%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL668+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:07:52 PM UTC 2026
% Result : Theorem 1.68s 1.29s
% Output : CNFRefutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 60 ( 5 unt; 2 def)
% Number of atoms : 1130 ( 0 equ)
% Maximal formula atoms : 84 ( 18 avg)
% Number of connectives : 2043 ( 973 ~; 820 |; 250 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 47 ( 17 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 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 : 686 ( 0 sgn 623 !; 63 ?; 75 :)
% 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,[status(cth)],[f2]) ).
fof(f4,plain,
~ ~ ? [X0] :
~ ( ! [X42] :
( ! [X43] :
( ! [X44] :
( ! [X45] :
( ! [X46] :
( ! [X47] :
( ( p1(X47)
& p2(X47)
& p3(X47)
& p4(X47)
& p5(X47)
& p6(X47) )
| ~ r1(X46,X47) )
| ~ r1(X45,X46) )
| ~ r1(X44,X45) )
| ~ r1(X43,X44) )
| ~ r1(X42,X43) )
| ~ r1(X0,X42) )
| ~ ! [X8] :
( ~ ( ~ ! [X17] :
( ~ ( ~ ! [X25] :
( ~ ( ~ ! [X32] :
( ~ ( ~ ! [X38] :
( ~ ~ ! [X39] :
( ! [X40] :
( ! [X41] :
( ~ ( ( p1(X41)
& p2(X41) )
| ( ~ p2(X41)
& ~ p1(X41) ) )
| ~ r1(X40,X41) )
| ~ r1(X39,X40) )
| ~ r1(X38,X39) )
| ~ r1(X32,X38) )
| ! [X37] :
( p3(X37)
| ~ r1(X32,X37) )
| ~ ! [X33] :
( ! [X34] :
( ! [X35] :
( ! [X36] :
( ~ ( ( p2(X36)
& p3(X36) )
| ( ~ p3(X36)
& ~ p2(X36) ) )
| ~ r1(X35,X36) )
| ~ r1(X34,X35) )
| ~ r1(X33,X34) )
| ~ r1(X32,X33) ) )
| ~ r1(X25,X32) )
| ! [X31] :
( p4(X31)
| ~ r1(X25,X31) )
| ~ ! [X26] :
( ! [X27] :
( ! [X28] :
( ! [X29] :
( ! [X30] :
( ~ ( ( p3(X30)
& p4(X30) )
| ( ~ p4(X30)
& ~ p3(X30) ) )
| ~ r1(X29,X30) )
| ~ r1(X28,X29) )
| ~ r1(X27,X28) )
| ~ r1(X26,X27) )
| ~ r1(X25,X26) ) )
| ~ r1(X17,X25) )
| ! [X24] :
( p5(X24)
| ~ r1(X17,X24) )
| ~ ! [X18] :
( ! [X19] :
( ! [X20] :
( ! [X21] :
( ! [X22] :
( ! [X23] :
( ~ ( ( p4(X23)
& p5(X23) )
| ( ~ p5(X23)
& ~ p4(X23) ) )
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) ) )
| ~ r1(X8,X17) )
| ! [X16] :
( p6(X16)
| ~ r1(X8,X16) )
| ~ ! [X9] :
( ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ! [X15] :
( ~ ( ( p5(X15)
& p1(X15) )
| ( ~ p1(X15)
& ~ p5(X15) ) )
| ~ r1(X14,X15) )
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) )
| ~ r1(X10,X11) )
| ~ r1(X9,X10) )
| ~ r1(X8,X9) ) )
| ~ r1(X0,X8) )
| ! [X7] :
( p7(X7)
| ~ r1(X0,X7) )
| ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ( ~ p2(X6)
& ~ p4(X6)
& ~ p6(X6)
& ~ p8(X6)
& ~ p10(X6)
& ~ p12(X6) )
| ~ r1(X5,X6) )
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) ) ),
inference(rectify,[],[f3]) ).
fof(f5,plain,
? [X0] :
~ ( ! [X42] :
( ! [X43] :
( ! [X44] :
( ! [X45] :
( ! [X46] :
( ! [X47] :
( ( p1(X47)
& p2(X47)
& p3(X47)
& p4(X47)
& p5(X47)
& p6(X47) )
| ~ r1(X46,X47) )
| ~ r1(X45,X46) )
| ~ r1(X44,X45) )
| ~ r1(X43,X44) )
| ~ r1(X42,X43) )
| ~ r1(X0,X42) )
| ~ ! [X8] :
( ~ ( ~ ! [X17] :
( ~ ( ~ ! [X25] :
( ~ ( ~ ! [X32] :
( ~ ( ~ ! [X38] :
( ! [X39] :
( ! [X40] :
( ! [X41] :
( ~ ( ( p1(X41)
& p2(X41) )
| ( ~ p2(X41)
& ~ p1(X41) ) )
| ~ r1(X40,X41) )
| ~ r1(X39,X40) )
| ~ r1(X38,X39) )
| ~ r1(X32,X38) )
| ! [X37] :
( p3(X37)
| ~ r1(X32,X37) )
| ~ ! [X33] :
( ! [X34] :
( ! [X35] :
( ! [X36] :
( ~ ( ( p2(X36)
& p3(X36) )
| ( ~ p3(X36)
& ~ p2(X36) ) )
| ~ r1(X35,X36) )
| ~ r1(X34,X35) )
| ~ r1(X33,X34) )
| ~ r1(X32,X33) ) )
| ~ r1(X25,X32) )
| ! [X31] :
( p4(X31)
| ~ r1(X25,X31) )
| ~ ! [X26] :
( ! [X27] :
( ! [X28] :
( ! [X29] :
( ! [X30] :
( ~ ( ( p3(X30)
& p4(X30) )
| ( ~ p4(X30)
& ~ p3(X30) ) )
| ~ r1(X29,X30) )
| ~ r1(X28,X29) )
| ~ r1(X27,X28) )
| ~ r1(X26,X27) )
| ~ r1(X25,X26) ) )
| ~ r1(X17,X25) )
| ! [X24] :
( p5(X24)
| ~ r1(X17,X24) )
| ~ ! [X18] :
( ! [X19] :
( ! [X20] :
( ! [X21] :
( ! [X22] :
( ! [X23] :
( ~ ( ( p4(X23)
& p5(X23) )
| ( ~ p5(X23)
& ~ p4(X23) ) )
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) ) )
| ~ r1(X8,X17) )
| ! [X16] :
( p6(X16)
| ~ r1(X8,X16) )
| ~ ! [X9] :
( ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ! [X15] :
( ~ ( ( p5(X15)
& p1(X15) )
| ( ~ p1(X15)
& ~ p5(X15) ) )
| ~ r1(X14,X15) )
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) )
| ~ r1(X10,X11) )
| ~ r1(X9,X10) )
| ~ r1(X8,X9) ) )
| ~ r1(X0,X8) )
| ! [X7] :
( p7(X7)
| ~ r1(X0,X7) )
| ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ( ~ p2(X6)
& ~ p4(X6)
& ~ p6(X6)
& ~ p8(X6)
& ~ p10(X6)
& ~ p12(X6) )
| ~ r1(X5,X6) )
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
? [X0] :
~ ( ! [X42] :
( ! [X43] :
( ! [X44] :
( ! [X45] :
( ! [X46] :
( ! [X47] :
( ( p1(X47)
& p2(X47)
& p3(X47)
& p4(X47)
& p5(X47)
& p6(X47) )
| ~ r1(X46,X47) )
| ~ r1(X45,X46) )
| ~ r1(X44,X45) )
| ~ r1(X43,X44) )
| ~ r1(X42,X43) )
| ~ r1(X0,X42) )
| ~ ! [X8] :
( ~ ( ~ ! [X17] :
( ~ ( ~ ! [X25] :
( ~ ( ~ ! [X32] :
( ~ ( ~ ! [X38] :
( ! [X39] :
( ! [X40] :
( ! [X41] :
( ~ ( ( p1(X41)
& p2(X41) )
| ( ~ p2(X41)
& ~ p1(X41) ) )
| ~ r1(X40,X41) )
| ~ r1(X39,X40) )
| ~ r1(X38,X39) )
| ~ r1(X32,X38) )
| ! [X37] :
( p3(X37)
| ~ r1(X32,X37) )
| ~ ! [X33] :
( ! [X34] :
( ! [X35] :
( ! [X36] :
( ~ ( ( p2(X36)
& p3(X36) )
| ( ~ p3(X36)
& ~ p2(X36) ) )
| ~ r1(X35,X36) )
| ~ r1(X34,X35) )
| ~ r1(X33,X34) )
| ~ r1(X32,X33) ) )
| ~ r1(X25,X32) )
| ! [X31] :
( p4(X31)
| ~ r1(X25,X31) )
| ~ ! [X26] :
( ! [X27] :
( ! [X28] :
( ! [X29] :
( ! [X30] :
( ~ ( ( p3(X30)
& p4(X30) )
| ( ~ p4(X30)
& ~ p3(X30) ) )
| ~ r1(X29,X30) )
| ~ r1(X28,X29) )
| ~ r1(X27,X28) )
| ~ r1(X26,X27) )
| ~ r1(X25,X26) ) )
| ~ r1(X17,X25) )
| ! [X24] :
( p5(X24)
| ~ r1(X17,X24) )
| ~ ! [X18] :
( ! [X19] :
( ! [X20] :
( ! [X21] :
( ! [X22] :
( ! [X23] :
( ~ ( ( p4(X23)
& p5(X23) )
| ( ~ p5(X23)
& ~ p4(X23) ) )
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) ) )
| ~ r1(X8,X17) )
| ! [X16] :
( p6(X16)
| ~ r1(X8,X16) )
| ~ ! [X9] :
( ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ! [X15] :
( ~ ( ( p5(X15)
& p1(X15) )
| ( ~ p1(X15)
& ~ p5(X15) ) )
| ~ r1(X14,X15) )
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) )
| ~ r1(X10,X11) )
| ~ r1(X9,X10) )
| ~ r1(X8,X9) ) )
| ~ r1(X0,X8) )
| ! [X7] : ~ r1(X0,X7)
| ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ( ~ p2(X6)
& ~ p4(X6)
& ~ p6(X6)
& ~ p8(X6)
& ~ p10(X6)
& ~ p12(X6) )
| ~ r1(X5,X6) )
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) ) ),
inference(pure_predicate_removal,[],[f5]) ).
fof(f7,plain,
? [X0] :
~ ( ! [X42] :
( ! [X43] :
( ! [X44] :
( ! [X45] :
( ! [X46] :
( ! [X47] :
( ( p1(X47)
& p2(X47)
& p3(X47)
& p4(X47)
& p5(X47)
& p6(X47) )
| ~ r1(X46,X47) )
| ~ r1(X45,X46) )
| ~ r1(X44,X45) )
| ~ r1(X43,X44) )
| ~ r1(X42,X43) )
| ~ r1(X0,X42) )
| ~ ! [X8] :
( ~ ( ~ ! [X17] :
( ~ ( ~ ! [X25] :
( ~ ( ~ ! [X32] :
( ~ ( ~ ! [X38] :
( ! [X39] :
( ! [X40] :
( ! [X41] :
( ~ ( ( p1(X41)
& p2(X41) )
| ( ~ p2(X41)
& ~ p1(X41) ) )
| ~ r1(X40,X41) )
| ~ r1(X39,X40) )
| ~ r1(X38,X39) )
| ~ r1(X32,X38) )
| ! [X37] :
( p3(X37)
| ~ r1(X32,X37) )
| ~ ! [X33] :
( ! [X34] :
( ! [X35] :
( ! [X36] :
( ~ ( ( p2(X36)
& p3(X36) )
| ( ~ p3(X36)
& ~ p2(X36) ) )
| ~ r1(X35,X36) )
| ~ r1(X34,X35) )
| ~ r1(X33,X34) )
| ~ r1(X32,X33) ) )
| ~ r1(X25,X32) )
| ! [X31] :
( p4(X31)
| ~ r1(X25,X31) )
| ~ ! [X26] :
( ! [X27] :
( ! [X28] :
( ! [X29] :
( ! [X30] :
( ~ ( ( p3(X30)
& p4(X30) )
| ( ~ p4(X30)
& ~ p3(X30) ) )
| ~ r1(X29,X30) )
| ~ r1(X28,X29) )
| ~ r1(X27,X28) )
| ~ r1(X26,X27) )
| ~ r1(X25,X26) ) )
| ~ r1(X17,X25) )
| ! [X24] :
( p5(X24)
| ~ r1(X17,X24) )
| ~ ! [X18] :
( ! [X19] :
( ! [X20] :
( ! [X21] :
( ! [X22] :
( ! [X23] :
( ~ ( ( p4(X23)
& p5(X23) )
| ( ~ p5(X23)
& ~ p4(X23) ) )
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) ) )
| ~ r1(X8,X17) )
| ! [X16] :
( p6(X16)
| ~ r1(X8,X16) )
| ~ ! [X9] :
( ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ! [X15] :
( ~ ( ( p5(X15)
& p1(X15) )
| ( ~ p1(X15)
& ~ p5(X15) ) )
| ~ r1(X14,X15) )
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) )
| ~ r1(X10,X11) )
| ~ r1(X9,X10) )
| ~ r1(X8,X9) ) )
| ~ r1(X0,X8) )
| ! [X7] : ~ r1(X0,X7)
| ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] : ~ r1(X5,X6)
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) ) ),
inference(pure_predicate_removal,[],[f6]) ).
fof(f8,plain,
? [X0] :
~ ( ! [X42] :
( ! [X43] :
( ! [X44] :
( ! [X45] :
( ! [X46] :
( ! [X47] : ~ r1(X46,X47)
| ~ r1(X45,X46) )
| ~ r1(X44,X45) )
| ~ r1(X43,X44) )
| ~ r1(X42,X43) )
| ~ r1(X0,X42) )
| ~ ! [X8] :
( ~ ( ~ ! [X17] :
( ~ ( ~ ! [X25] :
( ~ ( ~ ! [X32] :
( ~ ( ~ ! [X38] :
( ! [X39] :
( ! [X40] :
( ! [X41] :
( ~ ( ( p1(X41)
& p2(X41) )
| ( ~ p2(X41)
& ~ p1(X41) ) )
| ~ r1(X40,X41) )
| ~ r1(X39,X40) )
| ~ r1(X38,X39) )
| ~ r1(X32,X38) )
| ! [X37] :
( p3(X37)
| ~ r1(X32,X37) )
| ~ ! [X33] :
( ! [X34] :
( ! [X35] :
( ! [X36] :
( ~ ( ( p2(X36)
& p3(X36) )
| ( ~ p3(X36)
& ~ p2(X36) ) )
| ~ r1(X35,X36) )
| ~ r1(X34,X35) )
| ~ r1(X33,X34) )
| ~ r1(X32,X33) ) )
| ~ r1(X25,X32) )
| ! [X31] :
( p4(X31)
| ~ r1(X25,X31) )
| ~ ! [X26] :
( ! [X27] :
( ! [X28] :
( ! [X29] :
( ! [X30] :
( ~ ( ( p3(X30)
& p4(X30) )
| ( ~ p4(X30)
& ~ p3(X30) ) )
| ~ r1(X29,X30) )
| ~ r1(X28,X29) )
| ~ r1(X27,X28) )
| ~ r1(X26,X27) )
| ~ r1(X25,X26) ) )
| ~ r1(X17,X25) )
| ! [X24] :
( p5(X24)
| ~ r1(X17,X24) )
| ~ ! [X18] :
( ! [X19] :
( ! [X20] :
( ! [X21] :
( ! [X22] :
( ! [X23] :
( ~ ( ( p4(X23)
& p5(X23) )
| ( ~ p5(X23)
& ~ p4(X23) ) )
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) ) )
| ~ r1(X8,X17) )
| ! [X16] : ~ r1(X8,X16)
| ~ ! [X9] :
( ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ! [X15] :
( ~ ( ( p5(X15)
& p1(X15) )
| ( ~ p1(X15)
& ~ p5(X15) ) )
| ~ r1(X14,X15) )
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) )
| ~ r1(X10,X11) )
| ~ r1(X9,X10) )
| ~ r1(X8,X9) ) )
| ~ r1(X0,X8) )
| ! [X7] : ~ r1(X0,X7)
| ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] : ~ r1(X5,X6)
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) ) ),
inference(pure_predicate_removal,[],[f7]) ).
fof(f9,plain,
? [X0] :
( ? [X42] :
( ? [X43] :
( ? [X44] :
( ? [X45] :
( ? [X46] :
( ? [X47] : r1(X46,X47)
& r1(X45,X46) )
& r1(X44,X45) )
& r1(X43,X44) )
& r1(X42,X43) )
& r1(X0,X42) )
& ! [X8] :
( ( ! [X17] :
( ( ! [X25] :
( ( ! [X32] :
( ( ! [X38] :
( ! [X39] :
( ! [X40] :
( ! [X41] :
( ( ( ~ p1(X41)
| ~ p2(X41) )
& ( p2(X41)
| p1(X41) ) )
| ~ r1(X40,X41) )
| ~ r1(X39,X40) )
| ~ r1(X38,X39) )
| ~ r1(X32,X38) )
& ? [X37] :
( ~ p3(X37)
& r1(X32,X37) )
& ! [X33] :
( ! [X34] :
( ! [X35] :
( ! [X36] :
( ( ( ~ p2(X36)
| ~ p3(X36) )
& ( p3(X36)
| p2(X36) ) )
| ~ r1(X35,X36) )
| ~ r1(X34,X35) )
| ~ r1(X33,X34) )
| ~ r1(X32,X33) ) )
| ~ r1(X25,X32) )
& ? [X31] :
( ~ p4(X31)
& r1(X25,X31) )
& ! [X26] :
( ! [X27] :
( ! [X28] :
( ! [X29] :
( ! [X30] :
( ( ( ~ p3(X30)
| ~ p4(X30) )
& ( p4(X30)
| p3(X30) ) )
| ~ r1(X29,X30) )
| ~ r1(X28,X29) )
| ~ r1(X27,X28) )
| ~ r1(X26,X27) )
| ~ r1(X25,X26) ) )
| ~ r1(X17,X25) )
& ? [X24] :
( ~ p5(X24)
& r1(X17,X24) )
& ! [X18] :
( ! [X19] :
( ! [X20] :
( ! [X21] :
( ! [X22] :
( ! [X23] :
( ( ( ~ p4(X23)
| ~ p5(X23) )
& ( p5(X23)
| p4(X23) ) )
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) ) )
| ~ r1(X8,X17) )
& ? [X16] : r1(X8,X16)
& ! [X9] :
( ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ! [X15] :
( ( ( ~ p5(X15)
| ~ p1(X15) )
& ( p1(X15)
| p5(X15) ) )
| ~ r1(X14,X15) )
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) )
| ~ r1(X10,X11) )
| ~ r1(X9,X10) )
| ~ r1(X8,X9) ) )
| ~ r1(X0,X8) )
& ? [X7] : r1(X0,X7)
& ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] : r1(X5,X6)
& r1(X4,X5) )
& r1(X3,X4) )
& r1(X2,X3) )
& r1(X1,X2) )
& r1(X0,X1) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f13,plain,
! [X17] :
( ~ sP1(X17)
| ! [X25] :
( ( sP0(X25)
& ? [X31] :
( ~ p4(X31)
& r1(X25,X31) )
& ! [X26] :
( ! [X27] :
( ! [X28] :
( ! [X29] :
( ! [X30] :
( ( ( ~ p3(X30)
| ~ p4(X30) )
& ( p4(X30)
| p3(X30) ) )
| ~ r1(X29,X30) )
| ~ r1(X28,X29) )
| ~ r1(X27,X28) )
| ~ r1(X26,X27) )
| ~ r1(X25,X26) ) )
| ~ r1(X17,X25) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f14,plain,
! [X0] :
( ~ sP1(X0)
| ! [X1] :
( ( sP0(X1)
& ? [X7] :
( ~ p4(X7)
& r1(X1,X7) )
& ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ( ( ~ p3(X6)
| ~ p4(X6) )
& ( p4(X6)
| p3(X6) ) )
| ~ r1(X5,X6) )
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) ) )
| ~ r1(X0,X1) ) ),
inference(rectify,[],[f13]) ).
fof(f15,plain,
! [X0] :
( ~ sP1(X0)
| ! [X1] :
( ( sP0(X1)
& ~ p4(sK2(X1))
& r1(X1,sK2(X1))
& ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ( ( ~ p3(X6)
| ~ p4(X6) )
& ( p4(X6)
| p3(X6) ) )
| ~ r1(X5,X6) )
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) ) )
| ~ r1(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X7,sK2(X1))],[f14]) ).
fof(f19,plain,
? [X0] :
( ? [X25] :
( ? [X26] :
( ? [X27] :
( ? [X28] :
( ? [X29] :
( ? [X30] : r1(X29,X30)
& r1(X28,X29) )
& r1(X27,X28) )
& r1(X26,X27) )
& r1(X25,X26) )
& r1(X0,X25) )
& ! [X8] :
( ( ! [X17] :
( ( sP1(X17)
& ? [X24] :
( ~ p5(X24)
& r1(X17,X24) )
& ! [X18] :
( ! [X19] :
( ! [X20] :
( ! [X21] :
( ! [X22] :
( ! [X23] :
( ( ( ~ p4(X23)
| ~ p5(X23) )
& ( p5(X23)
| p4(X23) ) )
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) ) )
| ~ r1(X8,X17) )
& ? [X16] : r1(X8,X16)
& ! [X9] :
( ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ! [X15] :
( ( ( ~ p5(X15)
| ~ p1(X15) )
& ( p1(X15)
| p5(X15) ) )
| ~ r1(X14,X15) )
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) )
| ~ r1(X10,X11) )
| ~ r1(X9,X10) )
| ~ r1(X8,X9) ) )
| ~ r1(X0,X8) )
& ? [X7] : r1(X0,X7)
& ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] : r1(X5,X6)
& r1(X4,X5) )
& r1(X3,X4) )
& r1(X2,X3) )
& r1(X1,X2) )
& r1(X0,X1) ) ),
inference(rectify,[],[f12]) ).
fof(f20,plain,
( r1(sK18,sK19)
& r1(sK17,sK18)
& r1(sK16,sK17)
& r1(sK15,sK16)
& r1(sK14,sK15)
& r1(sK4,sK14)
& ! [X8] :
( ( ! [X17] :
( ( sP1(X17)
& ~ p5(sK13(X17))
& r1(X17,sK13(X17))
& ! [X18] :
( ! [X19] :
( ! [X20] :
( ! [X21] :
( ! [X22] :
( ! [X23] :
( ( ( ~ p4(X23)
| ~ p5(X23) )
& ( p5(X23)
| p4(X23) ) )
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) ) )
| ~ r1(X8,X17) )
& r1(X8,sK12(X8))
& ! [X9] :
( ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ! [X15] :
( ( ( ~ p5(X15)
| ~ p1(X15) )
& ( p1(X15)
| p5(X15) ) )
| ~ r1(X14,X15) )
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) )
| ~ r1(X10,X11) )
| ~ r1(X9,X10) )
| ~ r1(X8,X9) ) )
| ~ r1(sK4,X8) )
& r1(sK4,sK11)
& r1(sK9,sK10)
& r1(sK8,sK9)
& r1(sK7,sK8)
& r1(sK6,sK7)
& r1(sK5,sK6)
& r1(sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14,sK15,sK16,sK17,sK18,sK19]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7),skolemize(X4,sK8),skolemize(X5,sK9),skolemize(X6,sK10),skolemize(X7,sK11),skolemize(X16,sK12(X8)),skolemize(X24,sK13(X17)),skolemize(X25,sK14),skolemize(X26,sK15),skolemize(X27,sK16),skolemize(X28,sK17),skolemize(X29,sK18),skolemize(X30,sK19)],[f19]) ).
fof(f21,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f22,plain,
! [X0,X1] :
( ~ sP1(X0)
| sP0(X1)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f25,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sP1(X0)
| ~ p3(X6)
| ~ p4(X6)
| ~ r1(X5,X6)
| ~ r1(X4,X5)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sP1(X0)
| p4(X6)
| p3(X6)
| ~ r1(X5,X6)
| ~ r1(X4,X5)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f39,plain,
! [X8,X17] :
( sP1(X17)
| ~ r1(X8,X17)
| ~ r1(sK4,X8) ),
inference(cnf_transformation,[],[f20]) ).
fof(f42,plain,
! [X21,X18,X8,X19,X17,X22,X23,X20] :
( ~ p4(X23)
| ~ p5(X23)
| ~ r1(X22,X23)
| ~ r1(X21,X22)
| ~ r1(X20,X21)
| ~ r1(X19,X20)
| ~ r1(X18,X19)
| ~ r1(X17,X18)
| ~ r1(X8,X17)
| ~ r1(sK4,X8) ),
inference(cnf_transformation,[],[f20]) ).
fof(f43,plain,
! [X21,X18,X8,X19,X17,X22,X23,X20] :
( p5(X23)
| p4(X23)
| ~ r1(X22,X23)
| ~ r1(X21,X22)
| ~ r1(X20,X21)
| ~ r1(X19,X20)
| ~ r1(X18,X19)
| ~ r1(X17,X18)
| ~ r1(X8,X17)
| ~ r1(sK4,X8) ),
inference(cnf_transformation,[],[f20]) ).
fof(f45,plain,
! [X10,X11,X8,X9,X14,X15,X12,X13] :
( ~ p5(X15)
| ~ p1(X15)
| ~ r1(X14,X15)
| ~ r1(X13,X14)
| ~ r1(X12,X13)
| ~ r1(X11,X12)
| ~ r1(X10,X11)
| ~ r1(X9,X10)
| ~ r1(X8,X9)
| ~ r1(sK4,X8) ),
inference(cnf_transformation,[],[f20]) ).
fof(f46,plain,
! [X10,X11,X8,X9,X14,X15,X12,X13] :
( p1(X15)
| p5(X15)
| ~ r1(X14,X15)
| ~ r1(X13,X14)
| ~ r1(X12,X13)
| ~ r1(X11,X12)
| ~ r1(X10,X11)
| ~ r1(X9,X10)
| ~ r1(X8,X9)
| ~ r1(sK4,X8) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_49,plain,
! [X0: $i] : r1(X0,X0),
inference(cnf_transformation,[],[f21]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( p4(X6)
| p3(X6)
| ~ sP1(X0)
| ~ r1(X5,X6)
| ~ r1(X4,X5)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ sP1(X0)
| ~ p4(X6)
| ~ p3(X6)
| ~ r1(X5,X6)
| ~ r1(X4,X5)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( sP0(X1)
| ~ sP1(X0)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_68,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( p5(X7)
| p1(X7)
| ~ r1(sK4,X0)
| ~ r1(X6,X7)
| ~ r1(X5,X6)
| ~ r1(X4,X5)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_69,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( ~ p5(X7)
| ~ p1(X7)
| ~ r1(sK4,X0)
| ~ r1(X6,X7)
| ~ r1(X5,X6)
| ~ r1(X4,X5)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_71,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( p5(X7)
| p4(X7)
| ~ r1(sK4,X0)
| ~ r1(X6,X7)
| ~ r1(X5,X6)
| ~ r1(X4,X5)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_72,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( ~ p5(X7)
| ~ p4(X7)
| ~ r1(sK4,X0)
| ~ r1(X6,X7)
| ~ r1(X5,X6)
| ~ r1(X4,X5)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_75,negated_conjecture,
! [X0: $i,X1: $i] :
( sP1(X1)
| ~ r1(sK4,X0)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_82,plain,
r1(sK4,sK4),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_84,plain,
( sP0(sK4)
| ~ sP1(sK4)
| ~ r1(sK4,sK4) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_85,plain,
( sP1(sK4)
| ~ r1(sK4,sK4) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_96,plain,
( p4(sK4)
| p3(sK4)
| ~ sP1(sK4)
| ~ r1(sK4,sK4) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_97,plain,
( ~ sP1(sK4)
| ~ p4(sK4)
| ~ p3(sK4)
| ~ r1(sK4,sK4) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_98,plain,
( p5(sK4)
| p4(sK4)
| ~ r1(sK4,sK4) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_99,plain,
( p5(sK4)
| p1(sK4)
| ~ r1(sK4,sK4) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_100,plain,
( ~ p5(sK4)
| ~ p4(sK4)
| ~ r1(sK4,sK4) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_101,plain,
( ~ p5(sK4)
| ~ p1(sK4)
| ~ r1(sK4,sK4) ),
inference(instantiation,[status(thm)],[c_69]) ).
fof(f10,definition,
! [X25] :
( ~ sP0(X25)
| ! [X32] :
( ( ! [X38] :
( ! [X39] :
( ! [X40] :
( ! [X41] :
( ( ( ~ p1(X41)
| ~ p2(X41) )
& ( p2(X41)
| p1(X41) ) )
| ~ r1(X40,X41) )
| ~ r1(X39,X40) )
| ~ r1(X38,X39) )
| ~ r1(X32,X38) )
& ? [X37] :
( ~ p3(X37)
& r1(X32,X37) )
& ! [X33] :
( ! [X34] :
( ! [X35] :
( ! [X36] :
( ( ( ~ p2(X36)
| ~ p3(X36) )
& ( p3(X36)
| p2(X36) ) )
| ~ r1(X35,X36) )
| ~ r1(X34,X35) )
| ~ r1(X33,X34) )
| ~ r1(X32,X33) ) )
| ~ r1(X25,X32) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f11,definition,
! [X17] :
( ~ sP1(X17)
| ! [X25] :
( ( sP0(X25)
& ? [X31] :
( ~ p4(X31)
& r1(X25,X31) )
& ! [X26] :
( ! [X27] :
( ! [X28] :
( ! [X29] :
( ! [X30] :
( ( ( ~ p3(X30)
| ~ p4(X30) )
& ( p4(X30)
| p3(X30) ) )
| ~ r1(X29,X30) )
| ~ r1(X28,X29) )
| ~ r1(X27,X28) )
| ~ r1(X26,X27) )
| ~ r1(X25,X26) ) )
| ~ r1(X17,X25) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f12,plain,
? [X0] :
( ? [X42] :
( ? [X43] :
( ? [X44] :
( ? [X45] :
( ? [X46] :
( ? [X47] : r1(X46,X47)
& r1(X45,X46) )
& r1(X44,X45) )
& r1(X43,X44) )
& r1(X42,X43) )
& r1(X0,X42) )
& ! [X8] :
( ( ! [X17] :
( ( sP1(X17)
& ? [X24] :
( ~ p5(X24)
& r1(X17,X24) )
& ! [X18] :
( ! [X19] :
( ! [X20] :
( ! [X21] :
( ! [X22] :
( ! [X23] :
( ( ( ~ p4(X23)
| ~ p5(X23) )
& ( p5(X23)
| p4(X23) ) )
| ~ r1(X22,X23) )
| ~ r1(X21,X22) )
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X17,X18) ) )
| ~ r1(X8,X17) )
& ? [X16] : r1(X8,X16)
& ! [X9] :
( ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ! [X15] :
( ( ( ~ p5(X15)
| ~ p1(X15) )
& ( p1(X15)
| p5(X15) ) )
| ~ r1(X14,X15) )
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X11,X12) )
| ~ r1(X10,X11) )
| ~ r1(X9,X10) )
| ~ r1(X8,X9) ) )
| ~ r1(X0,X8) )
& ? [X7] : r1(X0,X7)
& ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] : r1(X5,X6)
& r1(X4,X5) )
& r1(X3,X4) )
& r1(X2,X3) )
& r1(X1,X2) )
& r1(X0,X1) ) ),
inference(definition_folding,[],[f9,f11,f10]) ).
fof(f16,plain,
! [X25] :
( ~ sP0(X25)
| ! [X32] :
( ( ! [X38] :
( ! [X39] :
( ! [X40] :
( ! [X41] :
( ( ( ~ p1(X41)
| ~ p2(X41) )
& ( p2(X41)
| p1(X41) ) )
| ~ r1(X40,X41) )
| ~ r1(X39,X40) )
| ~ r1(X38,X39) )
| ~ r1(X32,X38) )
& ? [X37] :
( ~ p3(X37)
& r1(X32,X37) )
& ! [X33] :
( ! [X34] :
( ! [X35] :
( ! [X36] :
( ( ( ~ p2(X36)
| ~ p3(X36) )
& ( p3(X36)
| p2(X36) ) )
| ~ r1(X35,X36) )
| ~ r1(X34,X35) )
| ~ r1(X33,X34) )
| ~ r1(X32,X33) ) )
| ~ r1(X25,X32) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f17,plain,
! [X0] :
( ~ sP0(X0)
| ! [X1] :
( ( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ( ( ~ p1(X10)
| ~ p2(X10) )
& ( p2(X10)
| p1(X10) ) )
| ~ r1(X9,X10) )
| ~ r1(X8,X9) )
| ~ r1(X7,X8) )
| ~ r1(X1,X7) )
& ? [X6] :
( ~ p3(X6)
& r1(X1,X6) )
& ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ( ( ~ p2(X5)
| ~ p3(X5) )
& ( p3(X5)
| p2(X5) ) )
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) ) )
| ~ r1(X0,X1) ) ),
inference(rectify,[],[f16]) ).
fof(f18,plain,
! [X0] :
( ~ sP0(X0)
| ! [X1] :
( ( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ( ( ~ p1(X10)
| ~ p2(X10) )
& ( p2(X10)
| p1(X10) ) )
| ~ r1(X9,X10) )
| ~ r1(X8,X9) )
| ~ r1(X7,X8) )
| ~ r1(X1,X7) )
& ~ p3(sK3(X1))
& r1(X1,sK3(X1))
& ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ( ( ~ p2(X5)
| ~ p3(X5) )
& ( p3(X5)
| p2(X5) ) )
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) ) )
| ~ r1(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X6,sK3(X1))],[f17]) ).
fof(f27,plain,
! [X10,X0,X1,X8,X9,X7] :
( ~ sP0(X0)
| ~ p1(X10)
| ~ p2(X10)
| ~ r1(X9,X10)
| ~ r1(X8,X9)
| ~ r1(X7,X8)
| ~ r1(X1,X7)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f28,plain,
! [X10,X0,X1,X8,X9,X7] :
( ~ sP0(X0)
| p2(X10)
| p1(X10)
| ~ r1(X9,X10)
| ~ r1(X8,X9)
| ~ r1(X7,X8)
| ~ r1(X1,X7)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ sP0(X0)
| ~ p2(X5)
| ~ p3(X5)
| ~ r1(X4,X5)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ sP0(X0)
| p3(X5)
| p2(X5)
| ~ r1(X4,X5)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( p2(X5)
| p3(X5)
| ~ sP0(X0)
| ~ r1(X4,X5)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ p2(X5)
| ~ sP0(X0)
| ~ p3(X5)
| ~ r1(X4,X5)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( p1(X5)
| p2(X5)
| ~ sP0(X0)
| ~ r1(X4,X5)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ p1(X5)
| ~ p2(X5)
| ~ sP0(X0)
| ~ r1(X4,X5)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_92,plain,
( p1(sK4)
| p2(sK4)
| ~ sP0(sK4)
| ~ r1(sK4,sK4) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_93,plain,
( p2(sK4)
| p3(sK4)
| ~ sP0(sK4)
| ~ r1(sK4,sK4) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_94,plain,
( ~ p1(sK4)
| ~ p2(sK4)
| ~ sP0(sK4)
| ~ r1(sK4,sK4) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_95,plain,
( ~ p2(sK4)
| ~ sP0(sK4)
| ~ p3(sK4)
| ~ r1(sK4,sK4) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(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
% 0.00/0.03 % Problem : LCL668+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n015.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 00:12:40 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 1.68/1.29 % SZS status Started for theBenchmark.p
% 1.68/1.29 % SZS status Theorem for theBenchmark.p
% 1.68/1.29
% 1.68/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.68/1.29
% 1.68/1.29 % ------ iProver source info
% 1.68/1.29
% 1.68/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.68/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.68/1.29 % git: non_committed_changes: false
% 1.68/1.29
% 1.68/1.29 % ------ Parsing...
% 1.68/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.68/1.29
% 1.68/1.29 % ------ Preprocessing...%
% 1.68/1.29
% 1.68/1.29 % SZS status Theorem for theBenchmark.p
% 1.68/1.29
% 1.68/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.68/1.29
% 1.68/1.29
%------------------------------------------------------------------------------