%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL652+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 : n005.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 02:07:08 PM UTC 2026
% Result : Theorem 1.32s 1.76s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 153 ( 6 unt; 4 def)
% Number of atoms : 1540 ( 0 equ)
% Maximal formula atoms : 74 ( 10 avg)
% Number of connectives : 2444 (1200 ~;1025 |; 219 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 9 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 5 con; 0-1 aty)
% Number of variables : 778 ( 0 sgn 664 !; 114 ?; 161 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
~ ? [X0] :
~ ( ~ ! [X1] :
( ~ ! [X0] :
( ~ p1(X0)
| ~ r1(X1,X0) )
| ! [X0] :
( ! [X1] :
( ~ p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( ~ ! [X0] :
( ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ! [X0] :
( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ( ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
& ~ ! [X0] :
( ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ( ( ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
& ! [X0] :
( ~ p2(X0)
| ! [X1] :
( p3(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ ! [X0] :
( ~ ( ! [X1] :
( ~ ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ! [X0] :
( p3(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
& ! [X1] :
( ~ ! [X0] :
( ~ p2(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ( ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
& ~ ! [X0] :
( ! [X1] :
( ~ ! [X0] :
( ~ p2(X0)
| ! [X1] :
( p3(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ ! [X0] :
( ~ ( ~ ! [X1] :
( ~ ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
& p2(X0)
& ~ ! [X1] :
( ~ ( ~ p2(X1)
| ! [X0] :
( p3(X0)
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ~ ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ! [X0] :
( p3(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ( ! [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] :
( ~ p4(X1)
| ~ r1(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).
fof(f2,negated_conjecture,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ ! [X0] :
( ~ p1(X0)
| ~ r1(X1,X0) )
| ! [X0] :
( ! [X1] :
( ~ p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( ~ ! [X0] :
( ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
| ! [X0] :
( ~ ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ( ! [X0] :
( p1(X0)
| ~ r1(X1,X0) )
& ~ ! [X0] :
( ! [X1] :
( p1(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ( ( ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
& ! [X0] :
( ~ p2(X0)
| ! [X1] :
( p3(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ ! [X0] :
( ~ ( ! [X1] :
( ~ ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ! [X0] :
( p3(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
& ! [X1] :
( ~ ! [X0] :
( ~ p2(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ( ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
& ~ ! [X0] :
( ! [X1] :
( ~ ! [X0] :
( ~ p2(X0)
| ! [X1] :
( p3(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ ! [X0] :
( ~ ( ~ ! [X1] :
( ~ ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
& p2(X0)
& ~ ! [X1] :
( ~ ( ~ p2(X1)
| ! [X0] :
( p3(X0)
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ~ ! [X0] :
( ~ ! [X1] :
( ~ p2(X1)
| ! [X0] :
( p3(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ( ! [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] :
( ~ p4(X1)
| ~ r1(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ~ ? [X0] :
~ ( ~ ! [X46] :
( ~ ! [X49] :
( ~ p1(X49)
| ~ r1(X46,X49) )
| ! [X47] :
( ! [X48] :
( ~ p1(X48)
| ~ r1(X47,X48) )
| ~ r1(X46,X47) )
| ~ r1(X0,X46) )
| ! [X43] :
( ~ ! [X44] :
( ~ ! [X45] :
( p2(X45)
| ~ r1(X44,X45) )
| ~ r1(X43,X44) )
| ~ r1(X0,X43) )
| ! [X39] :
( ! [X42] :
( p1(X42)
| ~ r1(X39,X42) )
| ! [X40] :
( ~ ! [X41] :
( p1(X41)
| ~ r1(X40,X41) )
| ~ r1(X39,X40) )
| ~ r1(X0,X39) )
| ~ ! [X35] :
( ~ ( ! [X38] :
( p1(X38)
| ~ r1(X35,X38) )
& ~ ! [X36] :
( ! [X37] :
( p1(X37)
| ~ r1(X36,X37) )
| ~ r1(X35,X36) ) )
| ~ r1(X0,X35) )
| ~ ! [X8] :
( ~ ( ( ! [X33] :
( ~ ! [X34] :
( ~ p2(X34)
| ~ r1(X33,X34) )
| ~ r1(X8,X33) )
& ! [X31] :
( ~ p2(X31)
| ! [X32] :
( p3(X32)
| ~ r1(X31,X32) )
| ~ r1(X8,X31) ) )
| ~ ! [X24] :
( ~ ( ! [X27] :
( ~ ! [X28] :
( ~ ! [X29] :
( ~ p2(X29)
| ! [X30] :
( p3(X30)
| ~ r1(X29,X30) )
| ~ r1(X28,X29) )
| ~ r1(X27,X28) )
| ~ r1(X24,X27) )
& ! [X25] :
( ~ ! [X26] :
( ~ p2(X26)
| ~ r1(X25,X26) )
| ~ r1(X24,X25) ) )
| ~ r1(X8,X24) )
| ( ! [X22] :
( ~ ! [X23] :
( ~ p2(X23)
| ~ r1(X22,X23) )
| ~ r1(X8,X22) )
& ~ ! [X18] :
( ! [X19] :
( ~ ! [X20] :
( ~ p2(X20)
| ! [X21] :
( p3(X21)
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X8,X18) ) )
| ~ ! [X12] :
( ~ ( ~ ! [X15] :
( ~ ! [X16] :
( ~ ! [X17] :
( ~ p2(X17)
| ~ r1(X16,X17) )
| ~ r1(X15,X16) )
| ~ r1(X12,X15) )
& p2(X12)
& ~ ! [X13] :
( ~ ( ~ p2(X13)
| ! [X14] :
( p3(X14)
| ~ r1(X13,X14) ) )
| ~ r1(X12,X13) ) )
| ~ r1(X8,X12) )
| ~ ! [X9] :
( ~ ! [X10] :
( ~ p2(X10)
| ! [X11] :
( p3(X11)
| ~ r1(X10,X11) )
| ~ r1(X9,X10) )
| ~ r1(X8,X9) ) )
| ~ r1(X0,X8) )
| ~ ! [X2] :
( ~ ( ! [X6] :
( ~ ! [X7] :
( ~ p1(X7)
| ~ r1(X6,X7) )
| ~ r1(X2,X6) )
& ~ ! [X3] :
( ! [X4] :
( ~ ! [X5] :
( ~ p1(X5)
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) ) )
| ~ r1(X0,X2) )
| ~ ! [X1] :
( ~ p4(X1)
| ~ r1(X0,X1) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
? [X0] :
~ ( ~ ! [X46] :
( ~ ! [X49] :
( ~ p1(X49)
| ~ r1(X46,X49) )
| ! [X47] :
( ! [X48] :
( ~ p1(X48)
| ~ r1(X47,X48) )
| ~ r1(X46,X47) )
| ~ r1(X0,X46) )
| ! [X43] :
( ~ ! [X44] :
( ~ ! [X45] :
( p2(X45)
| ~ r1(X44,X45) )
| ~ r1(X43,X44) )
| ~ r1(X0,X43) )
| ! [X39] :
( ! [X42] :
( p1(X42)
| ~ r1(X39,X42) )
| ! [X40] :
( ~ ! [X41] :
( p1(X41)
| ~ r1(X40,X41) )
| ~ r1(X39,X40) )
| ~ r1(X0,X39) )
| ~ ! [X35] :
( ~ ( ! [X38] :
( p1(X38)
| ~ r1(X35,X38) )
& ~ ! [X36] :
( ! [X37] :
( p1(X37)
| ~ r1(X36,X37) )
| ~ r1(X35,X36) ) )
| ~ r1(X0,X35) )
| ~ ! [X8] :
( ~ ( ( ! [X33] :
( ~ ! [X34] :
( ~ p2(X34)
| ~ r1(X33,X34) )
| ~ r1(X8,X33) )
& ! [X31] :
( ~ p2(X31)
| ! [X32] :
( p3(X32)
| ~ r1(X31,X32) )
| ~ r1(X8,X31) ) )
| ~ ! [X24] :
( ~ ( ! [X27] :
( ~ ! [X28] :
( ~ ! [X29] :
( ~ p2(X29)
| ! [X30] :
( p3(X30)
| ~ r1(X29,X30) )
| ~ r1(X28,X29) )
| ~ r1(X27,X28) )
| ~ r1(X24,X27) )
& ! [X25] :
( ~ ! [X26] :
( ~ p2(X26)
| ~ r1(X25,X26) )
| ~ r1(X24,X25) ) )
| ~ r1(X8,X24) )
| ( ! [X22] :
( ~ ! [X23] :
( ~ p2(X23)
| ~ r1(X22,X23) )
| ~ r1(X8,X22) )
& ~ ! [X18] :
( ! [X19] :
( ~ ! [X20] :
( ~ p2(X20)
| ! [X21] :
( p3(X21)
| ~ r1(X20,X21) )
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X8,X18) ) )
| ~ ! [X12] :
( ~ ( ~ ! [X15] :
( ~ ! [X16] :
( ~ ! [X17] :
( ~ p2(X17)
| ~ r1(X16,X17) )
| ~ r1(X15,X16) )
| ~ r1(X12,X15) )
& p2(X12)
& ~ ! [X13] :
( ~ ( ~ p2(X13)
| ! [X14] :
( p3(X14)
| ~ r1(X13,X14) ) )
| ~ r1(X12,X13) ) )
| ~ r1(X8,X12) )
| ~ ! [X9] :
( ~ ! [X10] :
( ~ p2(X10)
| ! [X11] :
( p3(X11)
| ~ r1(X10,X11) )
| ~ r1(X9,X10) )
| ~ r1(X8,X9) ) )
| ~ r1(X0,X8) )
| ~ ! [X2] :
( ~ ( ! [X6] :
( ~ ! [X7] :
( ~ p1(X7)
| ~ r1(X6,X7) )
| ~ r1(X2,X6) )
& ~ ! [X3] :
( ! [X4] :
( ~ ! [X5] :
( ~ p1(X5)
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) ) )
| ~ r1(X0,X2) )
| ~ ! [X1] :
( ~ p4(X1)
| ~ r1(X0,X1) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
? [X0] :
~ ( ~ ! [X46] :
( ~ ! [X49] :
( ~ p1(X49)
| ~ r1(X46,X49) )
| ! [X47] :
( ! [X48] :
( ~ p1(X48)
| ~ r1(X47,X48) )
| ~ r1(X46,X47) )
| ~ r1(X0,X46) )
| ! [X43] :
( ~ ! [X44] :
( ~ ! [X45] :
( p2(X45)
| ~ r1(X44,X45) )
| ~ r1(X43,X44) )
| ~ r1(X0,X43) )
| ! [X39] :
( ! [X42] :
( p1(X42)
| ~ r1(X39,X42) )
| ! [X40] :
( ~ ! [X41] :
( p1(X41)
| ~ r1(X40,X41) )
| ~ r1(X39,X40) )
| ~ r1(X0,X39) )
| ~ ! [X35] :
( ~ ( ! [X38] :
( p1(X38)
| ~ r1(X35,X38) )
& ~ ! [X36] :
( ! [X37] :
( p1(X37)
| ~ r1(X36,X37) )
| ~ r1(X35,X36) ) )
| ~ r1(X0,X35) )
| ~ ! [X8] :
( ~ ( ( ! [X33] :
( ~ ! [X34] :
( ~ p2(X34)
| ~ r1(X33,X34) )
| ~ r1(X8,X33) )
& ! [X31] :
( ~ p2(X31)
| ! [X32] : ~ r1(X31,X32)
| ~ r1(X8,X31) ) )
| ~ ! [X24] :
( ~ ( ! [X27] :
( ~ ! [X28] :
( ~ ! [X29] :
( ~ p2(X29)
| ! [X30] : ~ r1(X29,X30)
| ~ r1(X28,X29) )
| ~ r1(X27,X28) )
| ~ r1(X24,X27) )
& ! [X25] :
( ~ ! [X26] :
( ~ p2(X26)
| ~ r1(X25,X26) )
| ~ r1(X24,X25) ) )
| ~ r1(X8,X24) )
| ( ! [X22] :
( ~ ! [X23] :
( ~ p2(X23)
| ~ r1(X22,X23) )
| ~ r1(X8,X22) )
& ~ ! [X18] :
( ! [X19] :
( ~ ! [X20] :
( ~ p2(X20)
| ! [X21] : ~ r1(X20,X21)
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X8,X18) ) )
| ~ ! [X12] :
( ~ ( ~ ! [X15] :
( ~ ! [X16] :
( ~ ! [X17] :
( ~ p2(X17)
| ~ r1(X16,X17) )
| ~ r1(X15,X16) )
| ~ r1(X12,X15) )
& p2(X12)
& ~ ! [X13] :
( ~ ( ~ p2(X13)
| ! [X14] : ~ r1(X13,X14) )
| ~ r1(X12,X13) ) )
| ~ r1(X8,X12) )
| ~ ! [X9] :
( ~ ! [X10] :
( ~ p2(X10)
| ! [X11] : ~ r1(X10,X11)
| ~ r1(X9,X10) )
| ~ r1(X8,X9) ) )
| ~ r1(X0,X8) )
| ~ ! [X2] :
( ~ ( ! [X6] :
( ~ ! [X7] :
( ~ p1(X7)
| ~ r1(X6,X7) )
| ~ r1(X2,X6) )
& ~ ! [X3] :
( ! [X4] :
( ~ ! [X5] :
( ~ p1(X5)
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) ) )
| ~ r1(X0,X2) )
| ~ ! [X1] :
( ~ p4(X1)
| ~ r1(X0,X1) ) ),
inference(pure_predicate_removal,[],[f4]) ).
fof(f6,plain,
? [X0] :
~ ( ~ ! [X46] :
( ~ ! [X49] :
( ~ p1(X49)
| ~ r1(X46,X49) )
| ! [X47] :
( ! [X48] :
( ~ p1(X48)
| ~ r1(X47,X48) )
| ~ r1(X46,X47) )
| ~ r1(X0,X46) )
| ! [X43] :
( ~ ! [X44] :
( ~ ! [X45] :
( p2(X45)
| ~ r1(X44,X45) )
| ~ r1(X43,X44) )
| ~ r1(X0,X43) )
| ! [X39] :
( ! [X42] :
( p1(X42)
| ~ r1(X39,X42) )
| ! [X40] :
( ~ ! [X41] :
( p1(X41)
| ~ r1(X40,X41) )
| ~ r1(X39,X40) )
| ~ r1(X0,X39) )
| ~ ! [X35] :
( ~ ( ! [X38] :
( p1(X38)
| ~ r1(X35,X38) )
& ~ ! [X36] :
( ! [X37] :
( p1(X37)
| ~ r1(X36,X37) )
| ~ r1(X35,X36) ) )
| ~ r1(X0,X35) )
| ~ ! [X8] :
( ~ ( ( ! [X33] :
( ~ ! [X34] :
( ~ p2(X34)
| ~ r1(X33,X34) )
| ~ r1(X8,X33) )
& ! [X31] :
( ~ p2(X31)
| ! [X32] : ~ r1(X31,X32)
| ~ r1(X8,X31) ) )
| ~ ! [X24] :
( ~ ( ! [X27] :
( ~ ! [X28] :
( ~ ! [X29] :
( ~ p2(X29)
| ! [X30] : ~ r1(X29,X30)
| ~ r1(X28,X29) )
| ~ r1(X27,X28) )
| ~ r1(X24,X27) )
& ! [X25] :
( ~ ! [X26] :
( ~ p2(X26)
| ~ r1(X25,X26) )
| ~ r1(X24,X25) ) )
| ~ r1(X8,X24) )
| ( ! [X22] :
( ~ ! [X23] :
( ~ p2(X23)
| ~ r1(X22,X23) )
| ~ r1(X8,X22) )
& ~ ! [X18] :
( ! [X19] :
( ~ ! [X20] :
( ~ p2(X20)
| ! [X21] : ~ r1(X20,X21)
| ~ r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X8,X18) ) )
| ~ ! [X12] :
( ~ ( ~ ! [X15] :
( ~ ! [X16] :
( ~ ! [X17] :
( ~ p2(X17)
| ~ r1(X16,X17) )
| ~ r1(X15,X16) )
| ~ r1(X12,X15) )
& p2(X12)
& ~ ! [X13] :
( ~ ( ~ p2(X13)
| ! [X14] : ~ r1(X13,X14) )
| ~ r1(X12,X13) ) )
| ~ r1(X8,X12) )
| ~ ! [X9] :
( ~ ! [X10] :
( ~ p2(X10)
| ! [X11] : ~ r1(X10,X11)
| ~ r1(X9,X10) )
| ~ r1(X8,X9) ) )
| ~ r1(X0,X8) )
| ~ ! [X2] :
( ~ ( ! [X6] :
( ~ ! [X7] :
( ~ p1(X7)
| ~ r1(X6,X7) )
| ~ r1(X2,X6) )
& ~ ! [X3] :
( ! [X4] :
( ~ ! [X5] :
( ~ p1(X5)
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) ) )
| ~ r1(X0,X2) ) ),
inference(pure_predicate_removal,[],[f5]) ).
fof(f7,plain,
? [X0] :
( ! [X46] :
( ? [X49] :
( p1(X49)
& r1(X46,X49) )
| ! [X47] :
( ! [X48] :
( ~ p1(X48)
| ~ r1(X47,X48) )
| ~ r1(X46,X47) )
| ~ r1(X0,X46) )
& ? [X43] :
( ! [X44] :
( ? [X45] :
( ~ p2(X45)
& r1(X44,X45) )
| ~ r1(X43,X44) )
& r1(X0,X43) )
& ? [X39] :
( ? [X42] :
( ~ p1(X42)
& r1(X39,X42) )
& ? [X40] :
( ! [X41] :
( p1(X41)
| ~ r1(X40,X41) )
& r1(X39,X40) )
& r1(X0,X39) )
& ! [X35] :
( ? [X38] :
( ~ p1(X38)
& r1(X35,X38) )
| ! [X36] :
( ! [X37] :
( p1(X37)
| ~ r1(X36,X37) )
| ~ r1(X35,X36) )
| ~ r1(X0,X35) )
& ! [X8] :
( ( ( ? [X33] :
( ! [X34] :
( ~ p2(X34)
| ~ r1(X33,X34) )
& r1(X8,X33) )
| ? [X31] :
( p2(X31)
& ? [X32] : r1(X31,X32)
& r1(X8,X31) ) )
& ! [X24] :
( ? [X27] :
( ! [X28] :
( ? [X29] :
( p2(X29)
& ? [X30] : r1(X29,X30)
& r1(X28,X29) )
| ~ r1(X27,X28) )
& r1(X24,X27) )
| ? [X25] :
( ! [X26] :
( ~ p2(X26)
| ~ r1(X25,X26) )
& r1(X24,X25) )
| ~ r1(X8,X24) )
& ( ? [X22] :
( ! [X23] :
( ~ p2(X23)
| ~ r1(X22,X23) )
& r1(X8,X22) )
| ! [X18] :
( ! [X19] :
( ? [X20] :
( p2(X20)
& ? [X21] : r1(X20,X21)
& r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X8,X18) ) )
& ! [X12] :
( ! [X15] :
( ? [X16] :
( ! [X17] :
( ~ p2(X17)
| ~ r1(X16,X17) )
& r1(X15,X16) )
| ~ r1(X12,X15) )
| ~ p2(X12)
| ! [X13] :
( ( p2(X13)
& ? [X14] : r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X8,X12) )
& ! [X9] :
( ? [X10] :
( p2(X10)
& ? [X11] : r1(X10,X11)
& r1(X9,X10) )
| ~ r1(X8,X9) ) )
| ~ r1(X0,X8) )
& ! [X2] :
( ? [X6] :
( ! [X7] :
( ~ p1(X7)
| ~ r1(X6,X7) )
& r1(X2,X6) )
| ! [X3] :
( ! [X4] :
( ? [X5] :
( p1(X5)
& r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X0,X2) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f8,plain,
? [X0] :
( ! [X46] :
( ? [X49] :
( p1(X49)
& r1(X46,X49) )
| ! [X47] :
( ! [X48] :
( ~ p1(X48)
| ~ r1(X47,X48) )
| ~ r1(X46,X47) )
| ~ r1(X0,X46) )
& ? [X43] :
( ! [X44] :
( ? [X45] :
( ~ p2(X45)
& r1(X44,X45) )
| ~ r1(X43,X44) )
& r1(X0,X43) )
& ? [X39] :
( ? [X42] :
( ~ p1(X42)
& r1(X39,X42) )
& ? [X40] :
( ! [X41] :
( p1(X41)
| ~ r1(X40,X41) )
& r1(X39,X40) )
& r1(X0,X39) )
& ! [X35] :
( ? [X38] :
( ~ p1(X38)
& r1(X35,X38) )
| ! [X36] :
( ! [X37] :
( p1(X37)
| ~ r1(X36,X37) )
| ~ r1(X35,X36) )
| ~ r1(X0,X35) )
& ! [X8] :
( ( ( ? [X33] :
( ! [X34] :
( ~ p2(X34)
| ~ r1(X33,X34) )
& r1(X8,X33) )
| ? [X31] :
( p2(X31)
& ? [X32] : r1(X31,X32)
& r1(X8,X31) ) )
& ! [X24] :
( ? [X27] :
( ! [X28] :
( ? [X29] :
( p2(X29)
& ? [X30] : r1(X29,X30)
& r1(X28,X29) )
| ~ r1(X27,X28) )
& r1(X24,X27) )
| ? [X25] :
( ! [X26] :
( ~ p2(X26)
| ~ r1(X25,X26) )
& r1(X24,X25) )
| ~ r1(X8,X24) )
& ( ? [X22] :
( ! [X23] :
( ~ p2(X23)
| ~ r1(X22,X23) )
& r1(X8,X22) )
| ! [X18] :
( ! [X19] :
( ? [X20] :
( p2(X20)
& ? [X21] : r1(X20,X21)
& r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X8,X18) ) )
& ! [X12] :
( ! [X15] :
( ? [X16] :
( ! [X17] :
( ~ p2(X17)
| ~ r1(X16,X17) )
& r1(X15,X16) )
| ~ r1(X12,X15) )
| ~ p2(X12)
| ! [X13] :
( ( p2(X13)
& ? [X14] : r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X8,X12) )
& ! [X9] :
( ? [X10] :
( p2(X10)
& ? [X11] : r1(X10,X11)
& r1(X9,X10) )
| ~ r1(X8,X9) ) )
| ~ r1(X0,X8) )
& ! [X2] :
( ? [X6] :
( ! [X7] :
( ~ p1(X7)
| ~ r1(X6,X7) )
& r1(X2,X6) )
| ! [X3] :
( ! [X4] :
( ? [X5] :
( p1(X5)
& r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X0,X2) ) ),
inference(flattening,[],[f7]) ).
fof(f14,plain,
! [X8] :
( ~ sP3(X8)
| ! [X12] :
( ! [X15] :
( ? [X16] :
( ! [X17] :
( ~ p2(X17)
| ~ r1(X16,X17) )
& r1(X15,X16) )
| ~ r1(X12,X15) )
| ~ p2(X12)
| ! [X13] :
( ( p2(X13)
& ? [X14] : r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X8,X12) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f15,plain,
! [X0] :
( ~ sP3(X0)
| ! [X1] :
( ! [X4] :
( ? [X5] :
( ! [X6] :
( ~ p2(X6)
| ~ r1(X5,X6) )
& r1(X4,X5) )
| ~ r1(X1,X4) )
| ~ p2(X1)
| ! [X2] :
( ( p2(X2)
& ? [X3] : r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) ) ),
inference(rectify,[],[f14]) ).
fof(f16,plain,
! [X0] :
( ~ sP3(X0)
| ! [X1] :
( ! [X4] :
( ( ! [X6] :
( ~ p2(X6)
| ~ r1(sK5(X4),X6) )
& r1(X4,sK5(X4)) )
| ~ r1(X1,X4) )
| ~ p2(X1)
| ! [X2] :
( ( p2(X2)
& r1(X2,sK4(X2)) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X3,sK4(X2)),skolemize(X5,sK5(X4))],[f15]) ).
fof(f17,plain,
! [X8] :
( ~ sP2(X8)
| ? [X22] :
( ! [X23] :
( ~ p2(X23)
| ~ r1(X22,X23) )
& r1(X8,X22) )
| ! [X18] :
( ! [X19] :
( ? [X20] :
( p2(X20)
& ? [X21] : r1(X20,X21)
& r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X8,X18) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f18,plain,
! [X0] :
( ~ sP2(X0)
| ? [X5] :
( ! [X6] :
( ~ p2(X6)
| ~ r1(X5,X6) )
& r1(X0,X5) )
| ! [X1] :
( ! [X2] :
( ? [X3] :
( p2(X3)
& ? [X4] : r1(X3,X4)
& r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) ) ),
inference(rectify,[],[f17]) ).
fof(f19,plain,
! [X0] :
( ~ sP2(X0)
| ( ! [X6] :
( ~ p2(X6)
| ~ r1(sK8(X0),X6) )
& r1(X0,sK8(X0)) )
| ! [X1] :
( ! [X2] :
( ( p2(sK6(X2))
& r1(sK6(X2),sK7(X2))
& r1(X2,sK6(X2)) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X3,sK6(X2)),skolemize(X4,sK7(X2)),skolemize(X5,sK8(X0))],[f18]) ).
fof(f20,plain,
! [X8] :
( ~ sP1(X8)
| ? [X33] :
( ! [X34] :
( ~ p2(X34)
| ~ r1(X33,X34) )
& r1(X8,X33) )
| ? [X31] :
( p2(X31)
& ? [X32] : r1(X31,X32)
& r1(X8,X31) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f21,plain,
! [X0] :
( ~ sP1(X0)
| ? [X3] :
( ! [X4] :
( ~ p2(X4)
| ~ r1(X3,X4) )
& r1(X0,X3) )
| ? [X1] :
( p2(X1)
& ? [X2] : r1(X1,X2)
& r1(X0,X1) ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0] :
( ~ sP1(X0)
| ( ! [X4] :
( ~ p2(X4)
| ~ r1(sK11(X0),X4) )
& r1(X0,sK11(X0)) )
| ( p2(sK9(X0))
& r1(sK9(X0),sK10(X0))
& r1(X0,sK9(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X1,sK9(X0)),skolemize(X2,sK10(X0)),skolemize(X3,sK11(X0))],[f21]) ).
fof(f26,plain,
? [X0] :
( ! [X22] :
( ? [X25] :
( p1(X25)
& r1(X22,X25) )
| ! [X23] :
( ! [X24] :
( ~ p1(X24)
| ~ r1(X23,X24) )
| ~ r1(X22,X23) )
| ~ r1(X0,X22) )
& ? [X19] :
( ! [X20] :
( ? [X21] :
( ~ p2(X21)
& r1(X20,X21) )
| ~ r1(X19,X20) )
& r1(X0,X19) )
& ? [X15] :
( ? [X18] :
( ~ p1(X18)
& r1(X15,X18) )
& ? [X16] :
( ! [X17] :
( p1(X17)
| ~ r1(X16,X17) )
& r1(X15,X16) )
& r1(X0,X15) )
& ! [X11] :
( ? [X14] :
( ~ p1(X14)
& r1(X11,X14) )
| ! [X12] :
( ! [X13] :
( p1(X13)
| ~ r1(X12,X13) )
| ~ r1(X11,X12) )
| ~ r1(X0,X11) )
& ! [X7] :
( ( sP1(X7)
& sP0(X7)
& sP2(X7)
& sP3(X7)
& ! [X8] :
( ? [X9] :
( p2(X9)
& ? [X10] : r1(X9,X10)
& r1(X8,X9) )
| ~ r1(X7,X8) ) )
| ~ r1(X0,X7) )
& ! [X1] :
( ? [X5] :
( ! [X6] :
( ~ p1(X6)
| ~ r1(X5,X6) )
& r1(X1,X5) )
| ! [X2] :
( ! [X3] :
( ? [X4] :
( p1(X4)
& r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) ) ),
inference(rectify,[],[f13]) ).
fof(f27,plain,
( ! [X22] :
( ( p1(sK27(X22))
& r1(X22,sK27(X22)) )
| ! [X23] :
( ! [X24] :
( ~ p1(X24)
| ~ r1(X23,X24) )
| ~ r1(X22,X23) )
| ~ r1(sK16,X22) )
& ! [X20] :
( ( ~ p2(sK26(X20))
& r1(X20,sK26(X20)) )
| ~ r1(sK25,X20) )
& r1(sK16,sK25)
& ~ p1(sK24)
& r1(sK22,sK24)
& ! [X17] :
( p1(X17)
| ~ r1(sK23,X17) )
& r1(sK22,sK23)
& r1(sK16,sK22)
& ! [X11] :
( ( ~ p1(sK21(X11))
& r1(X11,sK21(X11)) )
| ! [X12] :
( ! [X13] :
( p1(X13)
| ~ r1(X12,X13) )
| ~ r1(X11,X12) )
| ~ r1(sK16,X11) )
& ! [X7] :
( ( sP1(X7)
& sP0(X7)
& sP2(X7)
& sP3(X7)
& ! [X8] :
( ( p2(sK19(X8))
& r1(sK19(X8),sK20(X8))
& r1(X8,sK19(X8)) )
| ~ r1(X7,X8) ) )
| ~ r1(sK16,X7) )
& ! [X1] :
( ( ! [X6] :
( ~ p1(X6)
| ~ r1(sK18(X1),X6) )
& r1(X1,sK18(X1)) )
| ! [X2] :
( ! [X3] :
( ( p1(sK17(X3))
& r1(X3,sK17(X3)) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(sK16,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18,sK19,sK20,sK21,sK22,sK23,sK24,sK25,sK26,sK27]),skolemize(X0,sK16),skolemize(X4,sK17(X3)),skolemize(X5,sK18(X1)),skolemize(X9,sK19(X8)),skolemize(X10,sK20(X8)),skolemize(X14,sK21(X11)),skolemize(X15,sK22),skolemize(X16,sK23),skolemize(X18,sK24),skolemize(X19,sK25),skolemize(X21,sK26(X20)),skolemize(X25,sK27(X22))],[f26]) ).
fof(f28,plain,
! [X2,X0,X1,X6,X4] :
( ~ sP3(X0)
| ~ p2(X6)
| ~ r1(sK5(X4),X6)
| ~ r1(X1,X4)
| ~ p2(X1)
| p2(X2)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
! [X2,X0,X1,X4] :
( ~ sP3(X0)
| r1(X4,sK5(X4))
| ~ r1(X1,X4)
| ~ p2(X1)
| p2(X2)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f32,plain,
! [X2,X0,X1,X6] :
( ~ sP2(X0)
| ~ p2(X6)
| ~ r1(sK8(X0),X6)
| p2(sK6(X2))
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ sP2(X0)
| r1(X0,sK8(X0))
| p2(sK6(X2))
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f36,plain,
! [X2,X0,X1,X6] :
( ~ sP2(X0)
| ~ p2(X6)
| ~ r1(sK8(X0),X6)
| r1(X2,sK6(X2))
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ sP2(X0)
| r1(X0,sK8(X0))
| r1(X2,sK6(X2))
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f38,plain,
! [X0,X4] :
( ~ sP1(X0)
| ~ p2(X4)
| ~ r1(sK11(X0),X4)
| p2(sK9(X0)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f39,plain,
! [X0] :
( ~ sP1(X0)
| r1(X0,sK11(X0))
| p2(sK9(X0)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f42,plain,
! [X0,X4] :
( ~ sP1(X0)
| ~ p2(X4)
| ~ r1(sK11(X0),X4)
| r1(X0,sK9(X0)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f43,plain,
! [X0] :
( ~ sP1(X0)
| r1(X0,sK11(X0))
| r1(X0,sK9(X0)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f54,plain,
! [X20] :
( ~ p2(sK26(X20))
| ~ r1(sK25,X20) ),
inference(cnf_transformation,[],[f27]) ).
fof(f55,plain,
! [X20] :
( r1(X20,sK26(X20))
| ~ r1(sK25,X20) ),
inference(cnf_transformation,[],[f27]) ).
fof(f56,plain,
r1(sK16,sK25),
inference(cnf_transformation,[],[f27]) ).
fof(f64,plain,
! [X7] :
( sP1(X7)
| ~ r1(sK16,X7) ),
inference(cnf_transformation,[],[f27]) ).
fof(f65,plain,
! [X7] :
( sP0(X7)
| ~ r1(sK16,X7) ),
inference(cnf_transformation,[],[f27]) ).
fof(f66,plain,
! [X7] :
( sP2(X7)
| ~ r1(sK16,X7) ),
inference(cnf_transformation,[],[f27]) ).
fof(f67,plain,
! [X7] :
( sP3(X7)
| ~ r1(sK16,X7) ),
inference(cnf_transformation,[],[f27]) ).
fof(f68,plain,
! [X8,X7] :
( p2(sK19(X8))
| ~ r1(X7,X8)
| ~ r1(sK16,X7) ),
inference(cnf_transformation,[],[f27]) ).
fof(f70,plain,
! [X8,X7] :
( r1(X8,sK19(X8))
| ~ r1(X7,X8)
| ~ r1(sK16,X7) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p2(X2)
| r1(X3,sK5(X3))
| ~ sP3(X0)
| ~ p2(X1)
| ~ r1(X1,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( p2(X4)
| ~ sP3(X2)
| ~ p2(X3)
| ~ p2(X1)
| ~ r1(X3,X4)
| ~ r1(X3,X0)
| ~ r1(X2,X3)
| ~ r1(sK5(X0),X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( r1(X2,sK6(X2))
| r1(X0,sK8(X0))
| ~ sP2(X0)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r1(X3,sK6(X3))
| ~ sP2(X0)
| ~ p2(X1)
| ~ r1(X2,X3)
| ~ r1(X0,X2)
| ~ r1(sK8(X0),X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( p2(sK6(X2))
| r1(X0,sK8(X0))
| ~ sP2(X0)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p2(sK6(X3))
| ~ sP2(X0)
| ~ p2(X1)
| ~ r1(X2,X3)
| ~ r1(X0,X2)
| ~ r1(sK8(X0),X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_59,plain,
! [X0: $i] :
( r1(X0,sK11(X0))
| r1(X0,sK9(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( r1(X0,sK9(X0))
| ~ sP1(X0)
| ~ p2(X1)
| ~ r1(sK11(X0),X1) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_63,plain,
! [X0: $i] :
( p2(sK9(X0))
| r1(X0,sK11(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( p2(sK9(X0))
| ~ sP1(X0)
| ~ p2(X1)
| ~ r1(sK11(X0),X1) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_77,negated_conjecture,
! [X0: $i,X1: $i] :
( r1(X1,sK19(X1))
| ~ r1(sK16,X0)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_79,negated_conjecture,
! [X0: $i,X1: $i] :
( p2(sK19(X1))
| ~ r1(sK16,X0)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_80,negated_conjecture,
! [X0: $i] :
( sP3(X0)
| ~ r1(sK16,X0) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_81,negated_conjecture,
! [X0: $i] :
( sP2(X0)
| ~ r1(sK16,X0) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_82,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| ~ r1(sK16,X0) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_83,negated_conjecture,
! [X0: $i] :
( sP1(X0)
| ~ r1(sK16,X0) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_91,negated_conjecture,
r1(sK16,sK25),
inference(cnf_transformation,[],[f56]) ).
tcf(c_92,negated_conjecture,
! [X0: $i] :
( r1(X0,sK26(X0))
| ~ r1(sK25,X0) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_93,negated_conjecture,
! [X0: $i] :
( ~ p2(sK26(X0))
| ~ r1(sK25,X0) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_528,plain,
! [X0: $i,X1: $i] :
( p2(sK9(X0))
| ~ p2(X1)
| ~ r1(sK16,X0)
| ~ r1(sK11(X0),X1) ),
inference(resolution,[status(thm)],[c_83,c_64]) ).
tcf(c_542,plain,
! [X0: $i] :
( p2(sK9(X0))
| r1(X0,sK11(X0))
| ~ r1(sK16,X0) ),
inference(resolution,[status(thm)],[c_83,c_63]) ).
tcf(c_578,plain,
! [X0: $i,X1: $i] :
( r1(X0,sK9(X0))
| ~ p2(X1)
| ~ r1(sK16,X0)
| ~ r1(sK11(X0),X1) ),
inference(resolution,[status(thm)],[c_83,c_60]) ).
tcf(c_592,plain,
! [X0: $i] :
( r1(X0,sK11(X0))
| r1(X0,sK9(X0))
| ~ r1(sK16,X0) ),
inference(resolution,[status(thm)],[c_83,c_59]) ).
tcf(c_624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p2(X2)
| r1(X3,sK5(X3))
| ~ p2(X1)
| ~ r1(sK16,X0)
| ~ r1(X1,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(resolution,[status(thm)],[c_80,c_51]) ).
tcf(c_669,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( p2(X4)
| ~ p2(X3)
| ~ p2(X1)
| ~ r1(sK16,X2)
| ~ r1(X3,X4)
| ~ r1(X3,X0)
| ~ r1(X2,X3)
| ~ r1(sK5(X0),X1) ),
inference(resolution,[status(thm)],[c_80,c_52]) ).
tcf(c_750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p2(sK6(X3))
| ~ p2(X1)
| ~ r1(sK16,X0)
| ~ r1(X2,X3)
| ~ r1(X0,X2)
| ~ r1(sK8(X0),X1) ),
inference(resolution,[status(thm)],[c_81,c_58]) ).
tcf(c_770,plain,
! [X0: $i,X1: $i,X2: $i] :
( p2(sK6(X2))
| r1(X0,sK8(X0))
| ~ r1(sK16,X0)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(resolution,[status(thm)],[c_81,c_57]) ).
tcf(c_824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r1(X3,sK6(X3))
| ~ p2(X1)
| ~ r1(sK16,X0)
| ~ r1(X2,X3)
| ~ r1(X0,X2)
| ~ r1(sK8(X0),X1) ),
inference(resolution,[status(thm)],[c_81,c_54]) ).
tcf(c_844,plain,
! [X0: $i,X1: $i,X2: $i] :
( r1(X2,sK6(X2))
| r1(X0,sK8(X0))
| ~ r1(sK16,X0)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(resolution,[status(thm)],[c_81,c_53]) ).
tcf(c_1477,plain,
! [X0: $i,X1: $i] :
( r1(sK25,sK8(sK25))
| r1(X1,sK6(X1))
| ~ r1(sK16,sK25)
| ~ r1(sK25,X0)
| ~ r1(X0,X1) ),
inference(instantiation,[status(thm)],[c_844]) ).
tcf(c_1480,plain,
! [X0: $i,X1: $i] :
( p2(sK6(X1))
| r1(sK25,sK8(sK25))
| ~ r1(sK16,sK25)
| ~ r1(sK25,X0)
| ~ r1(X0,X1) ),
inference(instantiation,[status(thm)],[c_770]) ).
tcf(c_1484,plain,
( r1(sK25,sK11(sK25))
| r1(sK25,sK9(sK25))
| ~ r1(sK16,sK25) ),
inference(instantiation,[status(thm)],[c_592]) ).
tcf(c_1487,plain,
! [X0: $i] :
( r1(X0,sK19(X0))
| ~ r1(sK16,sK25)
| ~ r1(sK25,X0) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_1488,plain,
! [X0: $i] :
( p2(sK19(X0))
| ~ r1(sK16,sK25)
| ~ r1(sK25,X0) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_1489,plain,
( p2(sK9(sK25))
| r1(sK25,sK11(sK25))
| ~ r1(sK16,sK25) ),
inference(instantiation,[status(thm)],[c_542]) ).
tcf(c_1515,plain,
( r1(sK11(sK25),sK19(sK11(sK25)))
| ~ r1(sK16,sK25)
| ~ r1(sK25,sK11(sK25)) ),
inference(instantiation,[status(thm)],[c_1487]) ).
tcf(c_1677,plain,
! [X0: $i] :
( r1(sK25,sK8(sK25))
| r1(X0,sK6(X0))
| ~ r1(sK16,sK25)
| ~ r1(sK25,sK9(sK25))
| ~ r1(sK9(sK25),X0) ),
inference(instantiation,[status(thm)],[c_1477]) ).
tcf(c_1679,plain,
! [X0: $i] :
( p2(sK6(X0))
| r1(sK25,sK8(sK25))
| ~ r1(sK16,sK25)
| ~ r1(sK25,sK9(sK25))
| ~ r1(sK9(sK25),X0) ),
inference(instantiation,[status(thm)],[c_1480]) ).
tcf(c_1683,plain,
( r1(sK9(sK25),sK26(sK9(sK25)))
| ~ r1(sK25,sK9(sK25)) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_1698,plain,
! [X0: $i,X1: $i,X2: $i] :
( p2(X0)
| r1(X1,sK5(X1))
| ~ p2(sK9(sK25))
| ~ r1(sK16,X2)
| ~ r1(X2,sK9(sK25))
| ~ r1(sK9(sK25),X1)
| ~ r1(sK9(sK25),X0) ),
inference(instantiation,[status(thm)],[c_624]) ).
tcf(c_1715,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p2(X2)
| ~ p2(X1)
| ~ p2(sK9(sK25))
| ~ r1(sK16,X3)
| ~ r1(X3,sK9(sK25))
| ~ r1(sK9(sK25),X2)
| ~ r1(sK9(sK25),X0)
| ~ r1(sK5(X0),X1) ),
inference(instantiation,[status(thm)],[c_669]) ).
tcf(c_1842,plain,
! [X0: $i] :
( r1(X0,sK9(X0))
| ~ r1(sK16,X0)
| ~ p2(sK19(sK11(sK25)))
| ~ r1(sK11(X0),sK19(sK11(sK25))) ),
inference(instantiation,[status(thm)],[c_578]) ).
tcf(c_1844,plain,
! [X0: $i] :
( p2(sK9(X0))
| ~ r1(sK16,X0)
| ~ p2(sK19(sK11(sK25)))
| ~ r1(sK11(X0),sK19(sK11(sK25))) ),
inference(instantiation,[status(thm)],[c_528]) ).
tcf(c_2166,plain,
! [X0: $i] :
( p2(sK19(X0))
| ~ r1(sK25,X0) ),
inference(resolution,[status(thm)],[c_79,c_91]) ).
tcf(c_2229,plain,
( p2(sK9(sK25))
| ~ r1(sK16,sK25)
| ~ p2(sK19(sK11(sK25)))
| ~ r1(sK11(sK25),sK19(sK11(sK25))) ),
inference(instantiation,[status(thm)],[c_1844]) ).
tcf(c_2249,plain,
( r1(sK25,sK9(sK25))
| ~ r1(sK16,sK25)
| ~ p2(sK19(sK11(sK25)))
| ~ r1(sK11(sK25),sK19(sK11(sK25))) ),
inference(instantiation,[status(thm)],[c_1842]) ).
tcf(c_2431,plain,
( r1(sK8(sK25),sK19(sK8(sK25)))
| ~ r1(sK16,sK25)
| ~ r1(sK25,sK8(sK25)) ),
inference(instantiation,[status(thm)],[c_1487]) ).
tcf(c_2433,plain,
( p2(sK19(sK8(sK25)))
| ~ r1(sK16,sK25)
| ~ r1(sK25,sK8(sK25)) ),
inference(instantiation,[status(thm)],[c_1488]) ).
tcf(c_2862,plain,
! [X0: $i,X1: $i] :
( p2(X0)
| r1(X1,sK5(X1))
| ~ p2(sK9(sK25))
| ~ r1(sK16,sK25)
| ~ r1(sK25,sK9(sK25))
| ~ r1(sK9(sK25),X1)
| ~ r1(sK9(sK25),X0) ),
inference(instantiation,[status(thm)],[c_1698]) ).
tcf(c_2867,plain,
! [X0: $i,X1: $i,X2: $i] :
( p2(X2)
| ~ p2(X1)
| ~ p2(sK9(sK25))
| ~ r1(sK16,sK25)
| ~ r1(sK25,sK9(sK25))
| ~ r1(sK9(sK25),X2)
| ~ r1(sK9(sK25),X0)
| ~ r1(sK5(X0),X1) ),
inference(instantiation,[status(thm)],[c_1715]) ).
tcf(c_2951,plain,
( r1(sK25,sK8(sK25))
| r1(sK12(sK9(sK25)),sK6(sK12(sK9(sK25))))
| ~ r1(sK16,sK25)
| ~ r1(sK25,sK9(sK25))
| ~ r1(sK9(sK25),sK12(sK9(sK25))) ),
inference(instantiation,[status(thm)],[c_1677]) ).
tcf(c_2959,plain,
( r1(sK25,sK8(sK25))
| p2(sK6(sK12(sK9(sK25))))
| ~ r1(sK16,sK25)
| ~ r1(sK25,sK9(sK25))
| ~ r1(sK9(sK25),sK12(sK9(sK25))) ),
inference(instantiation,[status(thm)],[c_1679]) ).
tcf(c_3480,plain,
! [X0: $i] :
( p2(X0)
| r1(sK13(sK9(sK25)),sK5(sK13(sK9(sK25))))
| ~ p2(sK9(sK25))
| ~ r1(sK16,sK25)
| ~ r1(sK25,sK9(sK25))
| ~ r1(sK9(sK25),X0)
| ~ r1(sK9(sK25),sK13(sK9(sK25))) ),
inference(instantiation,[status(thm)],[c_2862]) ).
tcf(c_3667,plain,
! [X0: $i,X1: $i,X2: $i] :
( r1(X2,sK6(X2))
| ~ r1(sK16,X0)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ p2(sK19(sK8(sK25)))
| ~ r1(sK8(X0),sK19(sK8(sK25))) ),
inference(instantiation,[status(thm)],[c_824]) ).
tcf(c_3670,plain,
! [X0: $i,X1: $i,X2: $i] :
( p2(sK6(X2))
| ~ r1(sK16,X0)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ p2(sK19(sK8(sK25)))
| ~ r1(sK8(X0),sK19(sK8(sK25))) ),
inference(instantiation,[status(thm)],[c_750]) ).
tcf(c_3812,plain,
( p2(sK9(sK25))
| ~ r1(sK16,sK25)
| ~ p2(sK26(sK11(sK25))) ),
inference(superposition,[status(thm)],[c_542,c_93]) ).
tcf(c_4245,plain,
! [X0: $i,X1: $i] :
( r1(X1,sK6(X1))
| ~ r1(sK16,sK25)
| ~ r1(sK25,X0)
| ~ r1(X0,X1)
| ~ p2(sK19(sK8(sK25)))
| ~ r1(sK8(sK25),sK19(sK8(sK25))) ),
inference(instantiation,[status(thm)],[c_3667]) ).
tcf(c_4318,plain,
! [X0: $i,X1: $i] :
( p2(sK6(X1))
| ~ r1(sK16,sK25)
| ~ r1(sK25,X0)
| ~ r1(X0,X1)
| ~ p2(sK19(sK8(sK25)))
| ~ r1(sK8(sK25),sK19(sK8(sK25))) ),
inference(instantiation,[status(thm)],[c_3670]) ).
tcf(c_4362,plain,
( p2(sK9(sK25))
| p2(sK19(sK11(sK25)))
| ~ r1(sK16,sK25) ),
inference(resolution,[status(thm)],[c_542,c_2166]) ).
tcf(c_4432,plain,
( r1(sK25,sK9(sK25))
| ~ r1(sK16,sK25)
| ~ p2(sK26(sK11(sK25))) ),
inference(superposition,[status(thm)],[c_592,c_93]) ).
tcf(c_4641,plain,
( p2(sK19(sK11(sK25)))
| r1(sK25,sK9(sK25))
| ~ r1(sK16,sK25) ),
inference(resolution,[status(thm)],[c_592,c_2166]) ).
tcf(c_4889,plain,
p2(sK9(sK25)),
inference(global_subsumption_just,[status(thm)],[c_3812,c_91,c_1489,c_1515,c_2229,c_4362]) ).
tcf(c_5413,plain,
! [X0: $i] :
( r1(X0,sK6(X0))
| ~ r1(sK16,sK25)
| ~ p2(sK19(sK8(sK25)))
| ~ r1(sK25,sK9(sK25))
| ~ r1(sK9(sK25),X0)
| ~ r1(sK8(sK25),sK19(sK8(sK25))) ),
inference(instantiation,[status(thm)],[c_4245]) ).
tcf(c_5453,plain,
! [X0: $i] :
( p2(sK6(X0))
| ~ r1(sK16,sK25)
| ~ p2(sK19(sK8(sK25)))
| ~ r1(sK25,sK9(sK25))
| ~ r1(sK9(sK25),X0)
| ~ r1(sK8(sK25),sK19(sK8(sK25))) ),
inference(instantiation,[status(thm)],[c_4318]) ).
tcf(c_5478,plain,
r1(sK25,sK9(sK25)),
inference(global_subsumption_just,[status(thm)],[c_4432,c_91,c_1484,c_1515,c_2249,c_4641]) ).
tcf(c_5489,plain,
~ p2(sK26(sK9(sK25))),
inference(superposition,[status(thm)],[c_5478,c_93]) ).
tcf(c_7651,plain,
( p2(sK26(sK9(sK25)))
| r1(sK13(sK9(sK25)),sK5(sK13(sK9(sK25))))
| ~ p2(sK9(sK25))
| ~ r1(sK16,sK25)
| ~ r1(sK25,sK9(sK25))
| ~ r1(sK9(sK25),sK26(sK9(sK25)))
| ~ r1(sK9(sK25),sK13(sK9(sK25))) ),
inference(instantiation,[status(thm)],[c_3480]) ).
tcf(c_8890,plain,
! [X0: $i] :
( p2(X0)
| ~ p2(sK9(sK25))
| ~ r1(sK16,sK25)
| ~ r1(sK25,sK9(sK25))
| ~ r1(sK9(sK25),X0)
| ~ p2(sK14(sK5(sK13(sK9(sK25)))))
| ~ r1(sK9(sK25),sK13(sK9(sK25)))
| ~ r1(sK5(sK13(sK9(sK25))),sK14(sK5(sK13(sK9(sK25))))) ),
inference(instantiation,[status(thm)],[c_2867]) ).
tcf(c_9620,plain,
( p2(sK26(sK9(sK25)))
| ~ p2(sK9(sK25))
| ~ r1(sK16,sK25)
| ~ r1(sK25,sK9(sK25))
| ~ p2(sK14(sK5(sK13(sK9(sK25)))))
| ~ r1(sK9(sK25),sK26(sK9(sK25)))
| ~ r1(sK9(sK25),sK13(sK9(sK25)))
| ~ r1(sK5(sK13(sK9(sK25))),sK14(sK5(sK13(sK9(sK25))))) ),
inference(instantiation,[status(thm)],[c_8890]) ).
tcf(c_9779,plain,
( r1(sK12(sK9(sK25)),sK6(sK12(sK9(sK25))))
| ~ r1(sK16,sK25)
| ~ p2(sK19(sK8(sK25)))
| ~ r1(sK25,sK9(sK25))
| ~ r1(sK9(sK25),sK12(sK9(sK25)))
| ~ r1(sK8(sK25),sK19(sK8(sK25))) ),
inference(instantiation,[status(thm)],[c_5413]) ).
tcf(c_9780,plain,
( p2(sK6(sK12(sK9(sK25))))
| ~ r1(sK16,sK25)
| ~ p2(sK19(sK8(sK25)))
| ~ r1(sK25,sK9(sK25))
| ~ r1(sK9(sK25),sK12(sK9(sK25)))
| ~ r1(sK8(sK25),sK19(sK8(sK25))) ),
inference(instantiation,[status(thm)],[c_5453]) ).
fof(f9,definition,
! [X8] :
( ~ sP0(X8)
| ! [X24] :
( ? [X27] :
( ! [X28] :
( ? [X29] :
( p2(X29)
& ? [X30] : r1(X29,X30)
& r1(X28,X29) )
| ~ r1(X27,X28) )
& r1(X24,X27) )
| ? [X25] :
( ! [X26] :
( ~ p2(X26)
| ~ r1(X25,X26) )
& r1(X24,X25) )
| ~ r1(X8,X24) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f10,definition,
! [X8] :
( ~ sP1(X8)
| ? [X33] :
( ! [X34] :
( ~ p2(X34)
| ~ r1(X33,X34) )
& r1(X8,X33) )
| ? [X31] :
( p2(X31)
& ? [X32] : r1(X31,X32)
& r1(X8,X31) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f11,definition,
! [X8] :
( ~ sP2(X8)
| ? [X22] :
( ! [X23] :
( ~ p2(X23)
| ~ r1(X22,X23) )
& r1(X8,X22) )
| ! [X18] :
( ! [X19] :
( ? [X20] :
( p2(X20)
& ? [X21] : r1(X20,X21)
& r1(X19,X20) )
| ~ r1(X18,X19) )
| ~ r1(X8,X18) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f12,definition,
! [X8] :
( ~ sP3(X8)
| ! [X12] :
( ! [X15] :
( ? [X16] :
( ! [X17] :
( ~ p2(X17)
| ~ r1(X16,X17) )
& r1(X15,X16) )
| ~ r1(X12,X15) )
| ~ p2(X12)
| ! [X13] :
( ( p2(X13)
& ? [X14] : r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X8,X12) ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f13,plain,
? [X0] :
( ! [X46] :
( ? [X49] :
( p1(X49)
& r1(X46,X49) )
| ! [X47] :
( ! [X48] :
( ~ p1(X48)
| ~ r1(X47,X48) )
| ~ r1(X46,X47) )
| ~ r1(X0,X46) )
& ? [X43] :
( ! [X44] :
( ? [X45] :
( ~ p2(X45)
& r1(X44,X45) )
| ~ r1(X43,X44) )
& r1(X0,X43) )
& ? [X39] :
( ? [X42] :
( ~ p1(X42)
& r1(X39,X42) )
& ? [X40] :
( ! [X41] :
( p1(X41)
| ~ r1(X40,X41) )
& r1(X39,X40) )
& r1(X0,X39) )
& ! [X35] :
( ? [X38] :
( ~ p1(X38)
& r1(X35,X38) )
| ! [X36] :
( ! [X37] :
( p1(X37)
| ~ r1(X36,X37) )
| ~ r1(X35,X36) )
| ~ r1(X0,X35) )
& ! [X8] :
( ( sP1(X8)
& sP0(X8)
& sP2(X8)
& sP3(X8)
& ! [X9] :
( ? [X10] :
( p2(X10)
& ? [X11] : r1(X10,X11)
& r1(X9,X10) )
| ~ r1(X8,X9) ) )
| ~ r1(X0,X8) )
& ! [X2] :
( ? [X6] :
( ! [X7] :
( ~ p1(X7)
| ~ r1(X6,X7) )
& r1(X2,X6) )
| ! [X3] :
( ! [X4] :
( ? [X5] :
( p1(X5)
& r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X0,X2) ) ),
inference(definition_folding,[],[f8,f12,f11,f10,f9]) ).
fof(f23,plain,
! [X8] :
( ~ sP0(X8)
| ! [X24] :
( ? [X27] :
( ! [X28] :
( ? [X29] :
( p2(X29)
& ? [X30] : r1(X29,X30)
& r1(X28,X29) )
| ~ r1(X27,X28) )
& r1(X24,X27) )
| ? [X25] :
( ! [X26] :
( ~ p2(X26)
| ~ r1(X25,X26) )
& r1(X24,X25) )
| ~ r1(X8,X24) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f24,plain,
! [X0] :
( ~ sP0(X0)
| ! [X1] :
( ? [X4] :
( ! [X5] :
( ? [X6] :
( p2(X6)
& ? [X7] : r1(X6,X7)
& r1(X5,X6) )
| ~ r1(X4,X5) )
& r1(X1,X4) )
| ? [X2] :
( ! [X3] :
( ~ p2(X3)
| ~ r1(X2,X3) )
& r1(X1,X2) )
| ~ r1(X0,X1) ) ),
inference(rectify,[],[f23]) ).
fof(f25,plain,
! [X0] :
( ~ sP0(X0)
| ! [X1] :
( ( ! [X5] :
( ( p2(sK14(X5))
& r1(sK14(X5),sK15(X5))
& r1(X5,sK14(X5)) )
| ~ r1(sK13(X1),X5) )
& r1(X1,sK13(X1)) )
| ( ! [X3] :
( ~ p2(X3)
| ~ r1(sK12(X1),X3) )
& r1(X1,sK12(X1)) )
| ~ r1(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15]),skolemize(X2,sK12(X1)),skolemize(X4,sK13(X1)),skolemize(X6,sK14(X5)),skolemize(X7,sK15(X5))],[f24]) ).
fof(f44,plain,
! [X3,X0,X1,X5] :
( ~ sP0(X0)
| p2(sK14(X5))
| ~ r1(sK13(X1),X5)
| ~ p2(X3)
| ~ r1(sK12(X1),X3)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
! [X3,X0,X1,X5] :
( ~ sP0(X0)
| r1(X5,sK14(X5))
| ~ r1(sK13(X1),X5)
| ~ p2(X3)
| ~ r1(sK12(X1),X3)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f47,plain,
! [X3,X0,X1] :
( ~ sP0(X0)
| r1(X1,sK13(X1))
| ~ p2(X3)
| ~ r1(sK12(X1),X3)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f48,plain,
! [X0,X1,X5] :
( ~ sP0(X0)
| p2(sK14(X5))
| ~ r1(sK13(X1),X5)
| r1(X1,sK12(X1))
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f50,plain,
! [X0,X1,X5] :
( ~ sP0(X0)
| r1(X5,sK14(X5))
| ~ r1(sK13(X1),X5)
| r1(X1,sK12(X1))
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f51,plain,
! [X0,X1] :
( ~ sP0(X0)
| r1(X1,sK13(X1))
| r1(X1,sK12(X1))
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( r1(X1,sK13(X1))
| r1(X1,sK12(X1))
| ~ sP0(X0)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( r1(X1,sK14(X1))
| r1(X0,sK12(X0))
| ~ sP0(X2)
| ~ r1(X2,X0)
| ~ r1(sK13(X0),X1) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( p2(sK14(X1))
| r1(X0,sK12(X0))
| ~ sP0(X2)
| ~ r1(X2,X0)
| ~ r1(sK13(X0),X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( r1(X0,sK13(X0))
| ~ sP0(X2)
| ~ p2(X1)
| ~ r1(X2,X0)
| ~ r1(sK12(X0),X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r1(X2,sK14(X2))
| ~ sP0(X3)
| ~ p2(X1)
| ~ r1(X3,X0)
| ~ r1(sK13(X0),X2)
| ~ r1(sK12(X0),X1) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p2(sK14(X2))
| ~ sP0(X3)
| ~ p2(X1)
| ~ r1(X3,X0)
| ~ r1(sK13(X0),X2)
| ~ r1(sK12(X0),X1) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_894,plain,
! [X0: $i,X1: $i] :
( r1(X1,sK13(X1))
| r1(X1,sK12(X1))
| ~ r1(sK16,X0)
| ~ r1(X0,X1) ),
inference(resolution,[status(thm)],[c_82,c_65]) ).
tcf(c_908,plain,
! [X0: $i,X1: $i,X2: $i] :
( r1(X0,sK13(X0))
| ~ p2(X1)
| ~ r1(sK16,X2)
| ~ r1(X2,X0)
| ~ r1(sK12(X0),X1) ),
inference(resolution,[status(thm)],[c_82,c_69]) ).
tcf(c_925,plain,
! [X0: $i,X1: $i,X2: $i] :
( p2(sK14(X1))
| r1(X0,sK12(X0))
| ~ r1(sK16,X2)
| ~ r1(X2,X0)
| ~ r1(sK13(X0),X1) ),
inference(resolution,[status(thm)],[c_82,c_68]) ).
tcf(c_959,plain,
! [X0: $i,X1: $i,X2: $i] :
( r1(X1,sK14(X1))
| r1(X0,sK12(X0))
| ~ r1(sK16,X2)
| ~ r1(X2,X0)
| ~ r1(sK13(X0),X1) ),
inference(resolution,[status(thm)],[c_82,c_66]) ).
tcf(c_976,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p2(sK14(X2))
| ~ p2(X1)
| ~ r1(sK16,X3)
| ~ r1(X3,X0)
| ~ r1(sK13(X0),X2)
| ~ r1(sK12(X0),X1) ),
inference(resolution,[status(thm)],[c_82,c_72]) ).
tcf(c_1016,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r1(X2,sK14(X2))
| ~ p2(X1)
| ~ r1(sK16,X3)
| ~ r1(X3,X0)
| ~ r1(sK13(X0),X2)
| ~ r1(sK12(X0),X1) ),
inference(resolution,[status(thm)],[c_82,c_70]) ).
tcf(c_1483,plain,
! [X0: $i] :
( r1(X0,sK13(X0))
| r1(X0,sK12(X0))
| ~ r1(sK16,sK25)
| ~ r1(sK25,X0) ),
inference(instantiation,[status(thm)],[c_894]) ).
tcf(c_1675,plain,
( r1(sK9(sK25),sK13(sK9(sK25)))
| r1(sK9(sK25),sK12(sK9(sK25)))
| ~ r1(sK16,sK25)
| ~ r1(sK25,sK9(sK25)) ),
inference(instantiation,[status(thm)],[c_1483]) ).
tcf(c_5085,plain,
! [X0: $i,X1: $i,X2: $i] :
( r1(X1,sK14(X1))
| ~ r1(sK16,X2)
| ~ r1(X2,X0)
| ~ r1(sK13(X0),X1)
| ~ p2(sK6(sK12(sK9(sK25))))
| ~ r1(sK12(X0),sK6(sK12(sK9(sK25)))) ),
inference(instantiation,[status(thm)],[c_1016]) ).
tcf(c_5089,plain,
! [X0: $i,X1: $i,X2: $i] :
( p2(sK14(X1))
| ~ r1(sK16,X2)
| ~ r1(X2,X0)
| ~ r1(sK13(X0),X1)
| ~ p2(sK6(sK12(sK9(sK25))))
| ~ r1(sK12(X0),sK6(sK12(sK9(sK25)))) ),
inference(instantiation,[status(thm)],[c_976]) ).
tcf(c_5091,plain,
! [X0: $i,X1: $i] :
( r1(X0,sK13(X0))
| ~ r1(sK16,X1)
| ~ r1(X1,X0)
| ~ p2(sK6(sK12(sK9(sK25))))
| ~ r1(sK12(X0),sK6(sK12(sK9(sK25)))) ),
inference(instantiation,[status(thm)],[c_908]) ).
tcf(c_5588,plain,
! [X0: $i] :
( r1(X0,sK13(X0))
| ~ r1(sK16,sK25)
| ~ r1(sK25,X0)
| ~ p2(sK6(sK12(sK9(sK25))))
| ~ r1(sK12(X0),sK6(sK12(sK9(sK25)))) ),
inference(instantiation,[status(thm)],[c_5091]) ).
tcf(c_5610,plain,
! [X0: $i,X1: $i] :
( p2(sK14(X1))
| ~ r1(sK16,sK25)
| ~ r1(sK25,X0)
| ~ r1(sK13(X0),X1)
| ~ p2(sK6(sK12(sK9(sK25))))
| ~ r1(sK12(X0),sK6(sK12(sK9(sK25)))) ),
inference(instantiation,[status(thm)],[c_5089]) ).
tcf(c_5641,plain,
! [X0: $i,X1: $i] :
( r1(X1,sK14(X1))
| ~ r1(sK16,sK25)
| ~ r1(sK25,X0)
| ~ r1(sK13(X0),X1)
| ~ p2(sK6(sK12(sK9(sK25))))
| ~ r1(sK12(X0),sK6(sK12(sK9(sK25)))) ),
inference(instantiation,[status(thm)],[c_5085]) ).
tcf(c_6911,plain,
( r1(sK9(sK25),sK13(sK9(sK25)))
| ~ r1(sK16,sK25)
| ~ r1(sK25,sK9(sK25))
| ~ p2(sK6(sK12(sK9(sK25))))
| ~ r1(sK12(sK9(sK25)),sK6(sK12(sK9(sK25)))) ),
inference(instantiation,[status(thm)],[c_5588]) ).
tcf(c_6914,plain,
! [X0: $i] :
( p2(sK14(X0))
| ~ r1(sK16,sK25)
| ~ r1(sK25,sK9(sK25))
| ~ p2(sK6(sK12(sK9(sK25))))
| ~ r1(sK13(sK9(sK25)),X0)
| ~ r1(sK12(sK9(sK25)),sK6(sK12(sK9(sK25)))) ),
inference(instantiation,[status(thm)],[c_5610]) ).
tcf(c_6954,plain,
! [X0: $i] :
( r1(X0,sK14(X0))
| ~ r1(sK16,sK25)
| ~ r1(sK25,sK9(sK25))
| ~ p2(sK6(sK12(sK9(sK25))))
| ~ r1(sK13(sK9(sK25)),X0)
| ~ r1(sK12(sK9(sK25)),sK6(sK12(sK9(sK25)))) ),
inference(instantiation,[status(thm)],[c_5641]) ).
tcf(c_8396,plain,
! [X0: $i] :
( r1(sK9(sK25),sK12(sK9(sK25)))
| r1(sK5(sK13(sK9(sK25))),sK14(sK5(sK13(sK9(sK25)))))
| ~ r1(sK16,X0)
| ~ r1(X0,sK9(sK25))
| ~ r1(sK13(sK9(sK25)),sK5(sK13(sK9(sK25)))) ),
inference(instantiation,[status(thm)],[c_959]) ).
tcf(c_8398,plain,
! [X0: $i] :
( p2(sK14(sK5(sK13(sK9(sK25)))))
| r1(sK9(sK25),sK12(sK9(sK25)))
| ~ r1(sK16,X0)
| ~ r1(X0,sK9(sK25))
| ~ r1(sK13(sK9(sK25)),sK5(sK13(sK9(sK25)))) ),
inference(instantiation,[status(thm)],[c_925]) ).
tcf(c_8439,plain,
( r1(sK5(sK13(sK9(sK25))),sK14(sK5(sK13(sK9(sK25)))))
| ~ r1(sK16,sK25)
| ~ r1(sK25,sK9(sK25))
| ~ p2(sK6(sK12(sK9(sK25))))
| ~ r1(sK13(sK9(sK25)),sK5(sK13(sK9(sK25))))
| ~ r1(sK12(sK9(sK25)),sK6(sK12(sK9(sK25)))) ),
inference(instantiation,[status(thm)],[c_6954]) ).
tcf(c_8440,plain,
( p2(sK14(sK5(sK13(sK9(sK25)))))
| ~ r1(sK16,sK25)
| ~ r1(sK25,sK9(sK25))
| ~ p2(sK6(sK12(sK9(sK25))))
| ~ r1(sK13(sK9(sK25)),sK5(sK13(sK9(sK25))))
| ~ r1(sK12(sK9(sK25)),sK6(sK12(sK9(sK25)))) ),
inference(instantiation,[status(thm)],[c_6914]) ).
tcf(c_9144,plain,
( r1(sK9(sK25),sK12(sK9(sK25)))
| r1(sK5(sK13(sK9(sK25))),sK14(sK5(sK13(sK9(sK25)))))
| ~ r1(sK16,sK25)
| ~ r1(sK25,sK9(sK25))
| ~ r1(sK13(sK9(sK25)),sK5(sK13(sK9(sK25)))) ),
inference(instantiation,[status(thm)],[c_8396]) ).
tcf(c_9146,plain,
( p2(sK14(sK5(sK13(sK9(sK25)))))
| r1(sK9(sK25),sK12(sK9(sK25)))
| ~ r1(sK16,sK25)
| ~ r1(sK25,sK9(sK25))
| ~ r1(sK13(sK9(sK25)),sK5(sK13(sK9(sK25)))) ),
inference(instantiation,[status(thm)],[c_8398]) ).
tcf(c_9795,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_9779,c_9780,c_9620,c_9146,c_9144,c_8439,c_8440,c_7651,c_6911,c_5489,c_5478,c_4889,c_2959,c_2951,c_2431,c_2433,c_1675,c_1683,c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL652+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 : n005.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 : Wed Sep 23 23:59:18 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
% 0.11/0.44 % Proving...
% 1.32/1.76 % SZS status Started for theBenchmark.p
% 1.32/1.76 % SZS status Theorem for theBenchmark.p
% 1.32/1.76
% 1.32/1.76 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.32/1.76
% 1.32/1.76 % ------ iProver source info
% 1.32/1.76
% 1.32/1.76 % git: date: 2026-07-19 20:42:38 +0200
% 1.32/1.76 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.32/1.76 % git: non_committed_changes: false
% 1.32/1.76
% 1.32/1.76 % ------ Parsing...
% 1.32/1.76 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.32/1.76
% 1.32/1.76 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.32/1.76
% 1.32/1.76 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.32/1.76 % ------ Proving...
% 1.32/1.76 % ------ Problem Properties
% 1.32/1.76
% 1.32/1.76 %
% 1.32/1.76 % clauses 43
% 1.32/1.76 % conjectures 19
% 1.32/1.76 % EPR 6
% 1.32/1.76 % Horn 28
% 1.32/1.76 % unary 5
% 1.32/1.76 % binary 3
% 1.32/1.76 % lits 188
% 1.32/1.76 % lits eq 0
% 1.32/1.76 % fd_pure 0
% 1.32/1.76 % fd_pseudo 0
% 1.32/1.76 % fd_cond 0
% 1.32/1.76 % fd_pseudo_cond 0
% 1.32/1.76 % AC symbols 0
% 1.32/1.76
% 1.32/1.76 % ------ Input Options Time Limit: Unbounded
% 1.32/1.76
% 1.32/1.76
% 1.32/1.76 % ------
% 1.32/1.76 % Current options:
% 1.32/1.76 % ------
% 1.32/1.76
% 1.32/1.76
% 1.32/1.76 %
% 1.32/1.76
% 1.32/1.76 % ------ Proving...
% 1.32/1.76 %
% 1.32/1.76
% 1.32/1.76 % SZS status Theorem for theBenchmark.p
% 1.32/1.76
% 1.32/1.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.32/1.76
% 1.32/1.76
%------------------------------------------------------------------------------