%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : LCL668+1.001 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 07:48:53 EDT 2023
% Result : Theorem 0.88s 1.15s
% Output : CNFRefutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 22
% Syntax : Number of formulae : 78 ( 5 unt; 0 def)
% Number of atoms : 1310 ( 0 equ)
% Maximal formula atoms : 84 ( 16 avg)
% Number of connectives : 2251 (1019 ~; 858 |; 356 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 42 ( 13 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 14 con; 0-1 aty)
% Number of variables : 828 ( 0 sgn; 582 !; 171 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : r1(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
fof(f2,conjecture,
~ ? [X0] :
~ ( ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ( p1(X0)
& p2(X0)
& p3(X0)
& p4(X0)
& p5(X0)
& p6(X0) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ( ~ ! [X0] :
( ~ ( ~ ! [X1] :
( ~ ( ~ ! [X0] :
( ~ ( ~ ! [X1] :
( ~ ~ ! [X0] :
( ! [X1] :
( ! [X0] :
( ~ ( ( p1(X0)
& p2(X0) )
| ( ~ p2(X0)
& ~ p1(X0) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( p3(X1)
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ~ ( ( p2(X0)
& p3(X0) )
| ( ~ p3(X0)
& ~ p2(X0) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ! [X0] :
( p4(X0)
| ~ r1(X1,X0) )
| ~ ! [X0] :
( ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ~ ( ( p3(X0)
& p4(X0) )
| ( ~ p4(X0)
& ~ p3(X0) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) )
| ! [X1] :
( p5(X1)
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ~ ( ( p4(X0)
& p5(X0) )
| ( ~ p5(X0)
& ~ p4(X0) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ! [X0] :
( p6(X0)
| ~ r1(X1,X0) )
| ~ ! [X0] :
( ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ~ ( ( p5(X0)
& p1(X0) )
| ( ~ p1(X0)
& ~ p5(X0) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) )
| ! [X1] :
( p7(X1)
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ( ~ p2(X0)
& ~ p4(X0)
& ~ p6(X0)
& ~ p8(X0)
& ~ p10(X0)
& ~ p12(X0) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).
fof(f3,negated_conjecture,
~ ~ ? [X0] :
~ ( ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ( p1(X0)
& p2(X0)
& p3(X0)
& p4(X0)
& p5(X0)
& p6(X0) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ( ~ ! [X0] :
( ~ ( ~ ! [X1] :
( ~ ( ~ ! [X0] :
( ~ ( ~ ! [X1] :
( ~ ~ ! [X0] :
( ! [X1] :
( ! [X0] :
( ~ ( ( p1(X0)
& p2(X0) )
| ( ~ p2(X0)
& ~ p1(X0) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( p3(X1)
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ~ ( ( p2(X0)
& p3(X0) )
| ( ~ p3(X0)
& ~ p2(X0) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ! [X0] :
( p4(X0)
| ~ r1(X1,X0) )
| ~ ! [X0] :
( ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ~ ( ( p3(X0)
& p4(X0) )
| ( ~ p4(X0)
& ~ p3(X0) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) )
| ! [X1] :
( p5(X1)
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ~ ( ( p4(X0)
& p5(X0) )
| ( ~ p5(X0)
& ~ p4(X0) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ! [X0] :
( p6(X0)
| ~ r1(X1,X0) )
| ~ ! [X0] :
( ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ~ ( ( p5(X0)
& p1(X0) )
| ( ~ p1(X0)
& ~ p5(X0) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) )
| ! [X1] :
( p7(X1)
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ( ~ p2(X0)
& ~ p4(X0)
& ~ p6(X0)
& ~ p8(X0)
& ~ p10(X0)
& ~ p12(X0) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) ) ),
inference(negated_conjecture,[],[f2]) ).
fof(f4,plain,
~ ~ ? [X0] :
~ ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ( p1(X6)
& p2(X6)
& p3(X6)
& p4(X6)
& p5(X6)
& p6(X6) )
| ~ r1(X5,X6) )
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) )
| ~ ! [X7] :
( ~ ( ~ ! [X8] :
( ~ ( ~ ! [X9] :
( ~ ( ~ ! [X10] :
( ~ ( ~ ! [X11] :
( ~ ~ ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ ( ( p1(X14)
& p2(X14) )
| ( ~ p2(X14)
& ~ p1(X14) ) )
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) )
| ~ r1(X10,X11) )
| ! [X15] :
( p3(X15)
| ~ r1(X10,X15) )
| ~ ! [X16] :
( ! [X17] :
( ! [X18] :
( ! [X19] :
( ~ ( ( p2(X19)
& p3(X19) )
| ( ~ p3(X19)
& ~ p2(X19) ) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) )
| ~ r1(X16,X17) )
| ~ r1(X10,X16) ) )
| ~ r1(X9,X10) )
| ! [X20] :
( p4(X20)
| ~ r1(X9,X20) )
| ~ ! [X21] :
( ! [X22] :
( ! [X23] :
( ! [X24] :
( ! [X25] :
( ~ ( ( p3(X25)
& p4(X25) )
| ( ~ p4(X25)
& ~ p3(X25) ) )
| ~ r1(X24,X25) )
| ~ r1(X23,X24) )
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X9,X21) ) )
| ~ r1(X8,X9) )
| ! [X26] :
( p5(X26)
| ~ r1(X8,X26) )
| ~ ! [X27] :
( ! [X28] :
( ! [X29] :
( ! [X30] :
( ! [X31] :
( ! [X32] :
( ~ ( ( p4(X32)
& p5(X32) )
| ( ~ p5(X32)
& ~ p4(X32) ) )
| ~ r1(X31,X32) )
| ~ r1(X30,X31) )
| ~ r1(X29,X30) )
| ~ r1(X28,X29) )
| ~ r1(X27,X28) )
| ~ r1(X8,X27) ) )
| ~ r1(X7,X8) )
| ! [X33] :
( p6(X33)
| ~ r1(X7,X33) )
| ~ ! [X34] :
( ! [X35] :
( ! [X36] :
( ! [X37] :
( ! [X38] :
( ! [X39] :
( ! [X40] :
( ~ ( ( p5(X40)
& p1(X40) )
| ( ~ p1(X40)
& ~ p5(X40) ) )
| ~ r1(X39,X40) )
| ~ r1(X38,X39) )
| ~ r1(X37,X38) )
| ~ r1(X36,X37) )
| ~ r1(X35,X36) )
| ~ r1(X34,X35) )
| ~ r1(X7,X34) ) )
| ~ r1(X0,X7) )
| ! [X41] :
( p7(X41)
| ~ r1(X0,X41) )
| ! [X42] :
( ! [X43] :
( ! [X44] :
( ! [X45] :
( ! [X46] :
( ! [X47] :
( ( ~ p2(X47)
& ~ p4(X47)
& ~ p6(X47)
& ~ p8(X47)
& ~ p10(X47)
& ~ p12(X47) )
| ~ r1(X46,X47) )
| ~ r1(X45,X46) )
| ~ r1(X44,X45) )
| ~ r1(X43,X44) )
| ~ r1(X42,X43) )
| ~ r1(X0,X42) ) ),
inference(rectify,[],[f3]) ).
fof(f5,plain,
? [X0] :
~ ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ( p1(X6)
& p2(X6)
& p3(X6)
& p4(X6)
& p5(X6)
& p6(X6) )
| ~ r1(X5,X6) )
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) )
| ~ ! [X7] :
( ~ ( ~ ! [X8] :
( ~ ( ~ ! [X9] :
( ~ ( ~ ! [X10] :
( ~ ( ~ ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ ( ( p1(X14)
& p2(X14) )
| ( ~ p2(X14)
& ~ p1(X14) ) )
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) )
| ~ r1(X10,X11) )
| ! [X15] :
( p3(X15)
| ~ r1(X10,X15) )
| ~ ! [X16] :
( ! [X17] :
( ! [X18] :
( ! [X19] :
( ~ ( ( p2(X19)
& p3(X19) )
| ( ~ p3(X19)
& ~ p2(X19) ) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) )
| ~ r1(X16,X17) )
| ~ r1(X10,X16) ) )
| ~ r1(X9,X10) )
| ! [X20] :
( p4(X20)
| ~ r1(X9,X20) )
| ~ ! [X21] :
( ! [X22] :
( ! [X23] :
( ! [X24] :
( ! [X25] :
( ~ ( ( p3(X25)
& p4(X25) )
| ( ~ p4(X25)
& ~ p3(X25) ) )
| ~ r1(X24,X25) )
| ~ r1(X23,X24) )
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X9,X21) ) )
| ~ r1(X8,X9) )
| ! [X26] :
( p5(X26)
| ~ r1(X8,X26) )
| ~ ! [X27] :
( ! [X28] :
( ! [X29] :
( ! [X30] :
( ! [X31] :
( ! [X32] :
( ~ ( ( p4(X32)
& p5(X32) )
| ( ~ p5(X32)
& ~ p4(X32) ) )
| ~ r1(X31,X32) )
| ~ r1(X30,X31) )
| ~ r1(X29,X30) )
| ~ r1(X28,X29) )
| ~ r1(X27,X28) )
| ~ r1(X8,X27) ) )
| ~ r1(X7,X8) )
| ! [X33] :
( p6(X33)
| ~ r1(X7,X33) )
| ~ ! [X34] :
( ! [X35] :
( ! [X36] :
( ! [X37] :
( ! [X38] :
( ! [X39] :
( ! [X40] :
( ~ ( ( p5(X40)
& p1(X40) )
| ( ~ p1(X40)
& ~ p5(X40) ) )
| ~ r1(X39,X40) )
| ~ r1(X38,X39) )
| ~ r1(X37,X38) )
| ~ r1(X36,X37) )
| ~ r1(X35,X36) )
| ~ r1(X34,X35) )
| ~ r1(X7,X34) ) )
| ~ r1(X0,X7) )
| ! [X41] :
( p7(X41)
| ~ r1(X0,X41) )
| ! [X42] :
( ! [X43] :
( ! [X44] :
( ! [X45] :
( ! [X46] :
( ! [X47] :
( ( ~ p2(X47)
& ~ p4(X47)
& ~ p6(X47)
& ~ p8(X47)
& ~ p10(X47)
& ~ p12(X47) )
| ~ r1(X46,X47) )
| ~ r1(X45,X46) )
| ~ r1(X44,X45) )
| ~ r1(X43,X44) )
| ~ r1(X42,X43) )
| ~ r1(X0,X42) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
? [X0] :
~ ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ( p1(X6)
& p2(X6)
& p3(X6)
& p4(X6)
& p5(X6)
& p6(X6) )
| ~ r1(X5,X6) )
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) )
| ~ ! [X7] :
( ~ ( ~ ! [X8] :
( ~ ( ~ ! [X9] :
( ~ ( ~ ! [X10] :
( ~ ( ~ ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ ( ( p1(X14)
& p2(X14) )
| ( ~ p2(X14)
& ~ p1(X14) ) )
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) )
| ~ r1(X10,X11) )
| ! [X15] :
( p3(X15)
| ~ r1(X10,X15) )
| ~ ! [X16] :
( ! [X17] :
( ! [X18] :
( ! [X19] :
( ~ ( ( p2(X19)
& p3(X19) )
| ( ~ p3(X19)
& ~ p2(X19) ) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) )
| ~ r1(X16,X17) )
| ~ r1(X10,X16) ) )
| ~ r1(X9,X10) )
| ! [X20] :
( p4(X20)
| ~ r1(X9,X20) )
| ~ ! [X21] :
( ! [X22] :
( ! [X23] :
( ! [X24] :
( ! [X25] :
( ~ ( ( p3(X25)
& p4(X25) )
| ( ~ p4(X25)
& ~ p3(X25) ) )
| ~ r1(X24,X25) )
| ~ r1(X23,X24) )
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X9,X21) ) )
| ~ r1(X8,X9) )
| ! [X26] :
( p5(X26)
| ~ r1(X8,X26) )
| ~ ! [X27] :
( ! [X28] :
( ! [X29] :
( ! [X30] :
( ! [X31] :
( ! [X32] :
( ~ ( ( p4(X32)
& p5(X32) )
| ( ~ p5(X32)
& ~ p4(X32) ) )
| ~ r1(X31,X32) )
| ~ r1(X30,X31) )
| ~ r1(X29,X30) )
| ~ r1(X28,X29) )
| ~ r1(X27,X28) )
| ~ r1(X8,X27) ) )
| ~ r1(X7,X8) )
| ! [X33] :
( p6(X33)
| ~ r1(X7,X33) )
| ~ ! [X34] :
( ! [X35] :
( ! [X36] :
( ! [X37] :
( ! [X38] :
( ! [X39] :
( ! [X40] :
( ~ ( ( p5(X40)
& p1(X40) )
| ( ~ p1(X40)
& ~ p5(X40) ) )
| ~ r1(X39,X40) )
| ~ r1(X38,X39) )
| ~ r1(X37,X38) )
| ~ r1(X36,X37) )
| ~ r1(X35,X36) )
| ~ r1(X34,X35) )
| ~ r1(X7,X34) ) )
| ~ r1(X0,X7) )
| ! [X41] : ~ r1(X0,X41)
| ! [X42] :
( ! [X43] :
( ! [X44] :
( ! [X45] :
( ! [X46] :
( ! [X47] :
( ( ~ p2(X47)
& ~ p4(X47)
& ~ p6(X47)
& ~ p8(X47)
& ~ p10(X47)
& ~ p12(X47) )
| ~ r1(X46,X47) )
| ~ r1(X45,X46) )
| ~ r1(X44,X45) )
| ~ r1(X43,X44) )
| ~ r1(X42,X43) )
| ~ r1(X0,X42) ) ),
inference(pure_predicate_removal,[],[f5]) ).
fof(f7,plain,
? [X0] :
~ ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ( p1(X6)
& p2(X6)
& p3(X6)
& p4(X6)
& p5(X6)
& p6(X6) )
| ~ r1(X5,X6) )
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) )
| ~ ! [X7] :
( ~ ( ~ ! [X8] :
( ~ ( ~ ! [X9] :
( ~ ( ~ ! [X10] :
( ~ ( ~ ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ ( ( p1(X14)
& p2(X14) )
| ( ~ p2(X14)
& ~ p1(X14) ) )
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) )
| ~ r1(X10,X11) )
| ! [X15] :
( p3(X15)
| ~ r1(X10,X15) )
| ~ ! [X16] :
( ! [X17] :
( ! [X18] :
( ! [X19] :
( ~ ( ( p2(X19)
& p3(X19) )
| ( ~ p3(X19)
& ~ p2(X19) ) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) )
| ~ r1(X16,X17) )
| ~ r1(X10,X16) ) )
| ~ r1(X9,X10) )
| ! [X20] :
( p4(X20)
| ~ r1(X9,X20) )
| ~ ! [X21] :
( ! [X22] :
( ! [X23] :
( ! [X24] :
( ! [X25] :
( ~ ( ( p3(X25)
& p4(X25) )
| ( ~ p4(X25)
& ~ p3(X25) ) )
| ~ r1(X24,X25) )
| ~ r1(X23,X24) )
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X9,X21) ) )
| ~ r1(X8,X9) )
| ! [X26] :
( p5(X26)
| ~ r1(X8,X26) )
| ~ ! [X27] :
( ! [X28] :
( ! [X29] :
( ! [X30] :
( ! [X31] :
( ! [X32] :
( ~ ( ( p4(X32)
& p5(X32) )
| ( ~ p5(X32)
& ~ p4(X32) ) )
| ~ r1(X31,X32) )
| ~ r1(X30,X31) )
| ~ r1(X29,X30) )
| ~ r1(X28,X29) )
| ~ r1(X27,X28) )
| ~ r1(X8,X27) ) )
| ~ r1(X7,X8) )
| ! [X33] :
( p6(X33)
| ~ r1(X7,X33) )
| ~ ! [X34] :
( ! [X35] :
( ! [X36] :
( ! [X37] :
( ! [X38] :
( ! [X39] :
( ! [X40] :
( ~ ( ( p5(X40)
& p1(X40) )
| ( ~ p1(X40)
& ~ p5(X40) ) )
| ~ r1(X39,X40) )
| ~ r1(X38,X39) )
| ~ r1(X37,X38) )
| ~ r1(X36,X37) )
| ~ r1(X35,X36) )
| ~ r1(X34,X35) )
| ~ r1(X7,X34) ) )
| ~ r1(X0,X7) )
| ! [X41] : ~ r1(X0,X41)
| ! [X42] :
( ! [X43] :
( ! [X44] :
( ! [X45] :
( ! [X46] :
( ! [X47] : ~ r1(X46,X47)
| ~ r1(X45,X46) )
| ~ r1(X44,X45) )
| ~ r1(X43,X44) )
| ~ r1(X42,X43) )
| ~ r1(X0,X42) ) ),
inference(pure_predicate_removal,[],[f6]) ).
fof(f8,plain,
? [X0] :
~ ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] : ~ r1(X5,X6)
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) )
| ~ ! [X7] :
( ~ ( ~ ! [X8] :
( ~ ( ~ ! [X9] :
( ~ ( ~ ! [X10] :
( ~ ( ~ ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ ( ( p1(X14)
& p2(X14) )
| ( ~ p2(X14)
& ~ p1(X14) ) )
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) )
| ~ r1(X10,X11) )
| ! [X15] :
( p3(X15)
| ~ r1(X10,X15) )
| ~ ! [X16] :
( ! [X17] :
( ! [X18] :
( ! [X19] :
( ~ ( ( p2(X19)
& p3(X19) )
| ( ~ p3(X19)
& ~ p2(X19) ) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) )
| ~ r1(X16,X17) )
| ~ r1(X10,X16) ) )
| ~ r1(X9,X10) )
| ! [X20] :
( p4(X20)
| ~ r1(X9,X20) )
| ~ ! [X21] :
( ! [X22] :
( ! [X23] :
( ! [X24] :
( ! [X25] :
( ~ ( ( p3(X25)
& p4(X25) )
| ( ~ p4(X25)
& ~ p3(X25) ) )
| ~ r1(X24,X25) )
| ~ r1(X23,X24) )
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X9,X21) ) )
| ~ r1(X8,X9) )
| ! [X26] :
( p5(X26)
| ~ r1(X8,X26) )
| ~ ! [X27] :
( ! [X28] :
( ! [X29] :
( ! [X30] :
( ! [X31] :
( ! [X32] :
( ~ ( ( p4(X32)
& p5(X32) )
| ( ~ p5(X32)
& ~ p4(X32) ) )
| ~ r1(X31,X32) )
| ~ r1(X30,X31) )
| ~ r1(X29,X30) )
| ~ r1(X28,X29) )
| ~ r1(X27,X28) )
| ~ r1(X8,X27) ) )
| ~ r1(X7,X8) )
| ! [X33] : ~ r1(X7,X33)
| ~ ! [X34] :
( ! [X35] :
( ! [X36] :
( ! [X37] :
( ! [X38] :
( ! [X39] :
( ! [X40] :
( ~ ( ( p5(X40)
& p1(X40) )
| ( ~ p1(X40)
& ~ p5(X40) ) )
| ~ r1(X39,X40) )
| ~ r1(X38,X39) )
| ~ r1(X37,X38) )
| ~ r1(X36,X37) )
| ~ r1(X35,X36) )
| ~ r1(X34,X35) )
| ~ r1(X7,X34) ) )
| ~ r1(X0,X7) )
| ! [X41] : ~ r1(X0,X41)
| ! [X42] :
( ! [X43] :
( ! [X44] :
( ! [X45] :
( ! [X46] :
( ! [X47] : ~ r1(X46,X47)
| ~ r1(X45,X46) )
| ~ r1(X44,X45) )
| ~ r1(X43,X44) )
| ~ r1(X42,X43) )
| ~ r1(X0,X42) ) ),
inference(pure_predicate_removal,[],[f7]) ).
fof(f9,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] : r1(X5,X6)
& r1(X4,X5) )
& r1(X3,X4) )
& r1(X2,X3) )
& r1(X1,X2) )
& r1(X0,X1) )
& ! [X7] :
( ( ! [X8] :
( ( ! [X9] :
( ( ! [X10] :
( ( ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ( ( ~ p1(X14)
| ~ p2(X14) )
& ( p2(X14)
| p1(X14) ) )
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) )
| ~ r1(X10,X11) )
& ? [X15] :
( ~ p3(X15)
& r1(X10,X15) )
& ! [X16] :
( ! [X17] :
( ! [X18] :
( ! [X19] :
( ( ( ~ p2(X19)
| ~ p3(X19) )
& ( p3(X19)
| p2(X19) ) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) )
| ~ r1(X16,X17) )
| ~ r1(X10,X16) ) )
| ~ r1(X9,X10) )
& ? [X20] :
( ~ p4(X20)
& r1(X9,X20) )
& ! [X21] :
( ! [X22] :
( ! [X23] :
( ! [X24] :
( ! [X25] :
( ( ( ~ p3(X25)
| ~ p4(X25) )
& ( p4(X25)
| p3(X25) ) )
| ~ r1(X24,X25) )
| ~ r1(X23,X24) )
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X9,X21) ) )
| ~ r1(X8,X9) )
& ? [X26] :
( ~ p5(X26)
& r1(X8,X26) )
& ! [X27] :
( ! [X28] :
( ! [X29] :
( ! [X30] :
( ! [X31] :
( ! [X32] :
( ( ( ~ p4(X32)
| ~ p5(X32) )
& ( p5(X32)
| p4(X32) ) )
| ~ r1(X31,X32) )
| ~ r1(X30,X31) )
| ~ r1(X29,X30) )
| ~ r1(X28,X29) )
| ~ r1(X27,X28) )
| ~ r1(X8,X27) ) )
| ~ r1(X7,X8) )
& ? [X33] : r1(X7,X33)
& ! [X34] :
( ! [X35] :
( ! [X36] :
( ! [X37] :
( ! [X38] :
( ! [X39] :
( ! [X40] :
( ( ( ~ p5(X40)
| ~ p1(X40) )
& ( p1(X40)
| p5(X40) ) )
| ~ r1(X39,X40) )
| ~ r1(X38,X39) )
| ~ r1(X37,X38) )
| ~ r1(X36,X37) )
| ~ r1(X35,X36) )
| ~ r1(X34,X35) )
| ~ r1(X7,X34) ) )
| ~ r1(X0,X7) )
& ? [X41] : r1(X0,X41)
& ? [X42] :
( ? [X43] :
( ? [X44] :
( ? [X45] :
( ? [X46] :
( ? [X47] : r1(X46,X47)
& r1(X45,X46) )
& r1(X44,X45) )
& r1(X43,X44) )
& r1(X42,X43) )
& r1(X0,X42) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f10,plain,
! [X9] :
( ! [X10] :
( ( ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ( ( ~ p1(X14)
| ~ p2(X14) )
& ( p2(X14)
| p1(X14) ) )
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) )
| ~ r1(X10,X11) )
& ? [X15] :
( ~ p3(X15)
& r1(X10,X15) )
& ! [X16] :
( ! [X17] :
( ! [X18] :
( ! [X19] :
( ( ( ~ p2(X19)
| ~ p3(X19) )
& ( p3(X19)
| p2(X19) ) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) )
| ~ r1(X16,X17) )
| ~ r1(X10,X16) ) )
| ~ r1(X9,X10) )
| ~ sP0(X9) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f11,plain,
! [X8] :
( ! [X9] :
( ( sP0(X9)
& ? [X20] :
( ~ p4(X20)
& r1(X9,X20) )
& ! [X21] :
( ! [X22] :
( ! [X23] :
( ! [X24] :
( ! [X25] :
( ( ( ~ p3(X25)
| ~ p4(X25) )
& ( p4(X25)
| p3(X25) ) )
| ~ r1(X24,X25) )
| ~ r1(X23,X24) )
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X9,X21) ) )
| ~ r1(X8,X9) )
| ~ sP1(X8) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f12,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] : r1(X5,X6)
& r1(X4,X5) )
& r1(X3,X4) )
& r1(X2,X3) )
& r1(X1,X2) )
& r1(X0,X1) )
& ! [X7] :
( ( ! [X8] :
( ( sP1(X8)
& ? [X26] :
( ~ p5(X26)
& r1(X8,X26) )
& ! [X27] :
( ! [X28] :
( ! [X29] :
( ! [X30] :
( ! [X31] :
( ! [X32] :
( ( ( ~ p4(X32)
| ~ p5(X32) )
& ( p5(X32)
| p4(X32) ) )
| ~ r1(X31,X32) )
| ~ r1(X30,X31) )
| ~ r1(X29,X30) )
| ~ r1(X28,X29) )
| ~ r1(X27,X28) )
| ~ r1(X8,X27) ) )
| ~ r1(X7,X8) )
& ? [X33] : r1(X7,X33)
& ! [X34] :
( ! [X35] :
( ! [X36] :
( ! [X37] :
( ! [X38] :
( ! [X39] :
( ! [X40] :
( ( ( ~ p5(X40)
| ~ p1(X40) )
& ( p1(X40)
| p5(X40) ) )
| ~ r1(X39,X40) )
| ~ r1(X38,X39) )
| ~ r1(X37,X38) )
| ~ r1(X36,X37) )
| ~ r1(X35,X36) )
| ~ r1(X34,X35) )
| ~ r1(X7,X34) ) )
| ~ r1(X0,X7) )
& ? [X41] : r1(X0,X41)
& ? [X42] :
( ? [X43] :
( ? [X44] :
( ? [X45] :
( ? [X46] :
( ? [X47] : r1(X46,X47)
& r1(X45,X46) )
& r1(X44,X45) )
& r1(X43,X44) )
& r1(X42,X43) )
& r1(X0,X42) ) ),
inference(definition_folding,[],[f9,f11,f10]) ).
fof(f13,plain,
! [X8] :
( ! [X9] :
( ( sP0(X9)
& ? [X20] :
( ~ p4(X20)
& r1(X9,X20) )
& ! [X21] :
( ! [X22] :
( ! [X23] :
( ! [X24] :
( ! [X25] :
( ( ( ~ p3(X25)
| ~ p4(X25) )
& ( p4(X25)
| p3(X25) ) )
| ~ r1(X24,X25) )
| ~ r1(X23,X24) )
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X9,X21) ) )
| ~ r1(X8,X9) )
| ~ sP1(X8) ),
inference(nnf_transformation,[],[f11]) ).
fof(f14,plain,
! [X0] :
( ! [X1] :
( ( sP0(X1)
& ? [X2] :
( ~ p4(X2)
& r1(X1,X2) )
& ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( ( ( ~ p3(X7)
| ~ p4(X7) )
& ( p4(X7)
| p3(X7) ) )
| ~ r1(X6,X7) )
| ~ r1(X5,X6) )
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X1,X3) ) )
| ~ r1(X0,X1) )
| ~ sP1(X0) ),
inference(rectify,[],[f13]) ).
fof(f15,plain,
! [X1] :
( ? [X2] :
( ~ p4(X2)
& r1(X1,X2) )
=> ( ~ p4(sK2(X1))
& r1(X1,sK2(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
! [X0] :
( ! [X1] :
( ( sP0(X1)
& ~ p4(sK2(X1))
& r1(X1,sK2(X1))
& ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( ( ( ~ p3(X7)
| ~ p4(X7) )
& ( p4(X7)
| p3(X7) ) )
| ~ r1(X6,X7) )
| ~ r1(X5,X6) )
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X1,X3) ) )
| ~ r1(X0,X1) )
| ~ sP1(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f14,f15]) ).
fof(f17,plain,
! [X9] :
( ! [X10] :
( ( ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ( ( ~ p1(X14)
| ~ p2(X14) )
& ( p2(X14)
| p1(X14) ) )
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) )
| ~ r1(X10,X11) )
& ? [X15] :
( ~ p3(X15)
& r1(X10,X15) )
& ! [X16] :
( ! [X17] :
( ! [X18] :
( ! [X19] :
( ( ( ~ p2(X19)
| ~ p3(X19) )
& ( p3(X19)
| p2(X19) ) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) )
| ~ r1(X16,X17) )
| ~ r1(X10,X16) ) )
| ~ r1(X9,X10) )
| ~ sP0(X9) ),
inference(nnf_transformation,[],[f10]) ).
fof(f18,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ( ( ~ p1(X5)
| ~ p2(X5) )
& ( p2(X5)
| p1(X5) ) )
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
& ? [X6] :
( ~ p3(X6)
& r1(X1,X6) )
& ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ( ( ~ p2(X10)
| ~ p3(X10) )
& ( p3(X10)
| p2(X10) ) )
| ~ r1(X9,X10) )
| ~ r1(X8,X9) )
| ~ r1(X7,X8) )
| ~ r1(X1,X7) ) )
| ~ r1(X0,X1) )
| ~ sP0(X0) ),
inference(rectify,[],[f17]) ).
fof(f19,plain,
! [X1] :
( ? [X6] :
( ~ p3(X6)
& r1(X1,X6) )
=> ( ~ p3(sK3(X1))
& r1(X1,sK3(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ( ( ~ p1(X5)
| ~ p2(X5) )
& ( p2(X5)
| p1(X5) ) )
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
& ~ p3(sK3(X1))
& r1(X1,sK3(X1))
& ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ( ( ~ p2(X10)
| ~ p3(X10) )
& ( p3(X10)
| p2(X10) ) )
| ~ r1(X9,X10) )
| ~ r1(X8,X9) )
| ~ r1(X7,X8) )
| ~ r1(X1,X7) ) )
| ~ r1(X0,X1) )
| ~ sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f18,f19]) ).
fof(f21,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] : r1(X5,X6)
& r1(X4,X5) )
& r1(X3,X4) )
& r1(X2,X3) )
& r1(X1,X2) )
& r1(X0,X1) )
& ! [X7] :
( ( ! [X8] :
( ( sP1(X8)
& ? [X9] :
( ~ p5(X9)
& r1(X8,X9) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ! [X15] :
( ( ( ~ p4(X15)
| ~ p5(X15) )
& ( p5(X15)
| p4(X15) ) )
| ~ r1(X14,X15) )
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) )
| ~ r1(X10,X11) )
| ~ r1(X8,X10) ) )
| ~ r1(X7,X8) )
& ? [X16] : r1(X7,X16)
& ! [X17] :
( ! [X18] :
( ! [X19] :
( ! [X20] :
( ! [X21] :
( ! [X22] :
( ! [X23] :
( ( ( ~ p5(X23)
| ~ p1(X23) )
& ( p1(X23)
| p5(X23) ) )
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) )
| ~ r1(X7,X17) ) )
| ~ r1(X0,X7) )
& ? [X24] : r1(X0,X24)
& ? [X25] :
( ? [X26] :
( ? [X27] :
( ? [X28] :
( ? [X29] :
( ? [X30] : r1(X29,X30)
& r1(X28,X29) )
& r1(X27,X28) )
& r1(X26,X27) )
& r1(X25,X26) )
& r1(X0,X25) ) ),
inference(rectify,[],[f12]) ).
fof(f22,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] : r1(X5,X6)
& r1(X4,X5) )
& r1(X3,X4) )
& r1(X2,X3) )
& r1(X1,X2) )
& r1(X0,X1) )
& ! [X7] :
( ( ! [X8] :
( ( sP1(X8)
& ? [X9] :
( ~ p5(X9)
& r1(X8,X9) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ! [X15] :
( ( ( ~ p4(X15)
| ~ p5(X15) )
& ( p5(X15)
| p4(X15) ) )
| ~ r1(X14,X15) )
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) )
| ~ r1(X10,X11) )
| ~ r1(X8,X10) ) )
| ~ r1(X7,X8) )
& ? [X16] : r1(X7,X16)
& ! [X17] :
( ! [X18] :
( ! [X19] :
( ! [X20] :
( ! [X21] :
( ! [X22] :
( ! [X23] :
( ( ( ~ p5(X23)
| ~ p1(X23) )
& ( p1(X23)
| p5(X23) ) )
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) )
| ~ r1(X7,X17) ) )
| ~ r1(X0,X7) )
& ? [X24] : r1(X0,X24)
& ? [X25] :
( ? [X26] :
( ? [X27] :
( ? [X28] :
( ? [X29] :
( ? [X30] : r1(X29,X30)
& r1(X28,X29) )
& r1(X27,X28) )
& r1(X26,X27) )
& r1(X25,X26) )
& r1(X0,X25) ) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] : r1(X5,X6)
& r1(X4,X5) )
& r1(X3,X4) )
& r1(X2,X3) )
& r1(X1,X2) )
& r1(sK4,X1) )
& ! [X7] :
( ( ! [X8] :
( ( sP1(X8)
& ? [X9] :
( ~ p5(X9)
& r1(X8,X9) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ! [X15] :
( ( ( ~ p4(X15)
| ~ p5(X15) )
& ( p5(X15)
| p4(X15) ) )
| ~ r1(X14,X15) )
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) )
| ~ r1(X10,X11) )
| ~ r1(X8,X10) ) )
| ~ r1(X7,X8) )
& ? [X16] : r1(X7,X16)
& ! [X17] :
( ! [X18] :
( ! [X19] :
( ! [X20] :
( ! [X21] :
( ! [X22] :
( ! [X23] :
( ( ( ~ p5(X23)
| ~ p1(X23) )
& ( p1(X23)
| p5(X23) ) )
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) )
| ~ r1(X7,X17) ) )
| ~ r1(sK4,X7) )
& ? [X24] : r1(sK4,X24)
& ? [X25] :
( ? [X26] :
( ? [X27] :
( ? [X28] :
( ? [X29] :
( ? [X30] : r1(X29,X30)
& r1(X28,X29) )
& r1(X27,X28) )
& r1(X26,X27) )
& r1(X25,X26) )
& r1(sK4,X25) ) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] : r1(X5,X6)
& r1(X4,X5) )
& r1(X3,X4) )
& r1(X2,X3) )
& r1(X1,X2) )
& r1(sK4,X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] : r1(X5,X6)
& r1(X4,X5) )
& r1(X3,X4) )
& r1(X2,X3) )
& r1(sK5,X2) )
& r1(sK4,sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] : r1(X5,X6)
& r1(X4,X5) )
& r1(X3,X4) )
& r1(X2,X3) )
& r1(sK5,X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] : r1(X5,X6)
& r1(X4,X5) )
& r1(X3,X4) )
& r1(sK6,X3) )
& r1(sK5,sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] : r1(X5,X6)
& r1(X4,X5) )
& r1(X3,X4) )
& r1(sK6,X3) )
=> ( ? [X4] :
( ? [X5] :
( ? [X6] : r1(X5,X6)
& r1(X4,X5) )
& r1(sK7,X4) )
& r1(sK6,sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
( ? [X4] :
( ? [X5] :
( ? [X6] : r1(X5,X6)
& r1(X4,X5) )
& r1(sK7,X4) )
=> ( ? [X5] :
( ? [X6] : r1(X5,X6)
& r1(sK8,X5) )
& r1(sK7,sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
( ? [X5] :
( ? [X6] : r1(X5,X6)
& r1(sK8,X5) )
=> ( ? [X6] : r1(sK9,X6)
& r1(sK8,sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
( ? [X6] : r1(sK9,X6)
=> r1(sK9,sK10) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X8] :
( ? [X9] :
( ~ p5(X9)
& r1(X8,X9) )
=> ( ~ p5(sK11(X8))
& r1(X8,sK11(X8)) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
! [X7] :
( ? [X16] : r1(X7,X16)
=> r1(X7,sK12(X7)) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
( ? [X24] : r1(sK4,X24)
=> r1(sK4,sK13) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
( ? [X25] :
( ? [X26] :
( ? [X27] :
( ? [X28] :
( ? [X29] :
( ? [X30] : r1(X29,X30)
& r1(X28,X29) )
& r1(X27,X28) )
& r1(X26,X27) )
& r1(X25,X26) )
& r1(sK4,X25) )
=> ( ? [X26] :
( ? [X27] :
( ? [X28] :
( ? [X29] :
( ? [X30] : r1(X29,X30)
& r1(X28,X29) )
& r1(X27,X28) )
& r1(X26,X27) )
& r1(sK14,X26) )
& r1(sK4,sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
( ? [X26] :
( ? [X27] :
( ? [X28] :
( ? [X29] :
( ? [X30] : r1(X29,X30)
& r1(X28,X29) )
& r1(X27,X28) )
& r1(X26,X27) )
& r1(sK14,X26) )
=> ( ? [X27] :
( ? [X28] :
( ? [X29] :
( ? [X30] : r1(X29,X30)
& r1(X28,X29) )
& r1(X27,X28) )
& r1(sK15,X27) )
& r1(sK14,sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
( ? [X27] :
( ? [X28] :
( ? [X29] :
( ? [X30] : r1(X29,X30)
& r1(X28,X29) )
& r1(X27,X28) )
& r1(sK15,X27) )
=> ( ? [X28] :
( ? [X29] :
( ? [X30] : r1(X29,X30)
& r1(X28,X29) )
& r1(sK16,X28) )
& r1(sK15,sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
( ? [X28] :
( ? [X29] :
( ? [X30] : r1(X29,X30)
& r1(X28,X29) )
& r1(sK16,X28) )
=> ( ? [X29] :
( ? [X30] : r1(X29,X30)
& r1(sK17,X29) )
& r1(sK16,sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f36,plain,
( ? [X29] :
( ? [X30] : r1(X29,X30)
& r1(sK17,X29) )
=> ( ? [X30] : r1(sK18,X30)
& r1(sK17,sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
( ? [X30] : r1(sK18,X30)
=> r1(sK18,sK19) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
( r1(sK9,sK10)
& r1(sK8,sK9)
& r1(sK7,sK8)
& r1(sK6,sK7)
& r1(sK5,sK6)
& r1(sK4,sK5)
& ! [X7] :
( ( ! [X8] :
( ( sP1(X8)
& ~ p5(sK11(X8))
& r1(X8,sK11(X8))
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ! [X15] :
( ( ( ~ p4(X15)
| ~ p5(X15) )
& ( p5(X15)
| p4(X15) ) )
| ~ r1(X14,X15) )
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) )
| ~ r1(X10,X11) )
| ~ r1(X8,X10) ) )
| ~ r1(X7,X8) )
& r1(X7,sK12(X7))
& ! [X17] :
( ! [X18] :
( ! [X19] :
( ! [X20] :
( ! [X21] :
( ! [X22] :
( ! [X23] :
( ( ( ~ p5(X23)
| ~ p1(X23) )
& ( p1(X23)
| p5(X23) ) )
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) )
| ~ r1(X7,X17) ) )
| ~ r1(sK4,X7) )
& r1(sK4,sK13)
& r1(sK18,sK19)
& r1(sK17,sK18)
& r1(sK16,sK17)
& r1(sK15,sK16)
& r1(sK14,sK15)
& r1(sK4,sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14,sK15,sK16,sK17,sK18,sK19])],[f21,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22]) ).
fof(f39,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f40,plain,
! [X3,X0,X1,X6,X7,X4,X5] :
( p4(X7)
| p3(X7)
| ~ r1(X6,X7)
| ~ r1(X5,X6)
| ~ r1(X4,X5)
| ~ r1(X3,X4)
| ~ r1(X1,X3)
| ~ r1(X0,X1)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f41,plain,
! [X3,X0,X1,X6,X7,X4,X5] :
( ~ p3(X7)
| ~ p4(X7)
| ~ r1(X6,X7)
| ~ r1(X5,X6)
| ~ r1(X4,X5)
| ~ r1(X3,X4)
| ~ r1(X1,X3)
| ~ r1(X0,X1)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f44,plain,
! [X0,X1] :
( sP0(X1)
| ~ r1(X0,X1)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f45,plain,
! [X10,X0,X1,X8,X9,X7] :
( p3(X10)
| p2(X10)
| ~ r1(X9,X10)
| ~ r1(X8,X9)
| ~ r1(X7,X8)
| ~ r1(X1,X7)
| ~ r1(X0,X1)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f46,plain,
! [X10,X0,X1,X8,X9,X7] :
( ~ p2(X10)
| ~ p3(X10)
| ~ r1(X9,X10)
| ~ r1(X8,X9)
| ~ r1(X7,X8)
| ~ r1(X1,X7)
| ~ r1(X0,X1)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f49,plain,
! [X2,X3,X0,X1,X4,X5] :
( p2(X5)
| p1(X5)
| ~ r1(X4,X5)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f50,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ p1(X5)
| ~ p2(X5)
| ~ r1(X4,X5)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f58,plain,
! [X21,X18,X19,X7,X17,X22,X23,X20] :
( p1(X23)
| p5(X23)
| ~ r1(X22,X23)
| ~ r1(X21,X22)
| ~ r1(X20,X21)
| ~ r1(X19,X20)
| ~ r1(X18,X19)
| ~ r1(X17,X18)
| ~ r1(X7,X17)
| ~ r1(sK4,X7) ),
inference(cnf_transformation,[],[f38]) ).
fof(f59,plain,
! [X21,X18,X19,X7,X17,X22,X23,X20] :
( ~ p5(X23)
| ~ p1(X23)
| ~ r1(X22,X23)
| ~ r1(X21,X22)
| ~ r1(X20,X21)
| ~ r1(X19,X20)
| ~ r1(X18,X19)
| ~ r1(X17,X18)
| ~ r1(X7,X17)
| ~ r1(sK4,X7) ),
inference(cnf_transformation,[],[f38]) ).
fof(f61,plain,
! [X10,X11,X8,X7,X14,X15,X12,X13] :
( p5(X15)
| p4(X15)
| ~ r1(X14,X15)
| ~ r1(X13,X14)
| ~ r1(X12,X13)
| ~ r1(X11,X12)
| ~ r1(X10,X11)
| ~ r1(X8,X10)
| ~ r1(X7,X8)
| ~ r1(sK4,X7) ),
inference(cnf_transformation,[],[f38]) ).
fof(f62,plain,
! [X10,X11,X8,X7,X14,X15,X12,X13] :
( ~ p4(X15)
| ~ p5(X15)
| ~ r1(X14,X15)
| ~ r1(X13,X14)
| ~ r1(X12,X13)
| ~ r1(X11,X12)
| ~ r1(X10,X11)
| ~ r1(X8,X10)
| ~ r1(X7,X8)
| ~ r1(sK4,X7) ),
inference(cnf_transformation,[],[f38]) ).
fof(f65,plain,
! [X8,X7] :
( sP1(X8)
| ~ r1(X7,X8)
| ~ r1(sK4,X7) ),
inference(cnf_transformation,[],[f38]) ).
cnf(c_49,plain,
r1(X0,X0),
inference(cnf_transformation,[],[f39]) ).
cnf(c_50,plain,
( ~ r1(X0,X1)
| ~ sP1(X0)
| sP0(X1) ),
inference(cnf_transformation,[],[f44]) ).
cnf(c_53,plain,
( ~ r1(X0,X1)
| ~ r1(X1,X2)
| ~ r1(X2,X6)
| ~ r1(X3,X4)
| ~ r1(X5,X3)
| ~ r1(X6,X5)
| ~ sP1(X0)
| ~ p4(X4)
| ~ p3(X4) ),
inference(cnf_transformation,[],[f41]) ).
cnf(c_54,plain,
( ~ r1(X0,X1)
| ~ r1(X1,X2)
| ~ r1(X2,X6)
| ~ r1(X3,X4)
| ~ r1(X5,X3)
| ~ r1(X6,X5)
| ~ sP1(X0)
| p4(X4)
| p3(X4) ),
inference(cnf_transformation,[],[f40]) ).
cnf(c_55,plain,
( ~ r1(X0,X1)
| ~ r1(X1,X2)
| ~ r1(X2,X5)
| ~ r1(X3,X4)
| ~ r1(X5,X3)
| ~ sP0(X0)
| ~ p1(X4)
| ~ p2(X4) ),
inference(cnf_transformation,[],[f50]) ).
cnf(c_56,plain,
( ~ r1(X0,X1)
| ~ r1(X1,X2)
| ~ r1(X2,X5)
| ~ r1(X3,X4)
| ~ r1(X5,X3)
| ~ sP0(X0)
| p1(X4)
| p2(X4) ),
inference(cnf_transformation,[],[f49]) ).
cnf(c_59,plain,
( ~ r1(X0,X1)
| ~ r1(X1,X2)
| ~ r1(X2,X3)
| ~ r1(X3,X4)
| ~ r1(X4,X5)
| ~ sP0(X0)
| ~ p3(X5)
| ~ p2(X5) ),
inference(cnf_transformation,[],[f46]) ).
cnf(c_60,plain,
( ~ r1(X0,X1)
| ~ r1(X1,X2)
| ~ r1(X2,X3)
| ~ r1(X3,X4)
| ~ r1(X4,X5)
| ~ sP0(X0)
| p3(X5)
| p2(X5) ),
inference(cnf_transformation,[],[f45]) ).
cnf(c_67,negated_conjecture,
( ~ r1(X0,X1)
| ~ r1(sK4,X0)
| sP1(X1) ),
inference(cnf_transformation,[],[f65]) ).
cnf(c_70,negated_conjecture,
( ~ r1(X0,X1)
| ~ r1(X1,X2)
| ~ r1(X2,X3)
| ~ r1(X3,X7)
| ~ r1(X4,X5)
| ~ r1(X6,X4)
| ~ r1(X7,X6)
| ~ r1(sK4,X0)
| ~ p4(X5)
| ~ p5(X5) ),
inference(cnf_transformation,[],[f62]) ).
cnf(c_71,negated_conjecture,
( ~ r1(X0,X1)
| ~ r1(X1,X2)
| ~ r1(X2,X3)
| ~ r1(X3,X7)
| ~ r1(X4,X5)
| ~ r1(X6,X4)
| ~ r1(X7,X6)
| ~ r1(sK4,X0)
| p4(X5)
| p5(X5) ),
inference(cnf_transformation,[],[f61]) ).
cnf(c_73,negated_conjecture,
( ~ r1(X0,X1)
| ~ r1(X1,X7)
| ~ r1(X2,X3)
| ~ r1(X4,X2)
| ~ r1(X5,X4)
| ~ r1(X6,X5)
| ~ r1(X7,X6)
| ~ r1(sK4,X0)
| ~ p1(X3)
| ~ p5(X3) ),
inference(cnf_transformation,[],[f59]) ).
cnf(c_74,negated_conjecture,
( ~ r1(X0,X1)
| ~ r1(X1,X7)
| ~ r1(X2,X3)
| ~ r1(X4,X2)
| ~ r1(X5,X4)
| ~ r1(X6,X5)
| ~ r1(X7,X6)
| ~ r1(sK4,X0)
| p1(X3)
| p5(X3) ),
inference(cnf_transformation,[],[f58]) ).
cnf(c_82,plain,
r1(sK4,sK4),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_84,plain,
( ~ r1(sK4,sK4)
| ~ sP1(sK4)
| sP0(sK4) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_85,plain,
( ~ r1(sK4,sK4)
| sP1(sK4) ),
inference(instantiation,[status(thm)],[c_67]) ).
cnf(c_92,plain,
( ~ r1(sK4,sK4)
| ~ sP0(sK4)
| p3(sK4)
| p2(sK4) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_93,plain,
( ~ r1(sK4,sK4)
| ~ sP0(sK4)
| p1(sK4)
| p2(sK4) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_94,plain,
( ~ r1(sK4,sK4)
| ~ sP0(sK4)
| ~ p3(sK4)
| ~ p2(sK4) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_95,plain,
( ~ r1(sK4,sK4)
| ~ sP0(sK4)
| ~ p1(sK4)
| ~ p2(sK4) ),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_96,plain,
( ~ r1(sK4,sK4)
| ~ sP1(sK4)
| p4(sK4)
| p3(sK4) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_97,plain,
( ~ r1(sK4,sK4)
| ~ sP1(sK4)
| ~ p4(sK4)
| ~ p3(sK4) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_98,plain,
( ~ r1(sK4,sK4)
| p1(sK4)
| p5(sK4) ),
inference(instantiation,[status(thm)],[c_74]) ).
cnf(c_99,plain,
( ~ r1(sK4,sK4)
| p4(sK4)
| p5(sK4) ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_100,plain,
( ~ r1(sK4,sK4)
| ~ p1(sK4)
| ~ p5(sK4) ),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_101,plain,
( ~ r1(sK4,sK4)
| ~ p4(sK4)
| ~ p5(sK4) ),
inference(instantiation,[status(thm)],[c_70]) ).
cnf(c_102,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_101,c_100,c_99,c_98,c_97,c_96,c_95,c_94,c_93,c_92,c_85,c_84,c_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL668+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 20:38:54 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.88/1.15 % SZS status Started for theBenchmark.p
% 0.88/1.15 % SZS status Theorem for theBenchmark.p
% 0.88/1.15
% 0.88/1.15 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.88/1.15
% 0.88/1.15 ------ iProver source info
% 0.88/1.15
% 0.88/1.15 git: date: 2023-05-31 18:12:56 +0000
% 0.88/1.15 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.88/1.15 git: non_committed_changes: false
% 0.88/1.15 git: last_make_outside_of_git: false
% 0.88/1.15
% 0.88/1.15 ------ Parsing...
% 0.88/1.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.88/1.15
% 0.88/1.15 ------ Preprocessing...
% 0.88/1.15
% 0.88/1.15 % SZS status Theorem for theBenchmark.p
% 0.88/1.15
% 0.88/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.88/1.16
% 0.88/1.16
%------------------------------------------------------------------------------