TSTP Solution File: LCL672+1.001 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL672+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 : n007.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 13:47:35 EDT 2024
% Result : Theorem 0.11s 0.36s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 37
% Syntax : Number of formulae : 112 ( 15 unt; 0 def)
% Number of atoms : 810 ( 0 equ)
% Maximal formula atoms : 96 ( 7 avg)
% Number of connectives : 1306 ( 608 ~; 504 |; 159 &)
% ( 24 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 28 ( 27 usr; 21 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-1 aty)
% Number of variables : 405 ( 343 !; 62 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f860,plain,
$false,
inference(avatar_sat_refutation,[],[f156,f161,f166,f171,f197,f209,f349,f380,f446,f495,f513,f581,f639,f748,f753,f857,f859]) ).
fof(f859,plain,
( ~ spl39_62
| spl39_82 ),
inference(avatar_contradiction_clause,[],[f858]) ).
fof(f858,plain,
( $false
| ~ spl39_62
| spl39_82 ),
inference(resolution,[],[f856,f755]) ).
fof(f755,plain,
( sP34(sK2)
| ~ spl39_62 ),
inference(resolution,[],[f638,f36]) ).
fof(f36,plain,
r1(sK2,sK4),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
( ~ p1(sK1)
& r1(sK0,sK1)
& ~ p1(sK3)
& r1(sK2,sK3)
& ! [X5] :
( p1(X5)
| ~ r1(sK4,X5) )
& r1(sK2,sK4)
& r1(sK0,sK2)
& ~ p2(sK5)
& r1(sK0,sK5)
& ( ! [X7] :
( p1(X7)
| ~ r1(sK0,X7) )
| ! [X8] :
( r1(X8,sK6(X8))
| ~ r1(sK0,X8) )
| ! [X10] :
( p2(X10)
| ~ r1(sK0,X10) ) )
& ( ! [X11] :
( p1(X11)
| ~ r1(sK0,X11) )
| ! [X12] :
( ! [X13] :
( ( ~ p1(sK7(X13))
& r1(X13,sK7(X13)) )
| ~ r1(X12,X13) )
| ! [X15] :
( ( ! [X17] :
( p1(X17)
| ~ r1(sK8(X15),X17) )
& r1(X15,sK8(X15)) )
| ~ r1(X12,X15) )
| ~ r1(sK0,X12) )
| ! [X18] :
( p2(X18)
| ~ r1(sK0,X18) ) )
& ( ! [X19] :
( p1(X19)
| ~ r1(sK0,X19) )
| ! [X20] :
( ! [X21] :
( ! [X22] :
( p1(X22)
| ~ r1(X21,X22) )
| ! [X23] :
( ( ~ p1(sK9(X23))
& r1(X23,sK9(X23)) )
| ~ r1(X21,X23) )
| ~ r1(X20,X21) )
| ~ r1(sK0,X20) )
| ! [X25] :
( p2(X25)
| ~ r1(sK0,X25) ) )
& ( ! [X26] :
( p1(X26)
| ~ r1(sK0,X26) )
| ! [X27] :
( ~ p1(X27)
| ! [X28] :
( ( p1(sK10(X28))
& r1(X28,sK10(X28)) )
| ~ r1(X27,X28) )
| ~ r1(sK0,X27) )
| ! [X30] :
( p2(X30)
| ~ r1(sK0,X30) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10])],[f9,f22,f21,f20,f19,f18,f17,f16,f15,f14,f13,f12]) ).
fof(f12,plain,
( ? [X0] :
( ? [X1] :
( ~ p1(X1)
& r1(X0,X1) )
& ? [X2] :
( ? [X3] :
( ~ p1(X3)
& r1(X2,X3) )
& ? [X4] :
( ! [X5] :
( p1(X5)
| ~ r1(X4,X5) )
& r1(X2,X4) )
& r1(X0,X2) )
& ? [X6] :
( ~ p2(X6)
& r1(X0,X6) )
& ( ! [X7] :
( p1(X7)
| ~ r1(X0,X7) )
| ! [X8] :
( ? [X9] : r1(X8,X9)
| ~ r1(X0,X8) )
| ! [X10] :
( p2(X10)
| ~ r1(X0,X10) ) )
& ( ! [X11] :
( p1(X11)
| ~ r1(X0,X11) )
| ! [X12] :
( ! [X13] :
( ? [X14] :
( ~ p1(X14)
& r1(X13,X14) )
| ~ r1(X12,X13) )
| ! [X15] :
( ? [X16] :
( ! [X17] :
( p1(X17)
| ~ r1(X16,X17) )
& r1(X15,X16) )
| ~ r1(X12,X15) )
| ~ r1(X0,X12) )
| ! [X18] :
( p2(X18)
| ~ r1(X0,X18) ) )
& ( ! [X19] :
( p1(X19)
| ~ r1(X0,X19) )
| ! [X20] :
( ! [X21] :
( ! [X22] :
( p1(X22)
| ~ r1(X21,X22) )
| ! [X23] :
( ? [X24] :
( ~ p1(X24)
& r1(X23,X24) )
| ~ r1(X21,X23) )
| ~ r1(X20,X21) )
| ~ r1(X0,X20) )
| ! [X25] :
( p2(X25)
| ~ r1(X0,X25) ) )
& ( ! [X26] :
( p1(X26)
| ~ r1(X0,X26) )
| ! [X27] :
( ~ p1(X27)
| ! [X28] :
( ? [X29] :
( p1(X29)
& r1(X28,X29) )
| ~ r1(X27,X28) )
| ~ r1(X0,X27) )
| ! [X30] :
( p2(X30)
| ~ r1(X0,X30) ) ) )
=> ( ? [X1] :
( ~ p1(X1)
& r1(sK0,X1) )
& ? [X2] :
( ? [X3] :
( ~ p1(X3)
& r1(X2,X3) )
& ? [X4] :
( ! [X5] :
( p1(X5)
| ~ r1(X4,X5) )
& r1(X2,X4) )
& r1(sK0,X2) )
& ? [X6] :
( ~ p2(X6)
& r1(sK0,X6) )
& ( ! [X7] :
( p1(X7)
| ~ r1(sK0,X7) )
| ! [X8] :
( ? [X9] : r1(X8,X9)
| ~ r1(sK0,X8) )
| ! [X10] :
( p2(X10)
| ~ r1(sK0,X10) ) )
& ( ! [X11] :
( p1(X11)
| ~ r1(sK0,X11) )
| ! [X12] :
( ! [X13] :
( ? [X14] :
( ~ p1(X14)
& r1(X13,X14) )
| ~ r1(X12,X13) )
| ! [X15] :
( ? [X16] :
( ! [X17] :
( p1(X17)
| ~ r1(X16,X17) )
& r1(X15,X16) )
| ~ r1(X12,X15) )
| ~ r1(sK0,X12) )
| ! [X18] :
( p2(X18)
| ~ r1(sK0,X18) ) )
& ( ! [X19] :
( p1(X19)
| ~ r1(sK0,X19) )
| ! [X20] :
( ! [X21] :
( ! [X22] :
( p1(X22)
| ~ r1(X21,X22) )
| ! [X23] :
( ? [X24] :
( ~ p1(X24)
& r1(X23,X24) )
| ~ r1(X21,X23) )
| ~ r1(X20,X21) )
| ~ r1(sK0,X20) )
| ! [X25] :
( p2(X25)
| ~ r1(sK0,X25) ) )
& ( ! [X26] :
( p1(X26)
| ~ r1(sK0,X26) )
| ! [X27] :
( ~ p1(X27)
| ! [X28] :
( ? [X29] :
( p1(X29)
& r1(X28,X29) )
| ~ r1(X27,X28) )
| ~ r1(sK0,X27) )
| ! [X30] :
( p2(X30)
| ~ r1(sK0,X30) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f13,plain,
( ? [X1] :
( ~ p1(X1)
& r1(sK0,X1) )
=> ( ~ p1(sK1)
& r1(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
( ? [X2] :
( ? [X3] :
( ~ p1(X3)
& r1(X2,X3) )
& ? [X4] :
( ! [X5] :
( p1(X5)
| ~ r1(X4,X5) )
& r1(X2,X4) )
& r1(sK0,X2) )
=> ( ? [X3] :
( ~ p1(X3)
& r1(sK2,X3) )
& ? [X4] :
( ! [X5] :
( p1(X5)
| ~ r1(X4,X5) )
& r1(sK2,X4) )
& r1(sK0,sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
( ? [X3] :
( ~ p1(X3)
& r1(sK2,X3) )
=> ( ~ p1(sK3)
& r1(sK2,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
( ? [X4] :
( ! [X5] :
( p1(X5)
| ~ r1(X4,X5) )
& r1(sK2,X4) )
=> ( ! [X5] :
( p1(X5)
| ~ r1(sK4,X5) )
& r1(sK2,sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
( ? [X6] :
( ~ p2(X6)
& r1(sK0,X6) )
=> ( ~ p2(sK5)
& r1(sK0,sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X8] :
( ? [X9] : r1(X8,X9)
=> r1(X8,sK6(X8)) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
! [X13] :
( ? [X14] :
( ~ p1(X14)
& r1(X13,X14) )
=> ( ~ p1(sK7(X13))
& r1(X13,sK7(X13)) ) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
! [X15] :
( ? [X16] :
( ! [X17] :
( p1(X17)
| ~ r1(X16,X17) )
& r1(X15,X16) )
=> ( ! [X17] :
( p1(X17)
| ~ r1(sK8(X15),X17) )
& r1(X15,sK8(X15)) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
! [X23] :
( ? [X24] :
( ~ p1(X24)
& r1(X23,X24) )
=> ( ~ p1(sK9(X23))
& r1(X23,sK9(X23)) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X28] :
( ? [X29] :
( p1(X29)
& r1(X28,X29) )
=> ( p1(sK10(X28))
& r1(X28,sK10(X28)) ) ),
introduced(choice_axiom,[]) ).
fof(f9,plain,
? [X0] :
( ? [X1] :
( ~ p1(X1)
& r1(X0,X1) )
& ? [X2] :
( ? [X3] :
( ~ p1(X3)
& r1(X2,X3) )
& ? [X4] :
( ! [X5] :
( p1(X5)
| ~ r1(X4,X5) )
& r1(X2,X4) )
& r1(X0,X2) )
& ? [X6] :
( ~ p2(X6)
& r1(X0,X6) )
& ( ! [X7] :
( p1(X7)
| ~ r1(X0,X7) )
| ! [X8] :
( ? [X9] : r1(X8,X9)
| ~ r1(X0,X8) )
| ! [X10] :
( p2(X10)
| ~ r1(X0,X10) ) )
& ( ! [X11] :
( p1(X11)
| ~ r1(X0,X11) )
| ! [X12] :
( ! [X13] :
( ? [X14] :
( ~ p1(X14)
& r1(X13,X14) )
| ~ r1(X12,X13) )
| ! [X15] :
( ? [X16] :
( ! [X17] :
( p1(X17)
| ~ r1(X16,X17) )
& r1(X15,X16) )
| ~ r1(X12,X15) )
| ~ r1(X0,X12) )
| ! [X18] :
( p2(X18)
| ~ r1(X0,X18) ) )
& ( ! [X19] :
( p1(X19)
| ~ r1(X0,X19) )
| ! [X20] :
( ! [X21] :
( ! [X22] :
( p1(X22)
| ~ r1(X21,X22) )
| ! [X23] :
( ? [X24] :
( ~ p1(X24)
& r1(X23,X24) )
| ~ r1(X21,X23) )
| ~ r1(X20,X21) )
| ~ r1(X0,X20) )
| ! [X25] :
( p2(X25)
| ~ r1(X0,X25) ) )
& ( ! [X26] :
( p1(X26)
| ~ r1(X0,X26) )
| ! [X27] :
( ~ p1(X27)
| ! [X28] :
( ? [X29] :
( p1(X29)
& r1(X28,X29) )
| ~ r1(X27,X28) )
| ~ r1(X0,X27) )
| ! [X30] :
( p2(X30)
| ~ r1(X0,X30) ) ) ),
inference(flattening,[],[f8]) ).
fof(f8,plain,
? [X0] :
( ? [X1] :
( ~ p1(X1)
& r1(X0,X1) )
& ? [X2] :
( ? [X3] :
( ~ p1(X3)
& r1(X2,X3) )
& ? [X4] :
( ! [X5] :
( p1(X5)
| ~ r1(X4,X5) )
& r1(X2,X4) )
& r1(X0,X2) )
& ? [X6] :
( ~ p2(X6)
& r1(X0,X6) )
& ( ! [X7] :
( p1(X7)
| ~ r1(X0,X7) )
| ! [X8] :
( ? [X9] : r1(X8,X9)
| ~ r1(X0,X8) )
| ! [X10] :
( p2(X10)
| ~ r1(X0,X10) ) )
& ( ! [X11] :
( p1(X11)
| ~ r1(X0,X11) )
| ! [X12] :
( ! [X13] :
( ? [X14] :
( ~ p1(X14)
& r1(X13,X14) )
| ~ r1(X12,X13) )
| ! [X15] :
( ? [X16] :
( ! [X17] :
( p1(X17)
| ~ r1(X16,X17) )
& r1(X15,X16) )
| ~ r1(X12,X15) )
| ~ r1(X0,X12) )
| ! [X18] :
( p2(X18)
| ~ r1(X0,X18) ) )
& ( ! [X19] :
( p1(X19)
| ~ r1(X0,X19) )
| ! [X20] :
( ! [X21] :
( ! [X22] :
( p1(X22)
| ~ r1(X21,X22) )
| ! [X23] :
( ? [X24] :
( ~ p1(X24)
& r1(X23,X24) )
| ~ r1(X21,X23) )
| ~ r1(X20,X21) )
| ~ r1(X0,X20) )
| ! [X25] :
( p2(X25)
| ~ r1(X0,X25) ) )
& ( ! [X26] :
( p1(X26)
| ~ r1(X0,X26) )
| ! [X27] :
( ~ p1(X27)
| ! [X28] :
( ? [X29] :
( p1(X29)
& r1(X28,X29) )
| ~ r1(X27,X28) )
| ~ r1(X0,X27) )
| ! [X30] :
( p2(X30)
| ~ r1(X0,X30) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,plain,
? [X0] :
~ ( ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ! [X2] :
( ! [X3] :
( p1(X3)
| ~ r1(X2,X3) )
| ! [X4] :
( ~ ! [X5] :
( p1(X5)
| ~ r1(X4,X5) )
| ~ r1(X2,X4) )
| ~ r1(X0,X2) )
| ! [X6] :
( p2(X6)
| ~ r1(X0,X6) )
| ( ~ ! [X7] :
( p1(X7)
| ~ r1(X0,X7) )
& ~ ! [X8] :
( ~ ! [X9] : ~ r1(X8,X9)
| ~ r1(X0,X8) )
& ~ ! [X10] :
( p2(X10)
| ~ r1(X0,X10) ) )
| ( ~ ! [X11] :
( p1(X11)
| ~ r1(X0,X11) )
& ~ ! [X12] :
( ~ ( ~ ! [X13] :
( ~ ! [X14] :
( p1(X14)
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
& ~ ! [X15] :
( ~ ! [X16] :
( ~ ! [X17] :
( p1(X17)
| ~ r1(X16,X17) )
| ~ r1(X15,X16) )
| ~ r1(X12,X15) ) )
| ~ r1(X0,X12) )
& ~ ! [X18] :
( p2(X18)
| ~ r1(X0,X18) ) )
| ( ~ ! [X19] :
( p1(X19)
| ~ r1(X0,X19) )
& ~ ! [X20] :
( ! [X21] :
( ~ ( ~ ! [X22] :
( p1(X22)
| ~ r1(X21,X22) )
& ~ ! [X23] :
( ~ ! [X24] :
( p1(X24)
| ~ r1(X23,X24) )
| ~ r1(X21,X23) ) )
| ~ r1(X20,X21) )
| ~ r1(X0,X20) )
& ~ ! [X25] :
( p2(X25)
| ~ r1(X0,X25) ) )
| ( ~ ! [X26] :
( p1(X26)
| ~ r1(X0,X26) )
& ~ ! [X27] :
( ~ ( p1(X27)
& ~ ! [X28] :
( ~ ! [X29] :
( ~ p1(X29)
| ~ r1(X28,X29) )
| ~ r1(X27,X28) ) )
| ~ r1(X0,X27) )
& ~ ! [X30] :
( p2(X30)
| ~ r1(X0,X30) ) ) ),
inference(flattening,[],[f6]) ).
fof(f6,plain,
~ ~ ? [X0] :
~ ( ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ! [X2] :
( ! [X3] :
( p1(X3)
| ~ r1(X2,X3) )
| ! [X4] :
( ~ ! [X5] :
( p1(X5)
| ~ r1(X4,X5) )
| ~ r1(X2,X4) )
| ~ r1(X0,X2) )
| ! [X6] :
( p2(X6)
| ~ r1(X0,X6) )
| ( ~ ! [X7] :
( p1(X7)
| ~ r1(X0,X7) )
& ~ ! [X8] :
( ~ ! [X9] : ~ r1(X8,X9)
| ~ r1(X0,X8) )
& ~ ! [X10] :
( p2(X10)
| ~ r1(X0,X10) ) )
| ( ~ ! [X11] :
( p1(X11)
| ~ r1(X0,X11) )
& ~ ! [X12] :
( ~ ( ~ ! [X13] :
( ~ ! [X14] :
( p1(X14)
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
& ~ ! [X15] :
( ~ ! [X16] :
( ~ ! [X17] :
( p1(X17)
| ~ r1(X16,X17) )
| ~ r1(X15,X16) )
| ~ r1(X12,X15) ) )
| ~ r1(X0,X12) )
& ~ ! [X18] :
( p2(X18)
| ~ r1(X0,X18) ) )
| ( ~ ! [X19] :
( p1(X19)
| ~ r1(X0,X19) )
& ~ ! [X20] :
( ! [X21] :
( ~ ( ~ ! [X22] :
( p1(X22)
| ~ r1(X21,X22) )
& ~ ! [X23] :
( ~ ! [X24] :
( p1(X24)
| ~ r1(X23,X24) )
| ~ r1(X21,X23) ) )
| ~ r1(X20,X21) )
| ~ r1(X0,X20) )
& ~ ! [X25] :
( p2(X25)
| ~ r1(X0,X25) ) )
| ( ~ ! [X26] :
( p1(X26)
| ~ r1(X0,X26) )
& ~ ! [X27] :
( ~ ( p1(X27)
& ~ ! [X28] :
( ~ ! [X29] :
( ~ p1(X29)
| ~ r1(X28,X29) )
| ~ r1(X27,X28) ) )
| ~ r1(X0,X27) )
& ~ ! [X30] :
( p2(X30)
| ~ r1(X0,X30) ) ) ),
inference(true_and_false_elimination,[],[f5]) ).
fof(f5,plain,
~ ~ ? [X0] :
~ ( ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ! [X2] :
( ! [X3] :
( p1(X3)
| ~ r1(X2,X3) )
| ! [X4] :
( ~ ! [X5] :
( p1(X5)
| ~ r1(X4,X5) )
| ~ r1(X2,X4) )
| ~ r1(X0,X2) )
| ! [X6] :
( p2(X6)
| ~ r1(X0,X6) )
| ( ~ ! [X7] :
( p1(X7)
| ~ r1(X0,X7) )
& ~ ! [X8] :
( ~ ! [X9] :
( $false
| ~ r1(X8,X9) )
| ~ r1(X0,X8) )
& ~ ! [X10] :
( p2(X10)
| ~ r1(X0,X10) ) )
| ( ~ ! [X11] :
( p1(X11)
| ~ r1(X0,X11) )
& ~ ! [X12] :
( ~ ( ~ ! [X13] :
( ~ ! [X14] :
( p1(X14)
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
& ~ ! [X15] :
( ~ ! [X16] :
( ~ ! [X17] :
( p1(X17)
| ~ r1(X16,X17) )
| ~ r1(X15,X16) )
| ~ r1(X12,X15) ) )
| ~ r1(X0,X12) )
& ~ ! [X18] :
( p2(X18)
| ~ r1(X0,X18) ) )
| ( ~ ! [X19] :
( p1(X19)
| ~ r1(X0,X19) )
& ~ ! [X20] :
( ! [X21] :
( ~ ( ~ ! [X22] :
( p1(X22)
| ~ r1(X21,X22) )
& ~ ! [X23] :
( ~ ! [X24] :
( p1(X24)
| ~ r1(X23,X24) )
| ~ r1(X21,X23) ) )
| ~ r1(X20,X21) )
| ~ r1(X0,X20) )
& ~ ! [X25] :
( p2(X25)
| ~ r1(X0,X25) ) )
| ( ~ ! [X26] :
( p1(X26)
| ~ r1(X0,X26) )
& ~ ! [X27] :
( ~ ( p1(X27)
& ~ ! [X28] :
( ~ ! [X29] :
( ~ p1(X29)
| ~ r1(X28,X29) )
| ~ r1(X27,X28) ) )
| ~ r1(X0,X27) )
& ~ ! [X30] :
( p2(X30)
| ~ r1(X0,X30) ) ) ),
inference(rectify,[],[f4]) ).
fof(f4,negated_conjecture,
~ ~ ? [X0] :
~ ( ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ! [X0] :
( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ~ ! [X0] :
( $false
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
& ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) )
| ( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ~ ( ~ ! [X0] :
( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
& ~ ! [X0] :
( ~ ! [X1] :
( ~ ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) )
& ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) )
| ( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ! [X0] :
( ~ ( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ~ ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
& ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) )
| ( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ~ ( p1(X1)
& ~ ! [X0] :
( ~ ! [X1] :
( ~ p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) )
& ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) ) ),
inference(negated_conjecture,[],[f3]) ).
fof(f3,conjecture,
~ ? [X0] :
~ ( ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ! [X0] :
( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ~ ! [X0] :
( $false
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
& ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) )
| ( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ~ ( ~ ! [X0] :
( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
& ~ ! [X0] :
( ~ ! [X1] :
( ~ ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) )
& ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) )
| ( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ! [X0] :
( ~ ( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ~ ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
& ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) )
| ( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
& ~ ! [X1] :
( ~ ( p1(X1)
& ~ ! [X0] :
( ~ ! [X1] :
( ~ p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) )
& ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).
fof(f638,plain,
( ! [X0] :
( ~ r1(X0,sK4)
| sP34(X0) )
| ~ spl39_62 ),
inference(avatar_component_clause,[],[f637]) ).
fof(f637,plain,
( spl39_62
<=> ! [X0] :
( ~ r1(X0,sK4)
| sP34(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl39_62])]) ).
fof(f856,plain,
( ~ sP34(sK2)
| spl39_82 ),
inference(avatar_component_clause,[],[f854]) ).
fof(f854,plain,
( spl39_82
<=> sP34(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl39_82])]) ).
fof(f857,plain,
( ~ spl39_82
| ~ spl39_48
| ~ spl39_68
| ~ spl39_37 ),
inference(avatar_split_clause,[],[f400,f378,f735,f492,f854]) ).
fof(f492,plain,
( spl39_48
<=> sP33(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl39_48])]) ).
fof(f735,plain,
( spl39_68
<=> r1(sK0,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl39_68])]) ).
fof(f378,plain,
( spl39_37
<=> ! [X20,X21] :
( ~ r1(X20,X21)
| ~ sP34(X21)
| ~ sP33(X21)
| ~ r1(sK0,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl39_37])]) ).
fof(f400,plain,
( ~ r1(sK0,sK0)
| ~ sP33(sK2)
| ~ sP34(sK2)
| ~ spl39_37 ),
inference(resolution,[],[f379,f35]) ).
fof(f35,plain,
r1(sK0,sK2),
inference(cnf_transformation,[],[f23]) ).
fof(f379,plain,
( ! [X21,X20] :
( ~ r1(sK0,X20)
| ~ r1(X20,X21)
| ~ sP33(X21)
| ~ sP34(X21) )
| ~ spl39_37 ),
inference(avatar_component_clause,[],[f378]) ).
fof(f753,plain,
spl39_68,
inference(avatar_contradiction_clause,[],[f751]) ).
fof(f751,plain,
( $false
| spl39_68 ),
inference(resolution,[],[f737,f42]) ).
fof(f42,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(f737,plain,
( ~ r1(sK0,sK0)
| spl39_68 ),
inference(avatar_component_clause,[],[f735]) ).
fof(f748,plain,
( ~ spl39_55
| ~ spl39_41
| ~ spl39_68
| ~ spl39_35 ),
inference(avatar_split_clause,[],[f365,f347,f735,f439,f574]) ).
fof(f574,plain,
( spl39_55
<=> sP30(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl39_55])]) ).
fof(f439,plain,
( spl39_41
<=> sP29(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl39_41])]) ).
fof(f347,plain,
( spl39_35
<=> ! [X20,X21] :
( ~ r1(X20,X21)
| ~ sP30(X21)
| ~ sP29(X21)
| ~ r1(sK0,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl39_35])]) ).
fof(f365,plain,
( ~ r1(sK0,sK0)
| ~ sP29(sK2)
| ~ sP30(sK2)
| ~ spl39_35 ),
inference(resolution,[],[f348,f35]) ).
fof(f348,plain,
( ! [X21,X20] :
( ~ r1(sK0,X20)
| ~ r1(X20,X21)
| ~ sP29(X21)
| ~ sP30(X21) )
| ~ spl39_35 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f639,plain,
( spl39_56
| spl39_62 ),
inference(avatar_split_clause,[],[f321,f637,f578]) ).
fof(f578,plain,
( spl39_56
<=> p1(sK9(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl39_56])]) ).
fof(f321,plain,
! [X0] :
( ~ r1(X0,sK4)
| sP34(X0)
| p1(sK9(sK4)) ),
inference(resolution,[],[f90,f37]) ).
fof(f37,plain,
! [X5] :
( ~ r1(sK4,X5)
| p1(X5) ),
inference(cnf_transformation,[],[f23]) ).
fof(f90,plain,
! [X21,X23] :
( r1(X23,sK9(X23))
| ~ r1(X21,X23)
| sP34(X21) ),
inference(cnf_transformation,[],[f90_D]) ).
fof(f90_D,plain,
! [X21] :
( ! [X23] :
( r1(X23,sK9(X23))
| ~ r1(X21,X23) )
<=> ~ sP34(X21) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP34])]) ).
fof(f581,plain,
( spl39_55
| ~ spl39_56 ),
inference(avatar_split_clause,[],[f275,f578,f574]) ).
fof(f275,plain,
( ~ p1(sK9(sK4))
| sP30(sK2) ),
inference(resolution,[],[f82,f36]) ).
fof(f82,plain,
! [X21,X23] :
( ~ p1(sK9(X23))
| ~ r1(X21,X23)
| sP30(X21) ),
inference(cnf_transformation,[],[f82_D]) ).
fof(f82_D,plain,
! [X21] :
( ! [X23] :
( ~ p1(sK9(X23))
| ~ r1(X21,X23) )
<=> ~ sP30(X21) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP30])]) ).
fof(f513,plain,
~ spl39_42,
inference(avatar_contradiction_clause,[],[f512]) ).
fof(f512,plain,
( $false
| ~ spl39_42 ),
inference(resolution,[],[f445,f39]) ).
fof(f39,plain,
~ p1(sK3),
inference(cnf_transformation,[],[f23]) ).
fof(f445,plain,
( p1(sK3)
| ~ spl39_42 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f443,plain,
( spl39_42
<=> p1(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl39_42])]) ).
fof(f495,plain,
( spl39_48
| spl39_42 ),
inference(avatar_split_clause,[],[f245,f443,f492]) ).
fof(f245,plain,
( p1(sK3)
| sP33(sK2) ),
inference(resolution,[],[f88,f38]) ).
fof(f38,plain,
r1(sK2,sK3),
inference(cnf_transformation,[],[f23]) ).
fof(f88,plain,
! [X21,X22] :
( ~ r1(X21,X22)
| p1(X22)
| sP33(X21) ),
inference(cnf_transformation,[],[f88_D]) ).
fof(f88_D,plain,
! [X21] :
( ! [X22] :
( ~ r1(X21,X22)
| p1(X22) )
<=> ~ sP33(X21) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP33])]) ).
fof(f446,plain,
( spl39_41
| spl39_42 ),
inference(avatar_split_clause,[],[f234,f443,f439]) ).
fof(f234,plain,
( p1(sK3)
| sP29(sK2) ),
inference(resolution,[],[f80,f38]) ).
fof(f80,plain,
! [X21,X22] :
( ~ r1(X21,X22)
| p1(X22)
| sP29(X21) ),
inference(cnf_transformation,[],[f80_D]) ).
fof(f80_D,plain,
! [X21] :
( ! [X22] :
( ~ r1(X21,X22)
| p1(X22) )
<=> ~ sP29(X21) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP29])]) ).
fof(f380,plain,
( ~ spl39_15
| ~ spl39_14
| spl39_37 ),
inference(avatar_split_clause,[],[f91,f378,f163,f168]) ).
fof(f168,plain,
( spl39_15
<=> sP32 ),
introduced(avatar_definition,[new_symbols(naming,[spl39_15])]) ).
fof(f163,plain,
( spl39_14
<=> sP31 ),
introduced(avatar_definition,[new_symbols(naming,[spl39_14])]) ).
fof(f91,plain,
! [X21,X20] :
( ~ r1(X20,X21)
| ~ r1(sK0,X20)
| ~ sP31
| ~ sP32
| ~ sP33(X21)
| ~ sP34(X21) ),
inference(general_splitting,[],[f89,f90_D]) ).
fof(f89,plain,
! [X21,X23,X20] :
( r1(X23,sK9(X23))
| ~ r1(X21,X23)
| ~ r1(X20,X21)
| ~ r1(sK0,X20)
| ~ sP31
| ~ sP32
| ~ sP33(X21) ),
inference(general_splitting,[],[f87,f88_D]) ).
fof(f87,plain,
! [X21,X22,X23,X20] :
( p1(X22)
| ~ r1(X21,X22)
| r1(X23,sK9(X23))
| ~ r1(X21,X23)
| ~ r1(X20,X21)
| ~ r1(sK0,X20)
| ~ sP31
| ~ sP32 ),
inference(general_splitting,[],[f85,f86_D]) ).
fof(f86,plain,
! [X25] :
( p2(X25)
| ~ r1(sK0,X25)
| sP32 ),
inference(cnf_transformation,[],[f86_D]) ).
fof(f86_D,plain,
( ! [X25] :
( p2(X25)
| ~ r1(sK0,X25) )
<=> ~ sP32 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP32])]) ).
fof(f85,plain,
! [X21,X22,X25,X23,X20] :
( p1(X22)
| ~ r1(X21,X22)
| r1(X23,sK9(X23))
| ~ r1(X21,X23)
| ~ r1(X20,X21)
| ~ r1(sK0,X20)
| p2(X25)
| ~ r1(sK0,X25)
| ~ sP31 ),
inference(general_splitting,[],[f26,f84_D]) ).
fof(f84,plain,
! [X19] :
( p1(X19)
| ~ r1(sK0,X19)
| sP31 ),
inference(cnf_transformation,[],[f84_D]) ).
fof(f84_D,plain,
( ! [X19] :
( p1(X19)
| ~ r1(sK0,X19) )
<=> ~ sP31 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP31])]) ).
fof(f26,plain,
! [X21,X19,X22,X25,X23,X20] :
( p1(X19)
| ~ r1(sK0,X19)
| p1(X22)
| ~ r1(X21,X22)
| r1(X23,sK9(X23))
| ~ r1(X21,X23)
| ~ r1(X20,X21)
| ~ r1(sK0,X20)
| p2(X25)
| ~ r1(sK0,X25) ),
inference(cnf_transformation,[],[f23]) ).
fof(f349,plain,
( ~ spl39_13
| ~ spl39_12
| spl39_35 ),
inference(avatar_split_clause,[],[f83,f347,f153,f158]) ).
fof(f158,plain,
( spl39_13
<=> sP28 ),
introduced(avatar_definition,[new_symbols(naming,[spl39_13])]) ).
fof(f153,plain,
( spl39_12
<=> sP27 ),
introduced(avatar_definition,[new_symbols(naming,[spl39_12])]) ).
fof(f83,plain,
! [X21,X20] :
( ~ r1(X20,X21)
| ~ r1(sK0,X20)
| ~ sP27
| ~ sP28
| ~ sP29(X21)
| ~ sP30(X21) ),
inference(general_splitting,[],[f81,f82_D]) ).
fof(f81,plain,
! [X21,X23,X20] :
( ~ p1(sK9(X23))
| ~ r1(X21,X23)
| ~ r1(X20,X21)
| ~ r1(sK0,X20)
| ~ sP27
| ~ sP28
| ~ sP29(X21) ),
inference(general_splitting,[],[f79,f80_D]) ).
fof(f79,plain,
! [X21,X22,X23,X20] :
( p1(X22)
| ~ r1(X21,X22)
| ~ p1(sK9(X23))
| ~ r1(X21,X23)
| ~ r1(X20,X21)
| ~ r1(sK0,X20)
| ~ sP27
| ~ sP28 ),
inference(general_splitting,[],[f77,f78_D]) ).
fof(f78,plain,
! [X25] :
( p2(X25)
| ~ r1(sK0,X25)
| sP28 ),
inference(cnf_transformation,[],[f78_D]) ).
fof(f78_D,plain,
( ! [X25] :
( p2(X25)
| ~ r1(sK0,X25) )
<=> ~ sP28 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP28])]) ).
fof(f77,plain,
! [X21,X22,X25,X23,X20] :
( p1(X22)
| ~ r1(X21,X22)
| ~ p1(sK9(X23))
| ~ r1(X21,X23)
| ~ r1(X20,X21)
| ~ r1(sK0,X20)
| p2(X25)
| ~ r1(sK0,X25)
| ~ sP27 ),
inference(general_splitting,[],[f27,f76_D]) ).
fof(f76,plain,
! [X19] :
( p1(X19)
| ~ r1(sK0,X19)
| sP27 ),
inference(cnf_transformation,[],[f76_D]) ).
fof(f76_D,plain,
( ! [X19] :
( p1(X19)
| ~ r1(sK0,X19) )
<=> ~ sP27 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP27])]) ).
fof(f27,plain,
! [X21,X19,X22,X25,X23,X20] :
( p1(X19)
| ~ r1(sK0,X19)
| p1(X22)
| ~ r1(X21,X22)
| ~ p1(sK9(X23))
| ~ r1(X21,X23)
| ~ r1(X20,X21)
| ~ r1(sK0,X20)
| p2(X25)
| ~ r1(sK0,X25) ),
inference(cnf_transformation,[],[f23]) ).
fof(f209,plain,
~ spl39_4,
inference(avatar_contradiction_clause,[],[f208]) ).
fof(f208,plain,
( $false
| ~ spl39_4 ),
inference(resolution,[],[f200,f41]) ).
fof(f41,plain,
~ p1(sK1),
inference(cnf_transformation,[],[f23]) ).
fof(f200,plain,
( p1(sK1)
| ~ spl39_4 ),
inference(resolution,[],[f115,f40]) ).
fof(f40,plain,
r1(sK0,sK1),
inference(cnf_transformation,[],[f23]) ).
fof(f115,plain,
( ! [X11] :
( ~ r1(sK0,X11)
| p1(X11) )
| ~ spl39_4 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f114,plain,
( spl39_4
<=> ! [X11] :
( p1(X11)
| ~ r1(sK0,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl39_4])]) ).
fof(f197,plain,
~ spl39_2,
inference(avatar_contradiction_clause,[],[f196]) ).
fof(f196,plain,
( $false
| ~ spl39_2 ),
inference(resolution,[],[f192,f34]) ).
fof(f34,plain,
~ p2(sK5),
inference(cnf_transformation,[],[f23]) ).
fof(f192,plain,
( p2(sK5)
| ~ spl39_2 ),
inference(resolution,[],[f107,f33]) ).
fof(f33,plain,
r1(sK0,sK5),
inference(cnf_transformation,[],[f23]) ).
fof(f107,plain,
( ! [X10] :
( ~ r1(sK0,X10)
| p2(X10) )
| ~ spl39_2 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f106,plain,
( spl39_2
<=> ! [X10] :
( p2(X10)
| ~ r1(sK0,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl39_2])]) ).
fof(f171,plain,
( spl39_15
| spl39_2 ),
inference(avatar_split_clause,[],[f86,f106,f168]) ).
fof(f166,plain,
( spl39_14
| spl39_4 ),
inference(avatar_split_clause,[],[f84,f114,f163]) ).
fof(f161,plain,
( spl39_13
| spl39_2 ),
inference(avatar_split_clause,[],[f78,f106,f158]) ).
fof(f156,plain,
( spl39_12
| spl39_4 ),
inference(avatar_split_clause,[],[f76,f114,f153]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LCL672+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Apr 29 23:01:32 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % (5563)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.35 % (5569)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.11/0.35 % (5567)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.11/0.35 % (5566)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)
% 0.11/0.35 % (5565)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.35 % (5570)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)
% 0.11/0.35 % (5568)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.11/0.35 % (5564)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.11/0.35 TRYING [1]
% 0.11/0.35 TRYING [2]
% 0.11/0.35 TRYING [1]
% 0.11/0.35 TRYING [1]
% 0.11/0.35 TRYING [1]
% 0.11/0.35 TRYING [2]
% 0.11/0.35 TRYING [2]
% 0.11/0.35 TRYING [3]
% 0.11/0.35 TRYING [2]
% 0.11/0.35 TRYING [3]
% 0.11/0.35 TRYING [3]
% 0.11/0.35 TRYING [3]
% 0.11/0.35 TRYING [4]
% 0.11/0.35 TRYING [4]
% 0.11/0.36 TRYING [4]
% 0.11/0.36 TRYING [4]
% 0.11/0.36 TRYING [5]
% 0.11/0.36 TRYING [5]
% 0.11/0.36 % (5566)First to succeed.
% 0.11/0.36 TRYING [5]
% 0.11/0.36 TRYING [5]
% 0.11/0.36 TRYING [6]
% 0.11/0.36 % (5566)Refutation found. Thanks to Tanya!
% 0.11/0.36 % SZS status Theorem for theBenchmark
% 0.11/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.36 % (5566)------------------------------
% 0.11/0.36 % (5566)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.11/0.36 % (5566)Termination reason: Refutation
% 0.11/0.36
% 0.11/0.36 % (5566)Memory used [KB]: 1100
% 0.11/0.36 % (5566)Time elapsed: 0.014 s
% 0.11/0.36 % (5566)Instructions burned: 23 (million)
% 0.11/0.36 % (5566)------------------------------
% 0.11/0.36 % (5566)------------------------------
% 0.11/0.36 % (5563)Success in time 0.028 s
%------------------------------------------------------------------------------