TSTP Solution File: LCL688+1.001 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL688+1.001 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n016.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 : Tue Apr 30 13:48:58 EDT 2024
% Result : Theorem 2.58s 0.72s
% Output : Refutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 21
% Syntax : Number of formulae : 82 ( 11 unt; 0 def)
% Number of atoms : 736 ( 0 equ)
% Maximal formula atoms : 54 ( 8 avg)
% Number of connectives : 1254 ( 600 ~; 455 |; 182 &)
% ( 4 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 5 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-1 aty)
% Number of variables : 428 ( 331 !; 97 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15559,plain,
$false,
inference(avatar_sat_refutation,[],[f426,f1145,f5419,f15530,f15558]) ).
fof(f15558,plain,
~ spl15_1257,
inference(avatar_contradiction_clause,[],[f15557]) ).
fof(f15557,plain,
( $false
| ~ spl15_1257 ),
inference(subsumption_resolution,[],[f15552,f79]) ).
fof(f79,plain,
sP0(sK7),
inference(resolution,[],[f47,f55]) ).
fof(f55,plain,
r1(sK5,sK7),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
( ! [X1] :
( ( p1(sK6(X1))
& r1(X1,sK6(X1)) )
| ! [X3] :
( ! [X4] :
( ~ p1(X4)
| ~ r1(X3,X4) )
| ~ r1(X1,X3) )
| ~ r1(sK5,X1) )
& ! [X6] :
( ( ~ p2(sK8(X6))
& r1(X6,sK8(X6)) )
| ~ r1(sK7,X6) )
& r1(sK5,sK7)
& ~ p1(sK10)
& r1(sK9,sK10)
& ! [X11] :
( p1(X11)
| ~ r1(sK11,X11) )
& r1(sK9,sK11)
& r1(sK5,sK9)
& ( sP1(sK5)
| ! [X12] :
( ( ~ p1(sK12(X12))
& r1(X12,sK12(X12)) )
| ~ r1(sK5,X12) )
| p1(sK5) )
& ! [X14] :
( ( sP0(X14)
& ! [X15] :
( ( p2(sK13(X15))
& r1(sK13(X15),sK14(X15))
& r1(X15,sK13(X15)) )
| ~ r1(X14,X15) ) )
| ~ r1(sK5,X14) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14])],[f25,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26]) ).
fof(f26,plain,
( ? [X0] :
( ! [X1] :
( ? [X2] :
( p1(X2)
& r1(X1,X2) )
| ! [X3] :
( ! [X4] :
( ~ p1(X4)
| ~ r1(X3,X4) )
| ~ r1(X1,X3) )
| ~ r1(X0,X1) )
& ? [X5] :
( ! [X6] :
( ? [X7] :
( ~ p2(X7)
& r1(X6,X7) )
| ~ r1(X5,X6) )
& r1(X0,X5) )
& ? [X8] :
( ? [X9] :
( ~ p1(X9)
& r1(X8,X9) )
& ? [X10] :
( ! [X11] :
( p1(X11)
| ~ r1(X10,X11) )
& r1(X8,X10) )
& r1(X0,X8) )
& ( sP1(X0)
| ! [X12] :
( ? [X13] :
( ~ p1(X13)
& r1(X12,X13) )
| ~ r1(X0,X12) )
| p1(X0) )
& ! [X14] :
( ( sP0(X14)
& ! [X15] :
( ? [X16] :
( p2(X16)
& ? [X17] : r1(X16,X17)
& r1(X15,X16) )
| ~ r1(X14,X15) ) )
| ~ r1(X0,X14) ) )
=> ( ! [X1] :
( ? [X2] :
( p1(X2)
& r1(X1,X2) )
| ! [X3] :
( ! [X4] :
( ~ p1(X4)
| ~ r1(X3,X4) )
| ~ r1(X1,X3) )
| ~ r1(sK5,X1) )
& ? [X5] :
( ! [X6] :
( ? [X7] :
( ~ p2(X7)
& r1(X6,X7) )
| ~ r1(X5,X6) )
& r1(sK5,X5) )
& ? [X8] :
( ? [X9] :
( ~ p1(X9)
& r1(X8,X9) )
& ? [X10] :
( ! [X11] :
( p1(X11)
| ~ r1(X10,X11) )
& r1(X8,X10) )
& r1(sK5,X8) )
& ( sP1(sK5)
| ! [X12] :
( ? [X13] :
( ~ p1(X13)
& r1(X12,X13) )
| ~ r1(sK5,X12) )
| p1(sK5) )
& ! [X14] :
( ( sP0(X14)
& ! [X15] :
( ? [X16] :
( p2(X16)
& ? [X17] : r1(X16,X17)
& r1(X15,X16) )
| ~ r1(X14,X15) ) )
| ~ r1(sK5,X14) ) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X1] :
( ? [X2] :
( p1(X2)
& r1(X1,X2) )
=> ( p1(sK6(X1))
& r1(X1,sK6(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
( ? [X5] :
( ! [X6] :
( ? [X7] :
( ~ p2(X7)
& r1(X6,X7) )
| ~ r1(X5,X6) )
& r1(sK5,X5) )
=> ( ! [X6] :
( ? [X7] :
( ~ p2(X7)
& r1(X6,X7) )
| ~ r1(sK7,X6) )
& r1(sK5,sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X6] :
( ? [X7] :
( ~ p2(X7)
& r1(X6,X7) )
=> ( ~ p2(sK8(X6))
& r1(X6,sK8(X6)) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
( ? [X8] :
( ? [X9] :
( ~ p1(X9)
& r1(X8,X9) )
& ? [X10] :
( ! [X11] :
( p1(X11)
| ~ r1(X10,X11) )
& r1(X8,X10) )
& r1(sK5,X8) )
=> ( ? [X9] :
( ~ p1(X9)
& r1(sK9,X9) )
& ? [X10] :
( ! [X11] :
( p1(X11)
| ~ r1(X10,X11) )
& r1(sK9,X10) )
& r1(sK5,sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
( ? [X9] :
( ~ p1(X9)
& r1(sK9,X9) )
=> ( ~ p1(sK10)
& r1(sK9,sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
( ? [X10] :
( ! [X11] :
( p1(X11)
| ~ r1(X10,X11) )
& r1(sK9,X10) )
=> ( ! [X11] :
( p1(X11)
| ~ r1(sK11,X11) )
& r1(sK9,sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
! [X12] :
( ? [X13] :
( ~ p1(X13)
& r1(X12,X13) )
=> ( ~ p1(sK12(X12))
& r1(X12,sK12(X12)) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
! [X15] :
( ? [X16] :
( p2(X16)
& ? [X17] : r1(X16,X17)
& r1(X15,X16) )
=> ( p2(sK13(X15))
& ? [X17] : r1(sK13(X15),X17)
& r1(X15,sK13(X15)) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
! [X15] :
( ? [X17] : r1(sK13(X15),X17)
=> r1(sK13(X15),sK14(X15)) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
? [X0] :
( ! [X1] :
( ? [X2] :
( p1(X2)
& r1(X1,X2) )
| ! [X3] :
( ! [X4] :
( ~ p1(X4)
| ~ r1(X3,X4) )
| ~ r1(X1,X3) )
| ~ r1(X0,X1) )
& ? [X5] :
( ! [X6] :
( ? [X7] :
( ~ p2(X7)
& r1(X6,X7) )
| ~ r1(X5,X6) )
& r1(X0,X5) )
& ? [X8] :
( ? [X9] :
( ~ p1(X9)
& r1(X8,X9) )
& ? [X10] :
( ! [X11] :
( p1(X11)
| ~ r1(X10,X11) )
& r1(X8,X10) )
& r1(X0,X8) )
& ( sP1(X0)
| ! [X12] :
( ? [X13] :
( ~ p1(X13)
& r1(X12,X13) )
| ~ r1(X0,X12) )
| p1(X0) )
& ! [X14] :
( ( sP0(X14)
& ! [X15] :
( ? [X16] :
( p2(X16)
& ? [X17] : r1(X16,X17)
& r1(X15,X16) )
| ~ r1(X14,X15) ) )
| ~ r1(X0,X14) ) ),
inference(rectify,[],[f15]) ).
fof(f15,plain,
? [X0] :
( ! [X1] :
( ? [X2] :
( p1(X2)
& r1(X1,X2) )
| ! [X3] :
( ! [X4] :
( ~ p1(X4)
| ~ r1(X3,X4) )
| ~ r1(X1,X3) )
| ~ r1(X0,X1) )
& ? [X5] :
( ! [X6] :
( ? [X7] :
( ~ p2(X7)
& r1(X6,X7) )
| ~ r1(X5,X6) )
& r1(X0,X5) )
& ? [X8] :
( ? [X9] :
( ~ p1(X9)
& r1(X8,X9) )
& ? [X10] :
( ! [X11] :
( p1(X11)
| ~ r1(X10,X11) )
& r1(X8,X10) )
& r1(X0,X8) )
& ( sP1(X0)
| ! [X15] :
( ? [X16] :
( ~ p1(X16)
& r1(X15,X16) )
| ~ r1(X0,X15) )
| p1(X0) )
& ! [X17] :
( ( sP0(X17)
& ! [X24] :
( ? [X25] :
( p2(X25)
& ? [X26] : r1(X25,X26)
& r1(X24,X25) )
| ~ r1(X17,X24) ) )
| ~ r1(X0,X17) ) ),
inference(definition_folding,[],[f10,f14,f13]) ).
fof(f13,plain,
! [X17] :
( ! [X18] :
( ! [X19] :
( ? [X20] :
( ! [X21] :
( ~ p2(X21)
| ~ r1(X20,X21) )
& r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ p2(X18)
| ! [X22] :
( ( p2(X22)
& ? [X23] : r1(X22,X23) )
| ~ r1(X18,X22) )
| ~ r1(X17,X18) )
| ~ sP0(X17) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f14,plain,
! [X0] :
( ? [X12] :
( ! [X13] :
( ~ p1(X13)
| ! [X14] :
( p1(X14)
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
& ~ p1(X12)
& r1(X0,X12) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f10,plain,
? [X0] :
( ! [X1] :
( ? [X2] :
( p1(X2)
& r1(X1,X2) )
| ! [X3] :
( ! [X4] :
( ~ p1(X4)
| ~ r1(X3,X4) )
| ~ r1(X1,X3) )
| ~ r1(X0,X1) )
& ? [X5] :
( ! [X6] :
( ? [X7] :
( ~ p2(X7)
& r1(X6,X7) )
| ~ r1(X5,X6) )
& r1(X0,X5) )
& ? [X8] :
( ? [X9] :
( ~ p1(X9)
& r1(X8,X9) )
& ? [X10] :
( ! [X11] :
( p1(X11)
| ~ r1(X10,X11) )
& r1(X8,X10) )
& r1(X0,X8) )
& ( ? [X12] :
( ! [X13] :
( ~ p1(X13)
| ! [X14] :
( p1(X14)
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
& ~ p1(X12)
& r1(X0,X12) )
| ! [X15] :
( ? [X16] :
( ~ p1(X16)
& r1(X15,X16) )
| ~ r1(X0,X15) )
| p1(X0) )
& ! [X17] :
( ( ! [X18] :
( ! [X19] :
( ? [X20] :
( ! [X21] :
( ~ p2(X21)
| ~ r1(X20,X21) )
& r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ p2(X18)
| ! [X22] :
( ( p2(X22)
& ? [X23] : r1(X22,X23) )
| ~ r1(X18,X22) )
| ~ r1(X17,X18) )
& ! [X24] :
( ? [X25] :
( p2(X25)
& ? [X26] : r1(X25,X26)
& r1(X24,X25) )
| ~ r1(X17,X24) ) )
| ~ r1(X0,X17) ) ),
inference(flattening,[],[f9]) ).
fof(f9,plain,
? [X0] :
( ! [X1] :
( ? [X2] :
( p1(X2)
& r1(X1,X2) )
| ! [X3] :
( ! [X4] :
( ~ p1(X4)
| ~ r1(X3,X4) )
| ~ r1(X1,X3) )
| ~ r1(X0,X1) )
& ? [X5] :
( ! [X6] :
( ? [X7] :
( ~ p2(X7)
& r1(X6,X7) )
| ~ r1(X5,X6) )
& r1(X0,X5) )
& ? [X8] :
( ? [X9] :
( ~ p1(X9)
& r1(X8,X9) )
& ? [X10] :
( ! [X11] :
( p1(X11)
| ~ r1(X10,X11) )
& r1(X8,X10) )
& r1(X0,X8) )
& ( ? [X12] :
( ! [X13] :
( ~ p1(X13)
| ! [X14] :
( p1(X14)
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
& ~ p1(X12)
& r1(X0,X12) )
| ! [X15] :
( ? [X16] :
( ~ p1(X16)
& r1(X15,X16) )
| ~ r1(X0,X15) )
| p1(X0) )
& ! [X17] :
( ( ! [X18] :
( ! [X19] :
( ? [X20] :
( ! [X21] :
( ~ p2(X21)
| ~ r1(X20,X21) )
& r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ p2(X18)
| ! [X22] :
( ( p2(X22)
& ? [X23] : r1(X22,X23) )
| ~ r1(X18,X22) )
| ~ r1(X17,X18) )
& ! [X24] :
( ? [X25] :
( p2(X25)
& ? [X26] : r1(X25,X26)
& r1(X24,X25) )
| ~ r1(X17,X24) ) )
| ~ r1(X0,X17) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ ! [X2] :
( ~ p1(X2)
| ~ r1(X1,X2) )
| ! [X3] :
( ! [X4] :
( ~ p1(X4)
| ~ r1(X3,X4) )
| ~ r1(X1,X3) )
| ~ r1(X0,X1) )
| ! [X5] :
( ~ ! [X6] :
( ~ ! [X7] :
( p2(X7)
| ~ r1(X6,X7) )
| ~ r1(X5,X6) )
| ~ r1(X0,X5) )
| ! [X8] :
( ! [X9] :
( p1(X9)
| ~ r1(X8,X9) )
| ! [X10] :
( ~ ! [X11] :
( p1(X11)
| ~ r1(X10,X11) )
| ~ r1(X8,X10) )
| ~ r1(X0,X8) )
| ( ! [X12] :
( ~ ! [X13] :
( ~ ( p1(X13)
& ~ ! [X14] :
( p1(X14)
| ~ r1(X13,X14) ) )
| ~ r1(X12,X13) )
| p1(X12)
| ~ r1(X0,X12) )
& ~ ! [X15] :
( ~ ! [X16] :
( p1(X16)
| ~ r1(X15,X16) )
| ~ r1(X0,X15) )
& ~ p1(X0) )
| ~ ! [X17] :
( ~ ( ~ ! [X18] :
( ~ ( ~ ! [X19] :
( ~ ! [X20] :
( ~ ! [X21] :
( ~ p2(X21)
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
& p2(X18)
& ~ ! [X22] :
( ~ ( ~ p2(X22)
| ! [X23] : ~ r1(X22,X23) )
| ~ r1(X18,X22) ) )
| ~ r1(X17,X18) )
| ~ ! [X24] :
( ~ ! [X25] :
( ~ p2(X25)
| ! [X26] : ~ r1(X25,X26)
| ~ r1(X24,X25) )
| ~ r1(X17,X24) ) )
| ~ r1(X0,X17) ) ),
inference(pure_predicate_removal,[],[f7]) ).
fof(f7,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ ! [X2] :
( ~ p1(X2)
| ~ r1(X1,X2) )
| ! [X3] :
( ! [X4] :
( ~ p1(X4)
| ~ r1(X3,X4) )
| ~ r1(X1,X3) )
| ~ r1(X0,X1) )
| ! [X5] :
( ~ ! [X6] :
( ~ ! [X7] :
( p2(X7)
| ~ r1(X6,X7) )
| ~ r1(X5,X6) )
| ~ r1(X0,X5) )
| ! [X8] :
( ! [X9] :
( p1(X9)
| ~ r1(X8,X9) )
| ! [X10] :
( ~ ! [X11] :
( p1(X11)
| ~ r1(X10,X11) )
| ~ r1(X8,X10) )
| ~ r1(X0,X8) )
| ( ! [X12] :
( ~ ! [X13] :
( ~ ( p1(X13)
& ~ ! [X14] :
( p1(X14)
| ~ r1(X13,X14) ) )
| ~ r1(X12,X13) )
| p1(X12)
| ~ r1(X0,X12) )
& ~ ! [X15] :
( ~ ! [X16] :
( p1(X16)
| ~ r1(X15,X16) )
| ~ r1(X0,X15) )
& ~ p1(X0) )
| ~ ! [X17] :
( ~ ( ~ ! [X18] :
( ~ ( ~ ! [X19] :
( ~ ! [X20] :
( ~ ! [X21] :
( ~ p2(X21)
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
& p2(X18)
& ~ ! [X22] :
( ~ ( ~ p2(X22)
| ! [X23] : ~ r1(X22,X23) )
| ~ r1(X18,X22) ) )
| ~ r1(X17,X18) )
| ~ ! [X24] :
( ~ ! [X25] :
( ~ p2(X25)
| ! [X26] : ~ r1(X25,X26)
| ~ r1(X24,X25) )
| ~ r1(X17,X24) ) )
| ~ r1(X0,X17) )
| ~ ! [X27] :
( ~ p4(X27)
| ~ r1(X0,X27) ) ),
inference(pure_predicate_removal,[],[f6]) ).
fof(f6,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ ! [X2] :
( ~ p1(X2)
| ~ r1(X1,X2) )
| ! [X3] :
( ! [X4] :
( ~ p1(X4)
| ~ r1(X3,X4) )
| ~ r1(X1,X3) )
| ~ r1(X0,X1) )
| ! [X5] :
( ~ ! [X6] :
( ~ ! [X7] :
( p2(X7)
| ~ r1(X6,X7) )
| ~ r1(X5,X6) )
| ~ r1(X0,X5) )
| ! [X8] :
( ! [X9] :
( p1(X9)
| ~ r1(X8,X9) )
| ! [X10] :
( ~ ! [X11] :
( p1(X11)
| ~ r1(X10,X11) )
| ~ r1(X8,X10) )
| ~ r1(X0,X8) )
| ( ! [X12] :
( ~ ! [X13] :
( ~ ( p1(X13)
& ~ ! [X14] :
( p1(X14)
| ~ r1(X13,X14) ) )
| ~ r1(X12,X13) )
| p1(X12)
| ~ r1(X0,X12) )
& ~ ! [X15] :
( ~ ! [X16] :
( p1(X16)
| ~ r1(X15,X16) )
| ~ r1(X0,X15) )
& ~ p1(X0) )
| ~ ! [X17] :
( ~ ( ~ ! [X18] :
( ~ ( ~ ! [X19] :
( ~ ! [X20] :
( ~ ! [X21] :
( ~ p2(X21)
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
& p2(X18)
& ~ ! [X22] :
( ~ ( ~ p2(X22)
| ! [X23] :
( p3(X23)
| ~ r1(X22,X23) ) )
| ~ r1(X18,X22) ) )
| ~ r1(X17,X18) )
| ~ ! [X24] :
( ~ ! [X25] :
( ~ p2(X25)
| ! [X26] :
( p3(X26)
| ~ r1(X25,X26) )
| ~ r1(X24,X25) )
| ~ r1(X17,X24) ) )
| ~ r1(X0,X17) )
| ~ ! [X27] :
( ~ p4(X27)
| ~ r1(X0,X27) ) ),
inference(flattening,[],[f5]) ).
fof(f5,plain,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ ! [X2] :
( ~ p1(X2)
| ~ r1(X1,X2) )
| ! [X3] :
( ! [X4] :
( ~ p1(X4)
| ~ r1(X3,X4) )
| ~ r1(X1,X3) )
| ~ r1(X0,X1) )
| ! [X5] :
( ~ ! [X6] :
( ~ ! [X7] :
( p2(X7)
| ~ r1(X6,X7) )
| ~ r1(X5,X6) )
| ~ r1(X0,X5) )
| ! [X8] :
( ! [X9] :
( p1(X9)
| ~ r1(X8,X9) )
| ! [X10] :
( ~ ! [X11] :
( p1(X11)
| ~ r1(X10,X11) )
| ~ r1(X8,X10) )
| ~ r1(X0,X8) )
| ( ! [X12] :
( ~ ! [X13] :
( ~ ( p1(X13)
& ~ ! [X14] :
( p1(X14)
| ~ r1(X13,X14) ) )
| ~ r1(X12,X13) )
| p1(X12)
| ~ r1(X0,X12) )
& ~ ! [X15] :
( ~ ! [X16] :
( p1(X16)
| ~ r1(X15,X16) )
| ~ r1(X0,X15) )
& ~ p1(X0) )
| ~ ! [X17] :
( ~ ( ~ ! [X18] :
( ~ ( ~ ! [X19] :
( ~ ! [X20] :
( ~ ! [X21] :
( ~ p2(X21)
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
& p2(X18)
& ~ ! [X22] :
( ~ ( ~ p2(X22)
| ! [X23] :
( p3(X23)
| ~ r1(X22,X23) ) )
| ~ r1(X18,X22) ) )
| ~ r1(X17,X18) )
| ~ ! [X24] :
( ~ ! [X25] :
( ~ p2(X25)
| ! [X26] :
( p3(X26)
| ~ r1(X25,X26) )
| ~ r1(X24,X25) )
| ~ r1(X17,X24) ) )
| ~ r1(X0,X17) )
| ~ ! [X27] :
( ~ p4(X27)
| ~ r1(X0,X27) ) ),
inference(rectify,[],[f4]) ).
fof(f4,negated_conjecture,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ ! [X0] :
( ~ p1(X0)
| ~ r1(X1,X0) )
| ! [X0] :
( ! [X1] :
( ~ p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( ~ ! [X0] :
( ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ! [X0] :
( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ( ! [X1] :
( ~ ! [X0] :
( ~ ( p1(X0)
& ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ~ ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
& ~ p1(X0) )
| ~ ! [X1] :
( ~ ( ~ ! [X0] :
( ~ ( ~ ! [X1] :
( ~ ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
& p2(X0)
& ~ ! [X1] :
( ~ ( ~ p2(X1)
| ! [X0] :
( p3(X0)
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ~ ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ! [X0] :
( p3(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ p4(X1)
| ~ r1(X0,X1) ) ),
inference(negated_conjecture,[],[f3]) ).
fof(f3,conjecture,
~ ? [X0] :
~ ( ~ ! [X1] :
( ~ ! [X0] :
( ~ p1(X0)
| ~ r1(X1,X0) )
| ! [X0] :
( ! [X1] :
( ~ p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( ~ ! [X0] :
( ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ! [X0] :
( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ( ! [X1] :
( ~ ! [X0] :
( ~ ( p1(X0)
& ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ~ ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
& ~ p1(X0) )
| ~ ! [X1] :
( ~ ( ~ ! [X0] :
( ~ ( ~ ! [X1] :
( ~ ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
& p2(X0)
& ~ ! [X1] :
( ~ ( ~ p2(X1)
| ! [X0] :
( p3(X0)
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ~ ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ! [X0] :
( p3(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ p4(X1)
| ~ r1(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).
fof(f47,plain,
! [X14] :
( ~ r1(sK5,X14)
| sP0(X14) ),
inference(cnf_transformation,[],[f36]) ).
fof(f15552,plain,
( ~ sP0(sK7)
| ~ spl15_1257 ),
inference(resolution,[],[f15529,f162]) ).
fof(f162,plain,
r1(sK7,sK13(sK7)),
inference(resolution,[],[f101,f60]) ).
fof(f60,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] : r1(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
fof(f101,plain,
! [X0] :
( ~ r1(sK7,X0)
| r1(X0,sK13(X0)) ),
inference(resolution,[],[f44,f55]) ).
fof(f44,plain,
! [X14,X15] :
( ~ r1(sK5,X14)
| ~ r1(X14,X15)
| r1(X15,sK13(X15)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f15529,plain,
( ! [X0] :
( ~ r1(X0,sK13(sK7))
| ~ sP0(X0) )
| ~ spl15_1257 ),
inference(avatar_component_clause,[],[f15528]) ).
fof(f15528,plain,
( spl15_1257
<=> ! [X0] :
( ~ sP0(X0)
| ~ r1(X0,sK13(sK7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_1257])]) ).
fof(f15530,plain,
( spl15_14
| spl15_1257
| ~ spl15_497 ),
inference(avatar_split_clause,[],[f15526,f5222,f15528,f315]) ).
fof(f315,plain,
( spl15_14
<=> ! [X1] :
( p2(X1)
| ~ r1(sK13(sK7),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_14])]) ).
fof(f5222,plain,
( spl15_497
<=> ! [X2,X0,X1] :
( ~ r1(X0,sK13(sK7))
| ~ sP0(X2)
| ~ r1(X2,X0)
| ~ r1(X0,X1)
| p2(X1)
| ~ p2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_497])]) ).
fof(f15526,plain,
( ! [X0,X1] :
( ~ sP0(X0)
| ~ r1(X0,sK13(sK7))
| ~ r1(sK13(sK7),X1)
| p2(X1) )
| ~ spl15_497 ),
inference(subsumption_resolution,[],[f15523,f110]) ).
fof(f110,plain,
p2(sK13(sK7)),
inference(resolution,[],[f86,f60]) ).
fof(f86,plain,
! [X0] :
( ~ r1(sK7,X0)
| p2(sK13(X0)) ),
inference(resolution,[],[f46,f55]) ).
fof(f46,plain,
! [X14,X15] :
( ~ r1(sK5,X14)
| ~ r1(X14,X15)
| p2(sK13(X15)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f15523,plain,
( ! [X0,X1] :
( ~ sP0(X0)
| ~ r1(X0,sK13(sK7))
| ~ r1(sK13(sK7),X1)
| p2(X1)
| ~ p2(sK13(sK7)) )
| ~ spl15_497 ),
inference(resolution,[],[f5223,f60]) ).
fof(f5223,plain,
( ! [X2,X0,X1] :
( ~ r1(X0,sK13(sK7))
| ~ sP0(X2)
| ~ r1(X2,X0)
| ~ r1(X0,X1)
| p2(X1)
| ~ p2(X0) )
| ~ spl15_497 ),
inference(avatar_component_clause,[],[f5222]) ).
fof(f5419,plain,
( spl15_497
| ~ spl15_15 ),
inference(avatar_split_clause,[],[f5418,f318,f5222]) ).
fof(f318,plain,
( spl15_15
<=> ! [X0] :
( ~ r1(sK13(sK7),X0)
| r1(X0,sK3(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_15])]) ).
fof(f5418,plain,
( ! [X2,X0,X1] :
( ~ r1(X0,sK13(sK7))
| ~ p2(X0)
| p2(X1)
| ~ r1(X0,X1)
| ~ r1(X2,X0)
| ~ sP0(X2) )
| ~ spl15_15 ),
inference(subsumption_resolution,[],[f5414,f2155]) ).
fof(f2155,plain,
( p2(sK13(sK3(sK13(sK7))))
| ~ spl15_15 ),
inference(resolution,[],[f1937,f86]) ).
fof(f1937,plain,
( r1(sK7,sK3(sK13(sK7)))
| ~ spl15_15 ),
inference(resolution,[],[f1167,f187]) ).
fof(f187,plain,
! [X0] :
( ~ r1(sK13(sK7),X0)
| r1(sK7,X0) ),
inference(resolution,[],[f162,f61]) ).
fof(f61,plain,
! [X2,X0,X1] :
( ~ r1(X0,X1)
| ~ r1(X1,X2)
| r1(X0,X2) ),
inference(cnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X1,X2] :
( r1(X0,X2)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(flattening,[],[f11]) ).
fof(f11,plain,
! [X0,X1,X2] :
( r1(X0,X2)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( r1(X1,X2)
& r1(X0,X1) )
=> r1(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
fof(f1167,plain,
( r1(sK13(sK7),sK3(sK13(sK7)))
| ~ spl15_15 ),
inference(resolution,[],[f319,f60]) ).
fof(f319,plain,
( ! [X0] :
( ~ r1(sK13(sK7),X0)
| r1(X0,sK3(X0)) )
| ~ spl15_15 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f5414,plain,
( ! [X2,X0,X1] :
( ~ p2(sK13(sK3(sK13(sK7))))
| ~ r1(X0,sK13(sK7))
| ~ p2(X0)
| p2(X1)
| ~ r1(X0,X1)
| ~ r1(X2,X0)
| ~ sP0(X2) )
| ~ spl15_15 ),
inference(resolution,[],[f3093,f43]) ).
fof(f43,plain,
! [X2,X0,X1,X4,X5] :
( ~ r1(sK3(X2),X4)
| ~ p2(X4)
| ~ r1(X1,X2)
| ~ p2(X1)
| p2(X5)
| ~ r1(X1,X5)
| ~ r1(X0,X1)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ! [X4] :
( ~ p2(X4)
| ~ r1(sK3(X2),X4) )
& r1(X2,sK3(X2)) )
| ~ r1(X1,X2) )
| ~ p2(X1)
| ! [X5] :
( ( p2(X5)
& r1(X5,sK4(X5)) )
| ~ r1(X1,X5) )
| ~ r1(X0,X1) )
| ~ sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f21,f23,f22]) ).
fof(f22,plain,
! [X2] :
( ? [X3] :
( ! [X4] :
( ~ p2(X4)
| ~ r1(X3,X4) )
& r1(X2,X3) )
=> ( ! [X4] :
( ~ p2(X4)
| ~ r1(sK3(X2),X4) )
& r1(X2,sK3(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X5] :
( ? [X6] : r1(X5,X6)
=> r1(X5,sK4(X5)) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ? [X3] :
( ! [X4] :
( ~ p2(X4)
| ~ r1(X3,X4) )
& r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ p2(X1)
| ! [X5] :
( ( p2(X5)
& ? [X6] : r1(X5,X6) )
| ~ r1(X1,X5) )
| ~ r1(X0,X1) )
| ~ sP0(X0) ),
inference(rectify,[],[f20]) ).
fof(f20,plain,
! [X17] :
( ! [X18] :
( ! [X19] :
( ? [X20] :
( ! [X21] :
( ~ p2(X21)
| ~ r1(X20,X21) )
& r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ p2(X18)
| ! [X22] :
( ( p2(X22)
& ? [X23] : r1(X22,X23) )
| ~ r1(X18,X22) )
| ~ r1(X17,X18) )
| ~ sP0(X17) ),
inference(nnf_transformation,[],[f13]) ).
fof(f3093,plain,
( r1(sK3(sK13(sK7)),sK13(sK3(sK13(sK7))))
| ~ spl15_15 ),
inference(resolution,[],[f243,f1167]) ).
fof(f243,plain,
! [X0] :
( ~ r1(sK13(sK7),X0)
| r1(X0,sK13(X0)) ),
inference(resolution,[],[f184,f44]) ).
fof(f184,plain,
r1(sK5,sK13(sK7)),
inference(resolution,[],[f162,f92]) ).
fof(f92,plain,
! [X0] :
( ~ r1(sK7,X0)
| r1(sK5,X0) ),
inference(resolution,[],[f61,f55]) ).
fof(f1145,plain,
~ spl15_14,
inference(avatar_contradiction_clause,[],[f1144]) ).
fof(f1144,plain,
( $false
| ~ spl15_14 ),
inference(subsumption_resolution,[],[f1141,f162]) ).
fof(f1141,plain,
( ~ r1(sK7,sK13(sK7))
| ~ spl15_14 ),
inference(resolution,[],[f1139,f57]) ).
fof(f57,plain,
! [X6] :
( ~ p2(sK8(X6))
| ~ r1(sK7,X6) ),
inference(cnf_transformation,[],[f36]) ).
fof(f1139,plain,
( p2(sK8(sK13(sK7)))
| ~ spl15_14 ),
inference(resolution,[],[f316,f186]) ).
fof(f186,plain,
r1(sK13(sK7),sK8(sK13(sK7))),
inference(resolution,[],[f162,f56]) ).
fof(f56,plain,
! [X6] :
( ~ r1(sK7,X6)
| r1(X6,sK8(X6)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f316,plain,
( ! [X1] :
( ~ r1(sK13(sK7),X1)
| p2(X1) )
| ~ spl15_14 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f426,plain,
( spl15_15
| spl15_14 ),
inference(avatar_split_clause,[],[f425,f315,f318]) ).
fof(f425,plain,
! [X0,X1] :
( p2(X0)
| ~ r1(sK13(sK7),X0)
| ~ r1(sK13(sK7),X1)
| r1(X1,sK3(X1)) ),
inference(subsumption_resolution,[],[f412,f110]) ).
fof(f412,plain,
! [X0,X1] :
( ~ p2(sK13(sK7))
| p2(X0)
| ~ r1(sK13(sK7),X0)
| ~ r1(sK13(sK7),X1)
| r1(X1,sK3(X1)) ),
inference(resolution,[],[f115,f162]) ).
fof(f115,plain,
! [X2,X0,X1] :
( ~ r1(sK7,X0)
| ~ p2(X0)
| p2(X2)
| ~ r1(X0,X2)
| ~ r1(X0,X1)
| r1(X1,sK3(X1)) ),
inference(resolution,[],[f41,f79]) ).
fof(f41,plain,
! [X2,X0,X1,X5] :
( ~ sP0(X0)
| ~ r1(X1,X2)
| ~ p2(X1)
| p2(X5)
| ~ r1(X1,X5)
| ~ r1(X0,X1)
| r1(X2,sK3(X2)) ),
inference(cnf_transformation,[],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : LCL688+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n016.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Apr 29 23:21:25 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.10/0.32 % (20195)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.33 % (20196)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.10/0.33 % (20200)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.10/0.33 % (20197)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.10/0.33 % (20202)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.10/0.33 % (20198)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.10/0.33 % (20201)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.10/0.33 % (20199)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.10/0.33 TRYING [1]
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% 1.73/0.62 TRYING [9]
% 2.26/0.63 TRYING [10]
% 2.58/0.71 % (20201)First to succeed.
% 2.58/0.72 % (20201)Refutation found. Thanks to Tanya!
% 2.58/0.72 % SZS status Theorem for theBenchmark
% 2.58/0.72 % SZS output start Proof for theBenchmark
% See solution above
% 2.58/0.72 % (20201)------------------------------
% 2.58/0.72 % (20201)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 2.58/0.72 % (20201)Termination reason: Refutation
% 2.58/0.72
% 2.58/0.72 % (20201)Memory used [KB]: 5839
% 2.58/0.72 % (20201)Time elapsed: 0.382 s
% 2.58/0.72 % (20201)Instructions burned: 778 (million)
% 2.58/0.72 % (20201)------------------------------
% 2.58/0.72 % (20201)------------------------------
% 2.58/0.72 % (20195)Success in time 0.381 s
%------------------------------------------------------------------------------