thm)],[c_253,c_221]) ).
cnf(c_14004,plain,
tl(sK56) = sK52(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_14000,c_3271]) ).
cnf(c_14148,plain,
( ~ ssList(sK56)
| nil = sK56
| ssItem(hd(sK56)) ),
inference(superposition,[status(thm)],[c_13829,c_220]) ).
cnf(c_14149,plain,
ssItem(hd(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_14148,c_3271,c_253]) ).
cnf(c_14158,plain,
( ~ ssList(sK56)
| nil = sK56
| ssList(tl(sK56)) ),
inference(superposition,[status(thm)],[c_14004,c_222]) ).
cnf(c_14159,plain,
ssList(tl(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_14158,c_3271,c_253]) ).
cnf(c_14170,plain,
app(nil,tl(sK56)) = tl(sK56),
inference(superposition,[status(thm)],[c_14159,c_155]) ).
cnf(c_14516,plain,
( ~ ssList(tl(sK56))
| ~ ssList(nil)
| frontsegP(tl(sK56),nil) ),
inference(superposition,[status(thm)],[c_14170,c_377]) ).
cnf(c_14517,plain,
frontsegP(tl(sK56),nil),
inference(forward_subsumption_resolution,[status(thm)],[c_14516,c_141,c_14159]) ).
cnf(c_16004,plain,
( ~ ssList(app(X0,X1))
| ~ ssList(X2)
| ssList(app(app(X0,X1),X2)) ),
inference(instantiation,[status(thm)],[c_153]) ).
cnf(c_16129,plain,
( ~ ssList(sK56)
| ~ ssList(sK55)
| app(sK55,sK11(sK56,sK55)) = sK56 ),
inference(superposition,[status(thm)],[c_249,c_62]) ).
cnf(c_16144,plain,
app(sK55,sK11(sK56,sK55)) = sK56,
inference(forward_subsumption_resolution,[status(thm)],[c_16129,c_254,c_253]) ).
cnf(c_22241,plain,
( cons(hd(sK56),X0) != nil
| ~ ssItem(hd(sK56))
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_148]) ).
cnf(c_22242,plain,
( ~ ssItem(hd(sK56))
| ~ ssList(X0)
| ssList(cons(hd(sK56),X0)) ),
inference(instantiation,[status(thm)],[c_140]) ).
cnf(c_22247,plain,
( ~ ssItem(hd(sK56))
| equalelemsP(cons(hd(sK56),nil)) ),
inference(instantiation,[status(thm)],[c_217]) ).
cnf(c_22252,plain,
( ~ ssItem(hd(sK56))
| ~ ssList(nil)
| ssList(cons(hd(sK56),nil)) ),
inference(instantiation,[status(thm)],[c_22242]) ).
cnf(c_22253,plain,
( cons(hd(sK56),nil) != nil
| ~ ssItem(hd(sK56))
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_22241]) ).
cnf(c_24846,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| segmentP(app(app(X0,X1),X2),X1) ),
inference(global_subsumption_just,[status(thm)],[c_67,c_153,c_67,c_16004]) ).
cnf(c_24861,plain,
( ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK55)
| segmentP(app(sK55,X0),sK55) ),
inference(superposition,[status(thm)],[c_12538,c_24846]) ).
cnf(c_24905,plain,
( ~ ssList(X0)
| segmentP(app(sK55,X0),sK55) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24861,c_254,c_141]) ).
cnf(c_25796,plain,
( ~ ssList(sK11(sK56,sK55))
| segmentP(sK56,sK55) ),
inference(superposition,[status(thm)],[c_16144,c_24905]) ).
cnf(c_26385,plain,
( ~ frontsegP(sK56,sK55)
| ~ ssList(sK56)
| ~ ssList(sK55)
| segmentP(sK56,sK55) ),
inference(superposition,[status(thm)],[c_63,c_25796]) ).
cnf(c_26386,plain,
segmentP(sK56,sK55),
inference(forward_subsumption_resolution,[status(thm)],[c_26385,c_254,c_253,c_249]) ).
cnf(c_99054,plain,
sK55 = nil,
inference(global_subsumption_just,[status(thm)],[c_3231,c_3231,c_26386]) ).
cnf(c_99067,plain,
( ~ frontsegP(sK56,X0)
| ~ segmentP(X0,nil)
| ~ ssList(X0)
| ~ equalelemsP(X0)
| X0 = nil ),
inference(light_normalisation,[status(thm)],[c_3247,c_99054]) ).
cnf(c_99210,plain,
( ~ frontsegP(sK56,X0)
| ~ ssList(X0)
| ~ equalelemsP(X0)
| X0 = nil ),
inference(backward_subsumption_resolution,[status(thm)],[c_99067,c_194]) ).
cnf(c_103059,plain,
( hd(sK56) = sK51(sK56)
| nil = sK56 ),
inference(superposition,[status(thm)],[c_253,c_219]) ).
cnf(c_103060,plain,
hd(sK56) = sK51(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_103059,c_3271]) ).
cnf(c_103184,plain,
( tl(sK56) = sK52(sK56)
| nil = sK56 ),
inference(superposition,[status(thm)],[c_253,c_221]) ).
cnf(c_103185,plain,
tl(sK56) = sK52(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_103184,c_3271]) ).
cnf(c_103469,plain,
( ~ ssList(sK56)
| nil = sK56
| ssItem(hd(sK56)) ),
inference(superposition,[status(thm)],[c_103060,c_220]) ).
cnf(c_103470,plain,
ssItem(hd(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_103469,c_3271,c_253]) ).
cnf(c_103477,plain,
( ~ ssList(sK56)
| nil = sK56
| ssList(tl(sK56)) ),
inference(superposition,[status(thm)],[c_103185,c_222]) ).
cnf(c_103478,plain,
ssList(tl(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_103477,c_3271,c_253]) ).
cnf(c_104912,plain,
( cons(hd(sK56),tl(sK56)) = sK56
| nil = sK56 ),
inference(superposition,[status(thm)],[c_253,c_224]) ).
cnf(c_104914,plain,
cons(hd(sK56),tl(sK56)) = sK56,
inference(forward_subsumption_resolution,[status(thm)],[c_104912,c_3271]) ).
cnf(c_109582,plain,
( ~ frontsegP(tl(sK56),X0)
| ~ ssItem(hd(sK56))
| ~ ssList(tl(sK56))
| ~ ssList(X0)
| frontsegP(sK56,cons(hd(sK56),X0)) ),
inference(superposition,[status(thm)],[c_104914,c_177]) ).
cnf(c_109609,plain,
( ~ frontsegP(tl(sK56),X0)
| ~ ssList(X0)
| frontsegP(sK56,cons(hd(sK56),X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109582,c_103478,c_103470]) ).
cnf(c_115868,plain,
( ~ ssList(cons(hd(sK56),X0))
| ~ equalelemsP(cons(hd(sK56),X0))
| ~ frontsegP(tl(sK56),X0)
| ~ ssList(X0)
| cons(hd(sK56),X0) = nil ),
inference(superposition,[status(thm)],[c_109609,c_99210]) ).
cnf(c_115900,plain,
( ~ ssList(cons(hd(sK56),nil))
| ~ equalelemsP(cons(hd(sK56),nil))
| ~ frontsegP(tl(sK56),nil)
| ~ ssList(nil)
| cons(hd(sK56),nil) = nil ),
inference(instantiation,[status(thm)],[c_115868]) ).
cnf(c_115901,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_115900,c_22253,c_22252,c_22247,c_14517,c_14149,c_141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC123+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n027.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 17:37:52 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 23.63/4.23 % SZS status Started for theBenchmark.p
% 23.63/4.23 % SZS status Theorem for theBenchmark.p
% 23.63/4.23
% 23.63/4.23 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 23.63/4.23
% 23.63/4.23 ------ iProver source info
% 23.63/4.23
% 23.63/4.23 git: date: 2023-05-31 18:12:56 +0000
% 23.63/4.23 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 23.63/4.23 git: non_committed_changes: false
% 23.63/4.23 git: last_make_outside_of_git: false
% 23.63/4.23
% 23.63/4.23 ------ Parsing...
% 23.63/4.23 ------ Clausification by vclausify_rel & Parsing by iProver...
% 23.63/4.23
% 23.63/4.23 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e
% 23.63/4.23
% 23.63/4.23 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 23.63/4.23
% 23.63/4.23 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 23.63/4.23 ------ Proving...
% 23.63/4.23 ------ Problem Properties
% 23.63/4.23
% 23.63/4.23
% 23.63/4.23 clauses 189
% 23.63/4.23 conjectures 4
% 23.63/4.23 EPR 58
% 23.63/4.23 Horn 121
% 23.63/4.23 unary 21
% 23.63/4.23 binary 42
% 23.63/4.23 lits 635
% 23.63/4.23 lits eq 83
% 23.63/4.23 fd_pure 0
% 23.63/4.23 fd_pseudo 0
% 23.63/4.23 fd_cond 22
% 23.63/4.23 fd_pseudo_cond 14
% 23.63/4.23 AC symbols 0
% 23.63/4.23
% 23.63/4.23 ------ Schedule dynamic 5 is on
% 23.63/4.23
% 23.63/4.23 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 23.63/4.23
% 23.63/4.23
% 23.63/4.23 ------
% 23.63/4.23 Current options:
% 23.63/4.23 ------
% 23.63/4.23
% 23.63/4.23
% 23.63/4.23
% 23.63/4.23
% 23.63/4.23 ------ Proving...
% 23.63/4.23
% 23.63/4.23
% 23.63/4.23 % SZS status Theorem for theBenchmark.p
% 23.63/4.23
% 23.63/4.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 23.63/4.23
% 23.63/4.23
%------------------------------------------------------------------------------