TSTP Solution File: RNG106+2 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : RNG106+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n017.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 02:57:41 EDT 2024
% Result : Theorem 8.04s 1.70s
% Output : CNFRefutation 8.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 77 ( 10 unt; 0 def)
% Number of atoms : 447 ( 104 equ)
% Maximal formula atoms : 29 ( 5 avg)
% Number of connectives : 523 ( 153 ~; 130 |; 209 &)
% ( 6 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 246 ( 18 sgn 120 !; 67 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f13,axiom,
! [X0] :
( aElement0(X0)
=> ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulUnit) ).
fof(f38,axiom,
aElement0(xc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1905) ).
fof(f39,conjecture,
( ! [X0,X1,X2] :
( ( aElement0(X2)
& ( aElementOf0(X1,slsdtgt0(xc))
| ? [X3] :
( sdtasdt0(xc,X3) = X1
& aElement0(X3) ) )
& ( aElementOf0(X0,slsdtgt0(xc))
| ? [X3] :
( sdtasdt0(xc,X3) = X0
& aElement0(X3) ) ) )
=> ? [X3] :
( ? [X4] :
( aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
& ? [X5] :
( sdtasdt0(X2,X0) = sdtasdt0(xc,X5)
& aElement0(X5) )
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& ? [X5] :
( sdtpldt0(X0,X1) = sdtasdt0(xc,X5)
& aElement0(X5) )
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X3,X2))
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X3,X4))
& sdtasdt0(xc,X4) = X1
& aElement0(X4) )
& sdtasdt0(xc,X3) = X0
& aElement0(X3) ) )
=> ( ( ! [X0] :
( aElementOf0(X0,slsdtgt0(xc))
<=> ? [X1] :
( sdtasdt0(xc,X1) = X0
& aElement0(X1) ) )
& aSet0(slsdtgt0(xc)) )
=> ( aIdeal0(slsdtgt0(xc))
| ! [X0] :
( aElementOf0(X0,slsdtgt0(xc))
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc)) )
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xc))
=> aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f40,negated_conjecture,
~ ( ! [X0,X1,X2] :
( ( aElement0(X2)
& ( aElementOf0(X1,slsdtgt0(xc))
| ? [X3] :
( sdtasdt0(xc,X3) = X1
& aElement0(X3) ) )
& ( aElementOf0(X0,slsdtgt0(xc))
| ? [X3] :
( sdtasdt0(xc,X3) = X0
& aElement0(X3) ) ) )
=> ? [X3] :
( ? [X4] :
( aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
& ? [X5] :
( sdtasdt0(X2,X0) = sdtasdt0(xc,X5)
& aElement0(X5) )
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& ? [X5] :
( sdtpldt0(X0,X1) = sdtasdt0(xc,X5)
& aElement0(X5) )
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X3,X2))
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X3,X4))
& sdtasdt0(xc,X4) = X1
& aElement0(X4) )
& sdtasdt0(xc,X3) = X0
& aElement0(X3) ) )
=> ( ( ! [X0] :
( aElementOf0(X0,slsdtgt0(xc))
<=> ? [X1] :
( sdtasdt0(xc,X1) = X0
& aElement0(X1) ) )
& aSet0(slsdtgt0(xc)) )
=> ( aIdeal0(slsdtgt0(xc))
| ! [X0] :
( aElementOf0(X0,slsdtgt0(xc))
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc)) )
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xc))
=> aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc)) ) ) ) ) ) ),
inference(negated_conjecture,[],[f39]) ).
fof(f48,plain,
~ ( ! [X0,X1,X2] :
( ( aElement0(X2)
& ( aElementOf0(X1,slsdtgt0(xc))
| ? [X3] :
( sdtasdt0(xc,X3) = X1
& aElement0(X3) ) )
& ( aElementOf0(X0,slsdtgt0(xc))
| ? [X4] :
( sdtasdt0(xc,X4) = X0
& aElement0(X4) ) ) )
=> ? [X5] :
( ? [X6] :
( aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
& ? [X7] :
( sdtasdt0(X2,X0) = sdtasdt0(xc,X7)
& aElement0(X7) )
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& ? [X8] :
( sdtpldt0(X0,X1) = sdtasdt0(xc,X8)
& aElement0(X8) )
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X5,X2))
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X5,X6))
& sdtasdt0(xc,X6) = X1
& aElement0(X6) )
& sdtasdt0(xc,X5) = X0
& aElement0(X5) ) )
=> ( ( ! [X9] :
( aElementOf0(X9,slsdtgt0(xc))
<=> ? [X10] :
( sdtasdt0(xc,X10) = X9
& aElement0(X10) ) )
& aSet0(slsdtgt0(xc)) )
=> ( aIdeal0(slsdtgt0(xc))
| ! [X11] :
( aElementOf0(X11,slsdtgt0(xc))
=> ( ! [X12] :
( aElement0(X12)
=> aElementOf0(sdtasdt0(X12,X11),slsdtgt0(xc)) )
& ! [X13] :
( aElementOf0(X13,slsdtgt0(xc))
=> aElementOf0(sdtpldt0(X11,X13),slsdtgt0(xc)) ) ) ) ) ) ),
inference(rectify,[],[f40]) ).
fof(f66,plain,
! [X0] :
( ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f99,plain,
( ~ aIdeal0(slsdtgt0(xc))
& ? [X11] :
( ( ? [X12] :
( ~ aElementOf0(sdtasdt0(X12,X11),slsdtgt0(xc))
& aElement0(X12) )
| ? [X13] :
( ~ aElementOf0(sdtpldt0(X11,X13),slsdtgt0(xc))
& aElementOf0(X13,slsdtgt0(xc)) ) )
& aElementOf0(X11,slsdtgt0(xc)) )
& ! [X9] :
( aElementOf0(X9,slsdtgt0(xc))
<=> ? [X10] :
( sdtasdt0(xc,X10) = X9
& aElement0(X10) ) )
& aSet0(slsdtgt0(xc))
& ! [X0,X1,X2] :
( ? [X5] :
( ? [X6] :
( aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
& ? [X7] :
( sdtasdt0(X2,X0) = sdtasdt0(xc,X7)
& aElement0(X7) )
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& ? [X8] :
( sdtpldt0(X0,X1) = sdtasdt0(xc,X8)
& aElement0(X8) )
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X5,X2))
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X5,X6))
& sdtasdt0(xc,X6) = X1
& aElement0(X6) )
& sdtasdt0(xc,X5) = X0
& aElement0(X5) )
| ~ aElement0(X2)
| ( ~ aElementOf0(X1,slsdtgt0(xc))
& ! [X3] :
( sdtasdt0(xc,X3) != X1
| ~ aElement0(X3) ) )
| ( ~ aElementOf0(X0,slsdtgt0(xc))
& ! [X4] :
( sdtasdt0(xc,X4) != X0
| ~ aElement0(X4) ) ) ) ),
inference(ennf_transformation,[],[f48]) ).
fof(f100,plain,
( ~ aIdeal0(slsdtgt0(xc))
& ? [X11] :
( ( ? [X12] :
( ~ aElementOf0(sdtasdt0(X12,X11),slsdtgt0(xc))
& aElement0(X12) )
| ? [X13] :
( ~ aElementOf0(sdtpldt0(X11,X13),slsdtgt0(xc))
& aElementOf0(X13,slsdtgt0(xc)) ) )
& aElementOf0(X11,slsdtgt0(xc)) )
& ! [X9] :
( aElementOf0(X9,slsdtgt0(xc))
<=> ? [X10] :
( sdtasdt0(xc,X10) = X9
& aElement0(X10) ) )
& aSet0(slsdtgt0(xc))
& ! [X0,X1,X2] :
( ? [X5] :
( ? [X6] :
( aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
& ? [X7] :
( sdtasdt0(X2,X0) = sdtasdt0(xc,X7)
& aElement0(X7) )
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& ? [X8] :
( sdtpldt0(X0,X1) = sdtasdt0(xc,X8)
& aElement0(X8) )
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X5,X2))
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X5,X6))
& sdtasdt0(xc,X6) = X1
& aElement0(X6) )
& sdtasdt0(xc,X5) = X0
& aElement0(X5) )
| ~ aElement0(X2)
| ( ~ aElementOf0(X1,slsdtgt0(xc))
& ! [X3] :
( sdtasdt0(xc,X3) != X1
| ~ aElement0(X3) ) )
| ( ~ aElementOf0(X0,slsdtgt0(xc))
& ! [X4] :
( sdtasdt0(xc,X4) != X0
| ~ aElement0(X4) ) ) ) ),
inference(flattening,[],[f99]) ).
fof(f104,plain,
! [X1,X0] :
( ? [X8] :
( sdtpldt0(X0,X1) = sdtasdt0(xc,X8)
& aElement0(X8) )
| ~ sP2(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f105,plain,
! [X0,X2] :
( ? [X7] :
( sdtasdt0(X2,X0) = sdtasdt0(xc,X7)
& aElement0(X7) )
| ~ sP3(X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f106,plain,
! [X0,X2,X1,X5] :
( ? [X6] :
( aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
& sP3(X0,X2)
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& sP2(X1,X0)
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X5,X2))
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X5,X6))
& sdtasdt0(xc,X6) = X1
& aElement0(X6) )
| ~ sP4(X0,X2,X1,X5) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f107,plain,
! [X1,X2,X0] :
( ? [X5] :
( sP4(X0,X2,X1,X5)
& sdtasdt0(xc,X5) = X0
& aElement0(X5) )
| ~ sP5(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f108,plain,
( ~ aIdeal0(slsdtgt0(xc))
& ? [X11] :
( ( ? [X12] :
( ~ aElementOf0(sdtasdt0(X12,X11),slsdtgt0(xc))
& aElement0(X12) )
| ? [X13] :
( ~ aElementOf0(sdtpldt0(X11,X13),slsdtgt0(xc))
& aElementOf0(X13,slsdtgt0(xc)) ) )
& aElementOf0(X11,slsdtgt0(xc)) )
& ! [X9] :
( aElementOf0(X9,slsdtgt0(xc))
<=> ? [X10] :
( sdtasdt0(xc,X10) = X9
& aElement0(X10) ) )
& aSet0(slsdtgt0(xc))
& ! [X0,X1,X2] :
( sP5(X1,X2,X0)
| ~ aElement0(X2)
| ( ~ aElementOf0(X1,slsdtgt0(xc))
& ! [X3] :
( sdtasdt0(xc,X3) != X1
| ~ aElement0(X3) ) )
| ( ~ aElementOf0(X0,slsdtgt0(xc))
& ! [X4] :
( sdtasdt0(xc,X4) != X0
| ~ aElement0(X4) ) ) ) ),
inference(definition_folding,[],[f100,f107,f106,f105,f104]) ).
fof(f158,plain,
! [X1,X2,X0] :
( ? [X5] :
( sP4(X0,X2,X1,X5)
& sdtasdt0(xc,X5) = X0
& aElement0(X5) )
| ~ sP5(X1,X2,X0) ),
inference(nnf_transformation,[],[f107]) ).
fof(f159,plain,
! [X0,X1,X2] :
( ? [X3] :
( sP4(X2,X1,X0,X3)
& sdtasdt0(xc,X3) = X2
& aElement0(X3) )
| ~ sP5(X0,X1,X2) ),
inference(rectify,[],[f158]) ).
fof(f160,plain,
! [X0,X1,X2] :
( ? [X3] :
( sP4(X2,X1,X0,X3)
& sdtasdt0(xc,X3) = X2
& aElement0(X3) )
=> ( sP4(X2,X1,X0,sK26(X0,X1,X2))
& sdtasdt0(xc,sK26(X0,X1,X2)) = X2
& aElement0(sK26(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f161,plain,
! [X0,X1,X2] :
( ( sP4(X2,X1,X0,sK26(X0,X1,X2))
& sdtasdt0(xc,sK26(X0,X1,X2)) = X2
& aElement0(sK26(X0,X1,X2)) )
| ~ sP5(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f159,f160]) ).
fof(f162,plain,
! [X0,X2,X1,X5] :
( ? [X6] :
( aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
& sP3(X0,X2)
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& sP2(X1,X0)
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X5,X2))
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X5,X6))
& sdtasdt0(xc,X6) = X1
& aElement0(X6) )
| ~ sP4(X0,X2,X1,X5) ),
inference(nnf_transformation,[],[f106]) ).
fof(f163,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc))
& sP3(X0,X1)
& aElementOf0(sdtpldt0(X0,X2),slsdtgt0(xc))
& sP2(X2,X0)
& sdtasdt0(X1,X0) = sdtasdt0(xc,sdtasdt0(X3,X1))
& sdtasdt0(xc,sdtpldt0(X3,X4)) = sdtpldt0(X0,X2)
& sdtasdt0(xc,X4) = X2
& aElement0(X4) )
| ~ sP4(X0,X1,X2,X3) ),
inference(rectify,[],[f162]) ).
fof(f164,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc))
& sP3(X0,X1)
& aElementOf0(sdtpldt0(X0,X2),slsdtgt0(xc))
& sP2(X2,X0)
& sdtasdt0(X1,X0) = sdtasdt0(xc,sdtasdt0(X3,X1))
& sdtasdt0(xc,sdtpldt0(X3,X4)) = sdtpldt0(X0,X2)
& sdtasdt0(xc,X4) = X2
& aElement0(X4) )
=> ( aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc))
& sP3(X0,X1)
& aElementOf0(sdtpldt0(X0,X2),slsdtgt0(xc))
& sP2(X2,X0)
& sdtasdt0(X1,X0) = sdtasdt0(xc,sdtasdt0(X3,X1))
& sdtpldt0(X0,X2) = sdtasdt0(xc,sdtpldt0(X3,sK27(X0,X1,X2,X3)))
& sdtasdt0(xc,sK27(X0,X1,X2,X3)) = X2
& aElement0(sK27(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f165,plain,
! [X0,X1,X2,X3] :
( ( aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc))
& sP3(X0,X1)
& aElementOf0(sdtpldt0(X0,X2),slsdtgt0(xc))
& sP2(X2,X0)
& sdtasdt0(X1,X0) = sdtasdt0(xc,sdtasdt0(X3,X1))
& sdtpldt0(X0,X2) = sdtasdt0(xc,sdtpldt0(X3,sK27(X0,X1,X2,X3)))
& sdtasdt0(xc,sK27(X0,X1,X2,X3)) = X2
& aElement0(sK27(X0,X1,X2,X3)) )
| ~ sP4(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f163,f164]) ).
fof(f174,plain,
( ~ aIdeal0(slsdtgt0(xc))
& ? [X11] :
( ( ? [X12] :
( ~ aElementOf0(sdtasdt0(X12,X11),slsdtgt0(xc))
& aElement0(X12) )
| ? [X13] :
( ~ aElementOf0(sdtpldt0(X11,X13),slsdtgt0(xc))
& aElementOf0(X13,slsdtgt0(xc)) ) )
& aElementOf0(X11,slsdtgt0(xc)) )
& ! [X9] :
( ( aElementOf0(X9,slsdtgt0(xc))
| ! [X10] :
( sdtasdt0(xc,X10) != X9
| ~ aElement0(X10) ) )
& ( ? [X10] :
( sdtasdt0(xc,X10) = X9
& aElement0(X10) )
| ~ aElementOf0(X9,slsdtgt0(xc)) ) )
& aSet0(slsdtgt0(xc))
& ! [X0,X1,X2] :
( sP5(X1,X2,X0)
| ~ aElement0(X2)
| ( ~ aElementOf0(X1,slsdtgt0(xc))
& ! [X3] :
( sdtasdt0(xc,X3) != X1
| ~ aElement0(X3) ) )
| ( ~ aElementOf0(X0,slsdtgt0(xc))
& ! [X4] :
( sdtasdt0(xc,X4) != X0
| ~ aElement0(X4) ) ) ) ),
inference(nnf_transformation,[],[f108]) ).
fof(f175,plain,
( ~ aIdeal0(slsdtgt0(xc))
& ? [X0] :
( ( ? [X1] :
( ~ aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc))
& aElement0(X1) )
| ? [X2] :
( ~ aElementOf0(sdtpldt0(X0,X2),slsdtgt0(xc))
& aElementOf0(X2,slsdtgt0(xc)) ) )
& aElementOf0(X0,slsdtgt0(xc)) )
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xc))
| ! [X4] :
( sdtasdt0(xc,X4) != X3
| ~ aElement0(X4) ) )
& ( ? [X5] :
( sdtasdt0(xc,X5) = X3
& aElement0(X5) )
| ~ aElementOf0(X3,slsdtgt0(xc)) ) )
& aSet0(slsdtgt0(xc))
& ! [X6,X7,X8] :
( sP5(X7,X8,X6)
| ~ aElement0(X8)
| ( ~ aElementOf0(X7,slsdtgt0(xc))
& ! [X9] :
( sdtasdt0(xc,X9) != X7
| ~ aElement0(X9) ) )
| ( ~ aElementOf0(X6,slsdtgt0(xc))
& ! [X10] :
( sdtasdt0(xc,X10) != X6
| ~ aElement0(X10) ) ) ) ),
inference(rectify,[],[f174]) ).
fof(f176,plain,
( ? [X0] :
( ( ? [X1] :
( ~ aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc))
& aElement0(X1) )
| ? [X2] :
( ~ aElementOf0(sdtpldt0(X0,X2),slsdtgt0(xc))
& aElementOf0(X2,slsdtgt0(xc)) ) )
& aElementOf0(X0,slsdtgt0(xc)) )
=> ( ( ? [X1] :
( ~ aElementOf0(sdtasdt0(X1,sK30),slsdtgt0(xc))
& aElement0(X1) )
| ? [X2] :
( ~ aElementOf0(sdtpldt0(sK30,X2),slsdtgt0(xc))
& aElementOf0(X2,slsdtgt0(xc)) ) )
& aElementOf0(sK30,slsdtgt0(xc)) ) ),
introduced(choice_axiom,[]) ).
fof(f177,plain,
( ? [X1] :
( ~ aElementOf0(sdtasdt0(X1,sK30),slsdtgt0(xc))
& aElement0(X1) )
=> ( ~ aElementOf0(sdtasdt0(sK31,sK30),slsdtgt0(xc))
& aElement0(sK31) ) ),
introduced(choice_axiom,[]) ).
fof(f178,plain,
( ? [X2] :
( ~ aElementOf0(sdtpldt0(sK30,X2),slsdtgt0(xc))
& aElementOf0(X2,slsdtgt0(xc)) )
=> ( ~ aElementOf0(sdtpldt0(sK30,sK32),slsdtgt0(xc))
& aElementOf0(sK32,slsdtgt0(xc)) ) ),
introduced(choice_axiom,[]) ).
fof(f179,plain,
! [X3] :
( ? [X5] :
( sdtasdt0(xc,X5) = X3
& aElement0(X5) )
=> ( sdtasdt0(xc,sK33(X3)) = X3
& aElement0(sK33(X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f180,plain,
( ~ aIdeal0(slsdtgt0(xc))
& ( ( ~ aElementOf0(sdtasdt0(sK31,sK30),slsdtgt0(xc))
& aElement0(sK31) )
| ( ~ aElementOf0(sdtpldt0(sK30,sK32),slsdtgt0(xc))
& aElementOf0(sK32,slsdtgt0(xc)) ) )
& aElementOf0(sK30,slsdtgt0(xc))
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xc))
| ! [X4] :
( sdtasdt0(xc,X4) != X3
| ~ aElement0(X4) ) )
& ( ( sdtasdt0(xc,sK33(X3)) = X3
& aElement0(sK33(X3)) )
| ~ aElementOf0(X3,slsdtgt0(xc)) ) )
& aSet0(slsdtgt0(xc))
& ! [X6,X7,X8] :
( sP5(X7,X8,X6)
| ~ aElement0(X8)
| ( ~ aElementOf0(X7,slsdtgt0(xc))
& ! [X9] :
( sdtasdt0(xc,X9) != X7
| ~ aElement0(X9) ) )
| ( ~ aElementOf0(X6,slsdtgt0(xc))
& ! [X10] :
( sdtasdt0(xc,X10) != X6
| ~ aElement0(X10) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31,sK32,sK33])],[f175,f179,f178,f177,f176]) ).
fof(f182,plain,
aElement0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f194,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f270,plain,
aElement0(xc),
inference(cnf_transformation,[],[f38]) ).
fof(f273,plain,
! [X2,X0,X1] :
( sP4(X2,X1,X0,sK26(X0,X1,X2))
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f161]) ).
fof(f279,plain,
! [X2,X3,X0,X1] :
( aElementOf0(sdtpldt0(X0,X2),slsdtgt0(xc))
| ~ sP4(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f165]) ).
fof(f281,plain,
! [X2,X3,X0,X1] :
( aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc))
| ~ sP4(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f165]) ).
fof(f289,plain,
! [X8,X6,X7] :
( sP5(X7,X8,X6)
| ~ aElement0(X8)
| ~ aElementOf0(X7,slsdtgt0(xc))
| ~ aElementOf0(X6,slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f180]) ).
fof(f293,plain,
! [X3,X4] :
( aElementOf0(X3,slsdtgt0(xc))
| sdtasdt0(xc,X4) != X3
| ~ aElement0(X4) ),
inference(cnf_transformation,[],[f180]) ).
fof(f294,plain,
aElementOf0(sK30,slsdtgt0(xc)),
inference(cnf_transformation,[],[f180]) ).
fof(f295,plain,
( aElement0(sK31)
| aElementOf0(sK32,slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f180]) ).
fof(f296,plain,
( aElement0(sK31)
| ~ aElementOf0(sdtpldt0(sK30,sK32),slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f180]) ).
fof(f297,plain,
( ~ aElementOf0(sdtasdt0(sK31,sK30),slsdtgt0(xc))
| aElementOf0(sK32,slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f180]) ).
fof(f298,plain,
( ~ aElementOf0(sdtasdt0(sK31,sK30),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(sK30,sK32),slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f180]) ).
fof(f312,plain,
! [X4] :
( aElementOf0(sdtasdt0(xc,X4),slsdtgt0(xc))
| ~ aElement0(X4) ),
inference(equality_resolution,[],[f293]) ).
cnf(c_50,plain,
aElement0(sz10),
inference(cnf_transformation,[],[f182]) ).
cnf(c_63,plain,
( ~ aElement0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f194]) ).
cnf(c_138,plain,
aElement0(xc),
inference(cnf_transformation,[],[f270]) ).
cnf(c_139,plain,
( ~ sP5(X0,X1,X2)
| sP4(X2,X1,X0,sK26(X0,X1,X2)) ),
inference(cnf_transformation,[],[f273]) ).
cnf(c_142,plain,
( ~ sP4(X0,X1,X2,X3)
| aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f281]) ).
cnf(c_144,plain,
( ~ sP4(X0,X1,X2,X3)
| aElementOf0(sdtpldt0(X0,X2),slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f279]) ).
cnf(c_155,negated_conjecture,
( ~ aElementOf0(sdtpldt0(sK30,sK32),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(sK31,sK30),slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f298]) ).
cnf(c_156,negated_conjecture,
( ~ aElementOf0(sdtasdt0(sK31,sK30),slsdtgt0(xc))
| aElementOf0(sK32,slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f297]) ).
cnf(c_157,negated_conjecture,
( ~ aElementOf0(sdtpldt0(sK30,sK32),slsdtgt0(xc))
| aElement0(sK31) ),
inference(cnf_transformation,[],[f296]) ).
cnf(c_158,negated_conjecture,
( aElementOf0(sK32,slsdtgt0(xc))
| aElement0(sK31) ),
inference(cnf_transformation,[],[f295]) ).
cnf(c_159,negated_conjecture,
aElementOf0(sK30,slsdtgt0(xc)),
inference(cnf_transformation,[],[f294]) ).
cnf(c_160,negated_conjecture,
( ~ aElement0(X0)
| aElementOf0(sdtasdt0(xc,X0),slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f312]) ).
cnf(c_164,negated_conjecture,
( ~ aElementOf0(X0,slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElement0(X2)
| sP5(X1,X2,X0) ),
inference(cnf_transformation,[],[f289]) ).
cnf(c_304,plain,
( ~ sP5(X0,X1,X2)
| sP4(X2,X1,X0,sK26(X0,X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_139]) ).
cnf(c_310,plain,
( ~ sP4(X0,X1,X2,X3)
| aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc)) ),
inference(prop_impl_just,[status(thm)],[c_142]) ).
cnf(c_314,plain,
( ~ sP4(X0,X1,X2,X3)
| aElementOf0(sdtpldt0(X0,X2),slsdtgt0(xc)) ),
inference(prop_impl_just,[status(thm)],[c_144]) ).
cnf(c_551,plain,
( sK26(X0,X1,X2) != X3
| X0 != X4
| X1 != X5
| X2 != X6
| ~ sP5(X0,X1,X2)
| aElementOf0(sdtpldt0(X6,X4),slsdtgt0(xc)) ),
inference(resolution_lifted,[status(thm)],[c_304,c_314]) ).
cnf(c_552,plain,
( ~ sP5(X0,X1,X2)
| aElementOf0(sdtpldt0(X2,X0),slsdtgt0(xc)) ),
inference(unflattening,[status(thm)],[c_551]) ).
cnf(c_560,plain,
( sK26(X0,X1,X2) != X3
| X0 != X4
| X1 != X5
| X2 != X6
| ~ sP5(X0,X1,X2)
| aElementOf0(sdtasdt0(X5,X6),slsdtgt0(xc)) ),
inference(resolution_lifted,[status(thm)],[c_304,c_310]) ).
cnf(c_561,plain,
( ~ sP5(X0,X1,X2)
| aElementOf0(sdtasdt0(X1,X2),slsdtgt0(xc)) ),
inference(unflattening,[status(thm)],[c_560]) ).
cnf(c_2732,plain,
( ~ sP5(X0,X1,X2)
| aElementOf0(sdtpldt0(X2,X0),slsdtgt0(xc)) ),
inference(prop_impl_just,[status(thm)],[c_552]) ).
cnf(c_2734,plain,
( ~ sP5(X0,X1,X2)
| aElementOf0(sdtasdt0(X1,X2),slsdtgt0(xc)) ),
inference(prop_impl_just,[status(thm)],[c_561]) ).
cnf(c_5125,plain,
sdtasdt0(xc,sz10) = xc,
inference(superposition,[status(thm)],[c_138,c_63]) ).
cnf(c_5874,plain,
( ~ sP5(X0,sK31,sK30)
| aElementOf0(sdtasdt0(sK31,sK30),slsdtgt0(xc)) ),
inference(instantiation,[status(thm)],[c_2734]) ).
cnf(c_5875,plain,
( ~ sP5(xc,sK31,sK30)
| aElementOf0(sdtasdt0(sK31,sK30),slsdtgt0(xc)) ),
inference(instantiation,[status(thm)],[c_5874]) ).
cnf(c_5991,plain,
( ~ sP5(sK32,X0,sK30)
| aElementOf0(sdtpldt0(sK30,sK32),slsdtgt0(xc)) ),
inference(instantiation,[status(thm)],[c_2732]) ).
cnf(c_5992,plain,
( ~ sP5(sK32,xc,sK30)
| aElementOf0(sdtpldt0(sK30,sK32),slsdtgt0(xc)) ),
inference(instantiation,[status(thm)],[c_5991]) ).
cnf(c_6963,plain,
( ~ aElementOf0(X0,slsdtgt0(xc))
| ~ aElementOf0(sK32,slsdtgt0(xc))
| ~ aElement0(X1)
| sP5(sK32,X1,X0) ),
inference(instantiation,[status(thm)],[c_164]) ).
cnf(c_10734,plain,
( ~ aElementOf0(X0,slsdtgt0(xc))
| ~ aElementOf0(sK30,slsdtgt0(xc))
| ~ aElement0(sK31)
| sP5(X0,sK31,sK30) ),
inference(instantiation,[status(thm)],[c_164]) ).
cnf(c_10735,plain,
( ~ aElementOf0(xc,slsdtgt0(xc))
| ~ aElementOf0(sK30,slsdtgt0(xc))
| ~ aElement0(sK31)
| sP5(xc,sK31,sK30) ),
inference(instantiation,[status(thm)],[c_10734]) ).
cnf(c_12620,plain,
( ~ aElement0(sz10)
| aElementOf0(xc,slsdtgt0(xc)) ),
inference(superposition,[status(thm)],[c_5125,c_160]) ).
cnf(c_12691,plain,
( ~ aElementOf0(sK30,slsdtgt0(xc))
| ~ aElementOf0(sK32,slsdtgt0(xc))
| ~ aElement0(X0)
| sP5(sK32,X0,sK30) ),
inference(instantiation,[status(thm)],[c_6963]) ).
cnf(c_12692,plain,
( ~ aElementOf0(sK30,slsdtgt0(xc))
| ~ aElementOf0(sK32,slsdtgt0(xc))
| ~ aElement0(xc)
| sP5(sK32,xc,sK30) ),
inference(instantiation,[status(thm)],[c_12691]) ).
cnf(c_12693,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_12692,c_12620,c_10735,c_5992,c_5875,c_155,c_156,c_157,c_158,c_159,c_50,c_138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG106+2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 2 20:50:21 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.04/1.70 % SZS status Started for theBenchmark.p
% 8.04/1.70 % SZS status Theorem for theBenchmark.p
% 8.04/1.70
% 8.04/1.70 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 8.04/1.70
% 8.04/1.70 ------ iProver source info
% 8.04/1.70
% 8.04/1.70 git: date: 2024-05-02 19:28:25 +0000
% 8.04/1.70 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 8.04/1.70 git: non_committed_changes: false
% 8.04/1.70
% 8.04/1.70 ------ Parsing...
% 8.04/1.70 ------ Clausification by vclausify_rel & Parsing by iProver...
% 8.04/1.70
% 8.04/1.70 ------ Preprocessing... sup_sim: 0 pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 pe_s pe_e
% 8.04/1.70
% 8.04/1.70 ------ Preprocessing... gs_s sp: 0 0s gs_e scvd_s sp: 1 0s scvd_e snvd_s sp: 0 0s snvd_e
% 8.04/1.70
% 8.04/1.70 ------ Preprocessing...
% 8.04/1.70 ------ Proving...
% 8.04/1.70 ------ Problem Properties
% 8.04/1.70
% 8.04/1.70
% 8.04/1.70 clauses 112
% 8.04/1.70 conjectures 14
% 8.04/1.70 EPR 14
% 8.04/1.70 Horn 87
% 8.04/1.70 unary 7
% 8.04/1.70 binary 33
% 8.04/1.70 lits 379
% 8.04/1.70 lits eq 49
% 8.04/1.70 fd_pure 0
% 8.04/1.70 fd_pseudo 0
% 8.04/1.70 fd_cond 3
% 8.04/1.70 fd_pseudo_cond 11
% 8.04/1.70 AC symbols 0
% 8.04/1.70
% 8.04/1.70 ------ Input Options Time Limit: Unbounded
% 8.04/1.70
% 8.04/1.70
% 8.04/1.70 ------
% 8.04/1.70 Current options:
% 8.04/1.70 ------
% 8.04/1.70
% 8.04/1.70
% 8.04/1.70
% 8.04/1.70
% 8.04/1.70 ------ Proving...
% 8.04/1.70
% 8.04/1.70
% 8.04/1.70 % SZS status Theorem for theBenchmark.p
% 8.04/1.70
% 8.04/1.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.04/1.71
% 8.04/1.71
%------------------------------------------------------------------------------