%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL656+1.005 : 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 : n006.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 02:07:40 PM UTC 2026
% Result : Theorem 4.04s 1.31s
% Output : CNFRefutation 4.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 89 ( 17 unt; 13 def)
% Number of atoms : 1397 ( 1 equ)
% Maximal formula atoms : 129 ( 15 avg)
% Number of connectives : 2261 ( 998 ~; 750 |; 513 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 9 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 : 30 ( 28 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 373 ( 0 sgn 327 !; 46 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : r1(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
fof(f2,conjecture,
~ ? [X0] :
~ ( ~ ( p100(X0)
& ~ p101(X0)
& ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ! [X1] :
( ( ( ~ p101(X1)
| p100(X1) )
& ( ~ p102(X1)
| p101(X1) )
& ( ~ p103(X1)
| p102(X1) )
& ( ~ p104(X1)
| p103(X1) )
& ( ~ p105(X1)
| p104(X1) )
& ( ~ p106(X1)
| p105(X1) )
& ( ~ p100(X1)
| ( ( ~ p1(X1)
| ! [X0] :
( ~ p100(X0)
| p1(X0)
| ~ r1(X1,X0) ) )
& ( p1(X1)
| ! [X0] :
( ~ p100(X0)
| ~ p1(X0)
| ~ r1(X1,X0) ) ) ) )
& ( ~ p101(X1)
| ( ( ~ p2(X1)
| ! [X0] :
( ~ p101(X0)
| p2(X0)
| ~ r1(X1,X0) ) )
& ( p2(X1)
| ! [X0] :
( ~ p101(X0)
| ~ p2(X0)
| ~ r1(X1,X0) ) ) ) )
& ( ~ p102(X1)
| ( ( ~ p3(X1)
| ! [X0] :
( ~ p102(X0)
| p3(X0)
| ~ r1(X1,X0) ) )
& ( p3(X1)
| ! [X0] :
( ~ p102(X0)
| ~ p3(X0)
| ~ r1(X1,X0) ) ) ) )
& ( ~ p103(X1)
| ( ( ~ p4(X1)
| ! [X0] :
( ~ p103(X0)
| p4(X0)
| ~ r1(X1,X0) ) )
& ( p4(X1)
| ! [X0] :
( ~ p103(X0)
| ~ p4(X0)
| ~ r1(X1,X0) ) ) ) )
& ( ~ p104(X1)
| ( ( ~ p5(X1)
| ! [X0] :
( ~ p104(X0)
| p5(X0)
| ~ r1(X1,X0) ) )
& ( p5(X1)
| ! [X0] :
( ~ p104(X0)
| ~ p5(X0)
| ~ r1(X1,X0) ) ) ) )
& ( ~ p105(X1)
| ( ( ~ p6(X1)
| ! [X0] :
( ~ p105(X0)
| p6(X0)
| ~ r1(X1,X0) ) )
& ( p6(X1)
| ! [X0] :
( ~ p105(X0)
| ~ p6(X0)
| ~ r1(X1,X0) ) ) ) )
& ( ~ ( p100(X1)
& ~ p101(X1) )
| ( ~ ! [X0] :
( ~ ( p101(X0)
& ~ p102(X0)
& p2(X0) )
| ~ r1(X1,X0) )
& ~ ! [X0] :
( ~ ( p101(X0)
& ~ p102(X0)
& ~ p2(X0) )
| ~ r1(X1,X0) ) ) )
& ( ~ ( p101(X1)
& ~ p102(X1) )
| ( ~ ! [X0] :
( ~ ( p102(X0)
& ~ p103(X0)
& p3(X0) )
| ~ r1(X1,X0) )
& ~ ! [X0] :
( ~ ( p102(X0)
& ~ p103(X0)
& ~ p3(X0) )
| ~ r1(X1,X0) ) ) )
& ( ~ ( p102(X1)
& ~ p103(X1) )
| ( ~ ! [X0] :
( ~ ( p103(X0)
& ~ p104(X0)
& p4(X0) )
| ~ r1(X1,X0) )
& ~ ! [X0] :
( ~ ( p103(X0)
& ~ p104(X0)
& ~ p4(X0) )
| ~ r1(X1,X0) ) ) )
& ( ~ ( p103(X1)
& ~ p104(X1) )
| ( ~ ! [X0] :
( ~ ( p104(X0)
& ~ p105(X0)
& p5(X0) )
| ~ r1(X1,X0) )
& ~ ! [X0] :
( ~ ( p104(X0)
& ~ p105(X0)
& ~ p5(X0) )
| ~ r1(X1,X0) ) ) )
& ( ~ ( p104(X1)
& ~ p105(X1) )
| ( ~ ! [X0] :
( ~ ( p105(X0)
& ~ p106(X0)
& p6(X0) )
| ~ r1(X1,X0) )
& ~ ! [X0] :
( ~ ( p105(X0)
& ~ p106(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] :
( p3(X1)
| ~ 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] :
~ ( ~ ( p100(X0)
& ~ p101(X0)
& ! [X1] :
( ! [X0] :
( ! [X1] :
( ! [X0] :
( ! [X1] :
( ( ( ~ p101(X1)
| p100(X1) )
& ( ~ p102(X1)
| p101(X1) )
& ( ~ p103(X1)
| p102(X1) )
& ( ~ p104(X1)
| p103(X1) )
& ( ~ p105(X1)
| p104(X1) )
& ( ~ p106(X1)
| p105(X1) )
& ( ~ p100(X1)
| ( ( ~ p1(X1)
| ! [X0] :
( ~ p100(X0)
| p1(X0)
| ~ r1(X1,X0) ) )
& ( p1(X1)
| ! [X0] :
( ~ p100(X0)
| ~ p1(X0)
| ~ r1(X1,X0) ) ) ) )
& ( ~ p101(X1)
| ( ( ~ p2(X1)
| ! [X0] :
( ~ p101(X0)
| p2(X0)
| ~ r1(X1,X0) ) )
& ( p2(X1)
| ! [X0] :
( ~ p101(X0)
| ~ p2(X0)
| ~ r1(X1,X0) ) ) ) )
& ( ~ p102(X1)
| ( ( ~ p3(X1)
| ! [X0] :
( ~ p102(X0)
| p3(X0)
| ~ r1(X1,X0) ) )
& ( p3(X1)
| ! [X0] :
( ~ p102(X0)
| ~ p3(X0)
| ~ r1(X1,X0) ) ) ) )
& ( ~ p103(X1)
| ( ( ~ p4(X1)
| ! [X0] :
( ~ p103(X0)
| p4(X0)
| ~ r1(X1,X0) ) )
& ( p4(X1)
| ! [X0] :
( ~ p103(X0)
| ~ p4(X0)
| ~ r1(X1,X0) ) ) ) )
& ( ~ p104(X1)
| ( ( ~ p5(X1)
| ! [X0] :
( ~ p104(X0)
| p5(X0)
| ~ r1(X1,X0) ) )
& ( p5(X1)
| ! [X0] :
( ~ p104(X0)
| ~ p5(X0)
| ~ r1(X1,X0) ) ) ) )
& ( ~ p105(X1)
| ( ( ~ p6(X1)
| ! [X0] :
( ~ p105(X0)
| p6(X0)
| ~ r1(X1,X0) ) )
& ( p6(X1)
| ! [X0] :
( ~ p105(X0)
| ~ p6(X0)
| ~ r1(X1,X0) ) ) ) )
& ( ~ ( p100(X1)
& ~ p101(X1) )
| ( ~ ! [X0] :
( ~ ( p101(X0)
& ~ p102(X0)
& p2(X0) )
| ~ r1(X1,X0) )
& ~ ! [X0] :
( ~ ( p101(X0)
& ~ p102(X0)
& ~ p2(X0) )
| ~ r1(X1,X0) ) ) )
& ( ~ ( p101(X1)
& ~ p102(X1) )
| ( ~ ! [X0] :
( ~ ( p102(X0)
& ~ p103(X0)
& p3(X0) )
| ~ r1(X1,X0) )
& ~ ! [X0] :
( ~ ( p102(X0)
& ~ p103(X0)
& ~ p3(X0) )
| ~ r1(X1,X0) ) ) )
& ( ~ ( p102(X1)
& ~ p103(X1) )
| ( ~ ! [X0] :
( ~ ( p103(X0)
& ~ p104(X0)
& p4(X0) )
| ~ r1(X1,X0) )
& ~ ! [X0] :
( ~ ( p103(X0)
& ~ p104(X0)
& ~ p4(X0) )
| ~ r1(X1,X0) ) ) )
& ( ~ ( p103(X1)
& ~ p104(X1) )
| ( ~ ! [X0] :
( ~ ( p104(X0)
& ~ p105(X0)
& p5(X0) )
| ~ r1(X1,X0) )
& ~ ! [X0] :
( ~ ( p104(X0)
& ~ p105(X0)
& ~ p5(X0) )
| ~ r1(X1,X0) ) ) )
& ( ~ ( p104(X1)
& ~ p105(X1) )
| ( ~ ! [X0] :
( ~ ( p105(X0)
& ~ p106(X0)
& p6(X0) )
| ~ r1(X1,X0) )
& ~ ! [X0] :
( ~ ( p105(X0)
& ~ p106(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] :
( p3(X1)
| ~ 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] :
~ ( ~ ( p100(X0)
& ~ p101(X0)
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ( ( ~ p101(X10)
| p100(X10) )
& ( ~ p102(X10)
| p101(X10) )
& ( ~ p103(X10)
| p102(X10) )
& ( ~ p104(X10)
| p103(X10) )
& ( ~ p105(X10)
| p104(X10) )
& ( ~ p106(X10)
| p105(X10) )
& ( ~ p100(X10)
| ( ( ~ p1(X10)
| ! [X32] :
( ~ p100(X32)
| p1(X32)
| ~ r1(X10,X32) ) )
& ( p1(X10)
| ! [X31] :
( ~ p100(X31)
| ~ p1(X31)
| ~ r1(X10,X31) ) ) ) )
& ( ~ p101(X10)
| ( ( ~ p2(X10)
| ! [X30] :
( ~ p101(X30)
| p2(X30)
| ~ r1(X10,X30) ) )
& ( p2(X10)
| ! [X29] :
( ~ p101(X29)
| ~ p2(X29)
| ~ r1(X10,X29) ) ) ) )
& ( ~ p102(X10)
| ( ( ~ p3(X10)
| ! [X28] :
( ~ p102(X28)
| p3(X28)
| ~ r1(X10,X28) ) )
& ( p3(X10)
| ! [X27] :
( ~ p102(X27)
| ~ p3(X27)
| ~ r1(X10,X27) ) ) ) )
& ( ~ p103(X10)
| ( ( ~ p4(X10)
| ! [X26] :
( ~ p103(X26)
| p4(X26)
| ~ r1(X10,X26) ) )
& ( p4(X10)
| ! [X25] :
( ~ p103(X25)
| ~ p4(X25)
| ~ r1(X10,X25) ) ) ) )
& ( ~ p104(X10)
| ( ( ~ p5(X10)
| ! [X24] :
( ~ p104(X24)
| p5(X24)
| ~ r1(X10,X24) ) )
& ( p5(X10)
| ! [X23] :
( ~ p104(X23)
| ~ p5(X23)
| ~ r1(X10,X23) ) ) ) )
& ( ~ p105(X10)
| ( ( ~ p6(X10)
| ! [X22] :
( ~ p105(X22)
| p6(X22)
| ~ r1(X10,X22) ) )
& ( p6(X10)
| ! [X21] :
( ~ p105(X21)
| ~ p6(X21)
| ~ r1(X10,X21) ) ) ) )
& ( ~ ( p100(X10)
& ~ p101(X10) )
| ( ~ ! [X20] :
( ~ ( p101(X20)
& ~ p102(X20)
& p2(X20) )
| ~ r1(X10,X20) )
& ~ ! [X19] :
( ~ ( p101(X19)
& ~ p102(X19)
& ~ p2(X19) )
| ~ r1(X10,X19) ) ) )
& ( ~ ( p101(X10)
& ~ p102(X10) )
| ( ~ ! [X18] :
( ~ ( p102(X18)
& ~ p103(X18)
& p3(X18) )
| ~ r1(X10,X18) )
& ~ ! [X17] :
( ~ ( p102(X17)
& ~ p103(X17)
& ~ p3(X17) )
| ~ r1(X10,X17) ) ) )
& ( ~ ( p102(X10)
& ~ p103(X10) )
| ( ~ ! [X16] :
( ~ ( p103(X16)
& ~ p104(X16)
& p4(X16) )
| ~ r1(X10,X16) )
& ~ ! [X15] :
( ~ ( p103(X15)
& ~ p104(X15)
& ~ p4(X15) )
| ~ r1(X10,X15) ) ) )
& ( ~ ( p103(X10)
& ~ p104(X10) )
| ( ~ ! [X14] :
( ~ ( p104(X14)
& ~ p105(X14)
& p5(X14) )
| ~ r1(X10,X14) )
& ~ ! [X13] :
( ~ ( p104(X13)
& ~ p105(X13)
& ~ p5(X13) )
| ~ r1(X10,X13) ) ) )
& ( ~ ( p104(X10)
& ~ p105(X10) )
| ( ~ ! [X12] :
( ~ ( p105(X12)
& ~ p106(X12)
& p6(X12) )
| ~ r1(X10,X12) )
& ~ ! [X11] :
( ~ ( p105(X11)
& ~ p106(X11)
& ~ p6(X11) )
| ~ r1(X10,X11) ) ) ) )
| ~ r1(X9,X10) )
| ~ r1(X8,X9) )
| ~ r1(X7,X8) )
| ~ r1(X6,X7) )
| ~ r1(X0,X6) ) )
| ~ ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( p3(X5)
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) ) ),
inference(rectify,[],[f3]) ).
fof(f5,plain,
? [X0] :
~ ( ~ ( p100(X0)
& ~ p101(X0)
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ( ( ~ p101(X10)
| p100(X10) )
& ( ~ p102(X10)
| p101(X10) )
& ( ~ p103(X10)
| p102(X10) )
& ( ~ p104(X10)
| p103(X10) )
& ( ~ p105(X10)
| p104(X10) )
& ( ~ p106(X10)
| p105(X10) )
& ( ~ p100(X10)
| ( ( ~ p1(X10)
| ! [X32] :
( ~ p100(X32)
| p1(X32)
| ~ r1(X10,X32) ) )
& ( p1(X10)
| ! [X31] :
( ~ p100(X31)
| ~ p1(X31)
| ~ r1(X10,X31) ) ) ) )
& ( ~ p101(X10)
| ( ( ~ p2(X10)
| ! [X30] :
( ~ p101(X30)
| p2(X30)
| ~ r1(X10,X30) ) )
& ( p2(X10)
| ! [X29] :
( ~ p101(X29)
| ~ p2(X29)
| ~ r1(X10,X29) ) ) ) )
& ( ~ p102(X10)
| ( ( ~ p3(X10)
| ! [X28] :
( ~ p102(X28)
| p3(X28)
| ~ r1(X10,X28) ) )
& ( p3(X10)
| ! [X27] :
( ~ p102(X27)
| ~ p3(X27)
| ~ r1(X10,X27) ) ) ) )
& ( ~ p103(X10)
| ( ( ~ p4(X10)
| ! [X26] :
( ~ p103(X26)
| p4(X26)
| ~ r1(X10,X26) ) )
& ( p4(X10)
| ! [X25] :
( ~ p103(X25)
| ~ p4(X25)
| ~ r1(X10,X25) ) ) ) )
& ( ~ p104(X10)
| ( ( ~ p5(X10)
| ! [X24] :
( ~ p104(X24)
| p5(X24)
| ~ r1(X10,X24) ) )
& ( p5(X10)
| ! [X23] :
( ~ p104(X23)
| ~ p5(X23)
| ~ r1(X10,X23) ) ) ) )
& ( ~ p105(X10)
| ( ( ~ p6(X10)
| ! [X22] :
( ~ p105(X22)
| p6(X22)
| ~ r1(X10,X22) ) )
& ( p6(X10)
| ! [X21] :
( ~ p105(X21)
| ~ p6(X21)
| ~ r1(X10,X21) ) ) ) )
& ( ~ ( p100(X10)
& ~ p101(X10) )
| ( ~ ! [X20] :
( ~ ( p101(X20)
& ~ p102(X20)
& p2(X20) )
| ~ r1(X10,X20) )
& ~ ! [X19] :
( ~ ( p101(X19)
& ~ p102(X19)
& ~ p2(X19) )
| ~ r1(X10,X19) ) ) )
& ( ~ ( p101(X10)
& ~ p102(X10) )
| ( ~ ! [X18] :
( ~ ( p102(X18)
& ~ p103(X18)
& p3(X18) )
| ~ r1(X10,X18) )
& ~ ! [X17] :
( ~ ( p102(X17)
& ~ p103(X17)
& ~ p3(X17) )
| ~ r1(X10,X17) ) ) )
& ( ~ ( p102(X10)
& ~ p103(X10) )
| ( ~ ! [X16] :
( ~ ( p103(X16)
& ~ p104(X16)
& p4(X16) )
| ~ r1(X10,X16) )
& ~ ! [X15] :
( ~ ( p103(X15)
& ~ p104(X15)
& ~ p4(X15) )
| ~ r1(X10,X15) ) ) )
& ( ~ ( p103(X10)
& ~ p104(X10) )
| ( ~ ! [X14] :
( ~ ( p104(X14)
& ~ p105(X14)
& p5(X14) )
| ~ r1(X10,X14) )
& ~ ! [X13] :
( ~ ( p104(X13)
& ~ p105(X13)
& ~ p5(X13) )
| ~ r1(X10,X13) ) ) )
& ( ~ ( p104(X10)
& ~ p105(X10) )
| ( ~ ! [X12] :
( ~ ( p105(X12)
& ~ p106(X12)
& p6(X12) )
| ~ r1(X10,X12) )
& ~ ! [X11] :
( ~ ( p105(X11)
& ~ p106(X11)
& ~ p6(X11) )
| ~ r1(X10,X11) ) ) ) )
| ~ r1(X9,X10) )
| ~ r1(X8,X9) )
| ~ r1(X7,X8) )
| ~ r1(X6,X7) )
| ~ r1(X0,X6) ) )
| ~ ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( p3(X5)
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
? [X0] :
~ ( ~ ( p100(X0)
& ~ p101(X0)
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ( ( ~ p101(X10)
| p100(X10) )
& ( ~ p102(X10)
| p101(X10) )
& ( ~ p103(X10)
| p102(X10) )
& ( ~ p104(X10)
| p103(X10) )
& ( ~ p105(X10)
| p104(X10) )
& ( ~ p100(X10)
| ( ( ~ p1(X10)
| ! [X32] :
( ~ p100(X32)
| p1(X32)
| ~ r1(X10,X32) ) )
& ( p1(X10)
| ! [X31] :
( ~ p100(X31)
| ~ p1(X31)
| ~ r1(X10,X31) ) ) ) )
& ( ~ p101(X10)
| ( ( ~ p2(X10)
| ! [X30] :
( ~ p101(X30)
| p2(X30)
| ~ r1(X10,X30) ) )
& ( p2(X10)
| ! [X29] :
( ~ p101(X29)
| ~ p2(X29)
| ~ r1(X10,X29) ) ) ) )
& ( ~ p102(X10)
| ( ( ~ p3(X10)
| ! [X28] :
( ~ p102(X28)
| p3(X28)
| ~ r1(X10,X28) ) )
& ( p3(X10)
| ! [X27] :
( ~ p102(X27)
| ~ p3(X27)
| ~ r1(X10,X27) ) ) ) )
& ( ~ p103(X10)
| ( ( ~ p4(X10)
| ! [X26] :
( ~ p103(X26)
| p4(X26)
| ~ r1(X10,X26) ) )
& ( p4(X10)
| ! [X25] :
( ~ p103(X25)
| ~ p4(X25)
| ~ r1(X10,X25) ) ) ) )
& ( ~ p104(X10)
| ( ( ~ p5(X10)
| ! [X24] :
( ~ p104(X24)
| p5(X24)
| ~ r1(X10,X24) ) )
& ( p5(X10)
| ! [X23] :
( ~ p104(X23)
| ~ p5(X23)
| ~ r1(X10,X23) ) ) ) )
& ( ~ p105(X10)
| ( ( ~ p6(X10)
| ! [X22] :
( ~ p105(X22)
| p6(X22)
| ~ r1(X10,X22) ) )
& ( p6(X10)
| ! [X21] :
( ~ p105(X21)
| ~ p6(X21)
| ~ r1(X10,X21) ) ) ) )
& ( ~ ( p100(X10)
& ~ p101(X10) )
| ( ~ ! [X20] :
( ~ ( p101(X20)
& ~ p102(X20)
& p2(X20) )
| ~ r1(X10,X20) )
& ~ ! [X19] :
( ~ ( p101(X19)
& ~ p102(X19)
& ~ p2(X19) )
| ~ r1(X10,X19) ) ) )
& ( ~ ( p101(X10)
& ~ p102(X10) )
| ( ~ ! [X18] :
( ~ ( p102(X18)
& ~ p103(X18)
& p3(X18) )
| ~ r1(X10,X18) )
& ~ ! [X17] :
( ~ ( p102(X17)
& ~ p103(X17)
& ~ p3(X17) )
| ~ r1(X10,X17) ) ) )
& ( ~ ( p102(X10)
& ~ p103(X10) )
| ( ~ ! [X16] :
( ~ ( p103(X16)
& ~ p104(X16)
& p4(X16) )
| ~ r1(X10,X16) )
& ~ ! [X15] :
( ~ ( p103(X15)
& ~ p104(X15)
& ~ p4(X15) )
| ~ r1(X10,X15) ) ) )
& ( ~ ( p103(X10)
& ~ p104(X10) )
| ( ~ ! [X14] :
( ~ ( p104(X14)
& ~ p105(X14)
& p5(X14) )
| ~ r1(X10,X14) )
& ~ ! [X13] :
( ~ ( p104(X13)
& ~ p105(X13)
& ~ p5(X13) )
| ~ r1(X10,X13) ) ) )
& ( ~ ( p104(X10)
& ~ p105(X10) )
| ( ~ ! [X12] :
( ~ ( p105(X12)
& p6(X12) )
| ~ r1(X10,X12) )
& ~ ! [X11] :
( ~ ( p105(X11)
& ~ p6(X11) )
| ~ r1(X10,X11) ) ) ) )
| ~ r1(X9,X10) )
| ~ r1(X8,X9) )
| ~ r1(X7,X8) )
| ~ r1(X6,X7) )
| ~ r1(X0,X6) ) )
| ~ ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( p3(X5)
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) ) ),
inference(pure_predicate_removal,[],[f5]) ).
fof(f7,plain,
? [X0] :
( p100(X0)
& ~ p101(X0)
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ( ( ~ p101(X10)
| p100(X10) )
& ( ~ p102(X10)
| p101(X10) )
& ( ~ p103(X10)
| p102(X10) )
& ( ~ p104(X10)
| p103(X10) )
& ( ~ p105(X10)
| p104(X10) )
& ( ~ p100(X10)
| ( ( ~ p1(X10)
| ! [X32] :
( ~ p100(X32)
| p1(X32)
| ~ r1(X10,X32) ) )
& ( p1(X10)
| ! [X31] :
( ~ p100(X31)
| ~ p1(X31)
| ~ r1(X10,X31) ) ) ) )
& ( ~ p101(X10)
| ( ( ~ p2(X10)
| ! [X30] :
( ~ p101(X30)
| p2(X30)
| ~ r1(X10,X30) ) )
& ( p2(X10)
| ! [X29] :
( ~ p101(X29)
| ~ p2(X29)
| ~ r1(X10,X29) ) ) ) )
& ( ~ p102(X10)
| ( ( ~ p3(X10)
| ! [X28] :
( ~ p102(X28)
| p3(X28)
| ~ r1(X10,X28) ) )
& ( p3(X10)
| ! [X27] :
( ~ p102(X27)
| ~ p3(X27)
| ~ r1(X10,X27) ) ) ) )
& ( ~ p103(X10)
| ( ( ~ p4(X10)
| ! [X26] :
( ~ p103(X26)
| p4(X26)
| ~ r1(X10,X26) ) )
& ( p4(X10)
| ! [X25] :
( ~ p103(X25)
| ~ p4(X25)
| ~ r1(X10,X25) ) ) ) )
& ( ~ p104(X10)
| ( ( ~ p5(X10)
| ! [X24] :
( ~ p104(X24)
| p5(X24)
| ~ r1(X10,X24) ) )
& ( p5(X10)
| ! [X23] :
( ~ p104(X23)
| ~ p5(X23)
| ~ r1(X10,X23) ) ) ) )
& ( ~ p105(X10)
| ( ( ~ p6(X10)
| ! [X22] :
( ~ p105(X22)
| p6(X22)
| ~ r1(X10,X22) ) )
& ( p6(X10)
| ! [X21] :
( ~ p105(X21)
| ~ p6(X21)
| ~ r1(X10,X21) ) ) ) )
& ( ~ p100(X10)
| p101(X10)
| ( ? [X20] :
( p101(X20)
& ~ p102(X20)
& p2(X20)
& r1(X10,X20) )
& ? [X19] :
( p101(X19)
& ~ p102(X19)
& ~ p2(X19)
& r1(X10,X19) ) ) )
& ( ~ p101(X10)
| p102(X10)
| ( ? [X18] :
( p102(X18)
& ~ p103(X18)
& p3(X18)
& r1(X10,X18) )
& ? [X17] :
( p102(X17)
& ~ p103(X17)
& ~ p3(X17)
& r1(X10,X17) ) ) )
& ( ~ p102(X10)
| p103(X10)
| ( ? [X16] :
( p103(X16)
& ~ p104(X16)
& p4(X16)
& r1(X10,X16) )
& ? [X15] :
( p103(X15)
& ~ p104(X15)
& ~ p4(X15)
& r1(X10,X15) ) ) )
& ( ~ p103(X10)
| p104(X10)
| ( ? [X14] :
( p104(X14)
& ~ p105(X14)
& p5(X14)
& r1(X10,X14) )
& ? [X13] :
( p104(X13)
& ~ p105(X13)
& ~ p5(X13)
& r1(X10,X13) ) ) )
& ( ~ p104(X10)
| p105(X10)
| ( ? [X12] :
( p105(X12)
& p6(X12)
& r1(X10,X12) )
& ? [X11] :
( p105(X11)
& ~ p6(X11)
& r1(X10,X11) ) ) ) )
| ~ r1(X9,X10) )
| ~ r1(X8,X9) )
| ~ r1(X7,X8) )
| ~ r1(X6,X7) )
| ~ r1(X0,X6) )
& ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( p3(X5)
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f8,plain,
? [X0] :
( p100(X0)
& ~ p101(X0)
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ( ( ~ p101(X10)
| p100(X10) )
& ( ~ p102(X10)
| p101(X10) )
& ( ~ p103(X10)
| p102(X10) )
& ( ~ p104(X10)
| p103(X10) )
& ( ~ p105(X10)
| p104(X10) )
& ( ~ p100(X10)
| ( ( ~ p1(X10)
| ! [X32] :
( ~ p100(X32)
| p1(X32)
| ~ r1(X10,X32) ) )
& ( p1(X10)
| ! [X31] :
( ~ p100(X31)
| ~ p1(X31)
| ~ r1(X10,X31) ) ) ) )
& ( ~ p101(X10)
| ( ( ~ p2(X10)
| ! [X30] :
( ~ p101(X30)
| p2(X30)
| ~ r1(X10,X30) ) )
& ( p2(X10)
| ! [X29] :
( ~ p101(X29)
| ~ p2(X29)
| ~ r1(X10,X29) ) ) ) )
& ( ~ p102(X10)
| ( ( ~ p3(X10)
| ! [X28] :
( ~ p102(X28)
| p3(X28)
| ~ r1(X10,X28) ) )
& ( p3(X10)
| ! [X27] :
( ~ p102(X27)
| ~ p3(X27)
| ~ r1(X10,X27) ) ) ) )
& ( ~ p103(X10)
| ( ( ~ p4(X10)
| ! [X26] :
( ~ p103(X26)
| p4(X26)
| ~ r1(X10,X26) ) )
& ( p4(X10)
| ! [X25] :
( ~ p103(X25)
| ~ p4(X25)
| ~ r1(X10,X25) ) ) ) )
& ( ~ p104(X10)
| ( ( ~ p5(X10)
| ! [X24] :
( ~ p104(X24)
| p5(X24)
| ~ r1(X10,X24) ) )
& ( p5(X10)
| ! [X23] :
( ~ p104(X23)
| ~ p5(X23)
| ~ r1(X10,X23) ) ) ) )
& ( ~ p105(X10)
| ( ( ~ p6(X10)
| ! [X22] :
( ~ p105(X22)
| p6(X22)
| ~ r1(X10,X22) ) )
& ( p6(X10)
| ! [X21] :
( ~ p105(X21)
| ~ p6(X21)
| ~ r1(X10,X21) ) ) ) )
& ( ~ p100(X10)
| p101(X10)
| ( ? [X20] :
( p101(X20)
& ~ p102(X20)
& p2(X20)
& r1(X10,X20) )
& ? [X19] :
( p101(X19)
& ~ p102(X19)
& ~ p2(X19)
& r1(X10,X19) ) ) )
& ( ~ p101(X10)
| p102(X10)
| ( ? [X18] :
( p102(X18)
& ~ p103(X18)
& p3(X18)
& r1(X10,X18) )
& ? [X17] :
( p102(X17)
& ~ p103(X17)
& ~ p3(X17)
& r1(X10,X17) ) ) )
& ( ~ p102(X10)
| p103(X10)
| ( ? [X16] :
( p103(X16)
& ~ p104(X16)
& p4(X16)
& r1(X10,X16) )
& ? [X15] :
( p103(X15)
& ~ p104(X15)
& ~ p4(X15)
& r1(X10,X15) ) ) )
& ( ~ p103(X10)
| p104(X10)
| ( ? [X14] :
( p104(X14)
& ~ p105(X14)
& p5(X14)
& r1(X10,X14) )
& ? [X13] :
( p104(X13)
& ~ p105(X13)
& ~ p5(X13)
& r1(X10,X13) ) ) )
& ( ~ p104(X10)
| p105(X10)
| ( ? [X12] :
( p105(X12)
& p6(X12)
& r1(X10,X12) )
& ? [X11] :
( p105(X11)
& ~ p6(X11)
& r1(X10,X11) ) ) ) )
| ~ r1(X9,X10) )
| ~ r1(X8,X9) )
| ~ r1(X7,X8) )
| ~ r1(X6,X7) )
| ~ r1(X0,X6) )
& ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( p3(X5)
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) ) ),
inference(flattening,[],[f7]) ).
fof(f22,plain,
! [X10] :
( ~ sP11(X10)
| ( ( ~ p101(X10)
| p100(X10) )
& ( ~ p102(X10)
| p101(X10) )
& ( ~ p103(X10)
| p102(X10) )
& ( ~ p104(X10)
| p103(X10) )
& ( ~ p105(X10)
| p104(X10) )
& sP5(X10)
& sP6(X10)
& sP7(X10)
& sP8(X10)
& sP9(X10)
& sP10(X10)
& sP0(X10)
& sP1(X10)
& sP2(X10)
& sP3(X10)
& sP4(X10) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f23,plain,
! [X0] :
( ~ sP11(X0)
| ( ( ~ p101(X0)
| p100(X0) )
& ( ~ p102(X0)
| p101(X0) )
& ( ~ p103(X0)
| p102(X0) )
& ( ~ p104(X0)
| p103(X0) )
& ( ~ p105(X0)
| p104(X0) )
& sP5(X0)
& sP6(X0)
& sP7(X0)
& sP8(X0)
& sP9(X0)
& sP10(X0)
& sP0(X0)
& sP1(X0)
& sP2(X0)
& sP3(X0)
& sP4(X0) ) ),
inference(rectify,[],[f22]) ).
fof(f45,plain,
! [X10] :
( ~ sP1(X10)
| ~ p101(X10)
| p102(X10)
| ( ? [X18] :
( p102(X18)
& ~ p103(X18)
& p3(X18)
& r1(X10,X18) )
& ? [X17] :
( p102(X17)
& ~ p103(X17)
& ~ p3(X17)
& r1(X10,X17) ) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f46,plain,
! [X0] :
( ~ sP1(X0)
| ~ p101(X0)
| p102(X0)
| ( ? [X2] :
( p102(X2)
& ~ p103(X2)
& p3(X2)
& r1(X0,X2) )
& ? [X1] :
( p102(X1)
& ~ p103(X1)
& ~ p3(X1)
& r1(X0,X1) ) ) ),
inference(rectify,[],[f45]) ).
fof(f47,plain,
! [X0] :
( ~ sP1(X0)
| ~ p101(X0)
| p102(X0)
| ( p102(sK19(X0))
& ~ p103(sK19(X0))
& p3(sK19(X0))
& r1(X0,sK19(X0))
& p102(sK18(X0))
& ~ p103(sK18(X0))
& ~ p3(sK18(X0))
& r1(X0,sK18(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18,sK19]),skolemize(X1,sK18(X0)),skolemize(X2,sK19(X0))],[f46]) ).
fof(f51,plain,
( p100(sK22)
& ~ p101(sK22)
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( sP11(X10)
| ~ r1(X9,X10) )
| ~ r1(X8,X9) )
| ~ r1(X7,X8) )
| ~ r1(X6,X7) )
| ~ r1(sK22,X6) )
& ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( p3(X5)
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(sK22,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(X0,sK22)],[f21]) ).
fof(f52,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f64,plain,
! [X0] :
( ~ sP11(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f65,plain,
! [X0] :
( ~ sP11(X0)
| sP1(X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f109,plain,
! [X0] :
( ~ sP1(X0)
| ~ p101(X0)
| p102(X0)
| ~ p3(sK18(X0)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f110,plain,
! [X0] :
( ~ sP1(X0)
| ~ p101(X0)
| p102(X0)
| r1(X0,sK18(X0)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f119,plain,
p100(sK22),
inference(cnf_transformation,[],[f51]) ).
fof(f120,plain,
~ p101(sK22),
inference(cnf_transformation,[],[f51]) ).
fof(f121,plain,
! [X10,X8,X6,X9,X7] :
( sP11(X10)
| ~ r1(X9,X10)
| ~ r1(X8,X9)
| ~ r1(X7,X8)
| ~ r1(X6,X7)
| ~ r1(sK22,X6) ),
inference(cnf_transformation,[],[f51]) ).
fof(f122,plain,
! [X2,X3,X1,X4,X5] :
( p3(X5)
| ~ r1(X4,X5)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(sK22,X1) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_49,plain,
! [X0: $i] : r1(X0,X0),
inference(cnf_transformation,[],[f52]) ).
tcf(c_53,plain,
! [X0: $i] :
( sP1(X0)
| ~ sP11(X0) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_54,plain,
! [X0: $i] :
( sP0(X0)
| ~ sP11(X0) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_100,plain,
! [X0: $i] :
( p102(X0)
| r1(X0,sK18(X0))
| ~ p101(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_101,plain,
! [X0: $i] :
( p102(X0)
| ~ p101(X0)
| ~ sP1(X0)
| ~ p3(sK18(X0)) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_116,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( p3(X4)
| ~ r1(sK22,X0)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_117,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sP11(X4)
| ~ r1(sK22,X0)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_118,negated_conjecture,
~ p101(sK22),
inference(cnf_transformation,[],[f120]) ).
tcf(c_119,negated_conjecture,
p100(sK22),
inference(cnf_transformation,[],[f119]) ).
tcf(c_120,plain,
r1(sK22,sK22),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_127,plain,
( sP0(sK22)
| ~ sP11(sK22) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_166,plain,
( sP11(sK22)
| ~ r1(sK22,sK22) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_1444,plain,
! [X0: $i] :
( p102(X0)
| ~ p101(X0)
| ~ sP11(X0)
| ~ p3(sK18(X0)) ),
inference(resolution,[status(thm)],[c_53,c_101]) ).
tcf(c_1457,plain,
! [X0: $i] :
( p102(X0)
| r1(X0,sK18(X0))
| ~ p101(X0)
| ~ sP11(X0) ),
inference(resolution,[status(thm)],[c_53,c_100]) ).
tcf(c_5116,definition,
iPr_def_10 = sK21(sK22),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_5127,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sP11(X4)
| ~ r1(sK22,X0)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_5128,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( p3(X4)
| ~ r1(sK22,X0)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_6996,plain,
( p102(iPr_def_10)
| ~ p101(iPr_def_10)
| ~ sP11(iPr_def_10)
| ~ p3(sK18(iPr_def_10)) ),
inference(instantiation,[status(thm)],[c_1444]) ).
tcf(c_7141,plain,
( p102(iPr_def_10)
| r1(iPr_def_10,sK18(iPr_def_10))
| ~ p101(iPr_def_10)
| ~ sP11(iPr_def_10) ),
inference(instantiation,[status(thm)],[c_1457]) ).
tcf(c_7839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p3(sK18(iPr_def_10))
| ~ r1(sK22,X1)
| ~ r1(X3,X0)
| ~ r1(X2,X3)
| ~ r1(X1,X2)
| ~ r1(X0,sK18(iPr_def_10)) ),
inference(instantiation,[status(thm)],[c_5128]) ).
tcf(c_8079,plain,
! [X0: $i,X1: $i,X2: $i] :
( p3(sK18(iPr_def_10))
| ~ r1(sK22,X0)
| ~ r1(X2,iPr_def_10)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(iPr_def_10,sK18(iPr_def_10)) ),
inference(instantiation,[status(thm)],[c_7839]) ).
tcf(c_8080,plain,
( p3(sK18(iPr_def_10))
| ~ r1(sK22,iPr_def_10)
| ~ r1(sK22,sK22)
| ~ r1(iPr_def_10,sK18(iPr_def_10)) ),
inference(instantiation,[status(thm)],[c_8079]) ).
fof(f9,definition,
! [X10] :
( ~ sP0(X10)
| ~ p100(X10)
| p101(X10)
| ( ? [X20] :
( p101(X20)
& ~ p102(X20)
& p2(X20)
& r1(X10,X20) )
& ? [X19] :
( p101(X19)
& ~ p102(X19)
& ~ p2(X19)
& r1(X10,X19) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f10,definition,
! [X10] :
( ~ sP1(X10)
| ~ p101(X10)
| p102(X10)
| ( ? [X18] :
( p102(X18)
& ~ p103(X18)
& p3(X18)
& r1(X10,X18) )
& ? [X17] :
( p102(X17)
& ~ p103(X17)
& ~ p3(X17)
& r1(X10,X17) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f11,definition,
! [X10] :
( ~ sP2(X10)
| ~ p102(X10)
| p103(X10)
| ( ? [X16] :
( p103(X16)
& ~ p104(X16)
& p4(X16)
& r1(X10,X16) )
& ? [X15] :
( p103(X15)
& ~ p104(X15)
& ~ p4(X15)
& r1(X10,X15) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f12,definition,
! [X10] :
( ~ sP3(X10)
| ~ p103(X10)
| p104(X10)
| ( ? [X14] :
( p104(X14)
& ~ p105(X14)
& p5(X14)
& r1(X10,X14) )
& ? [X13] :
( p104(X13)
& ~ p105(X13)
& ~ p5(X13)
& r1(X10,X13) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f13,definition,
! [X10] :
( ~ sP4(X10)
| ~ p104(X10)
| p105(X10)
| ( ? [X12] :
( p105(X12)
& p6(X12)
& r1(X10,X12) )
& ? [X11] :
( p105(X11)
& ~ p6(X11)
& r1(X10,X11) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f14,definition,
! [X10] :
( ~ sP5(X10)
| ~ p100(X10)
| ( ( ~ p1(X10)
| ! [X32] :
( ~ p100(X32)
| p1(X32)
| ~ r1(X10,X32) ) )
& ( p1(X10)
| ! [X31] :
( ~ p100(X31)
| ~ p1(X31)
| ~ r1(X10,X31) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f15,definition,
! [X10] :
( ~ sP6(X10)
| ~ p101(X10)
| ( ( ~ p2(X10)
| ! [X30] :
( ~ p101(X30)
| p2(X30)
| ~ r1(X10,X30) ) )
& ( p2(X10)
| ! [X29] :
( ~ p101(X29)
| ~ p2(X29)
| ~ r1(X10,X29) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f16,definition,
! [X10] :
( ~ sP7(X10)
| ~ p102(X10)
| ( ( ~ p3(X10)
| ! [X28] :
( ~ p102(X28)
| p3(X28)
| ~ r1(X10,X28) ) )
& ( p3(X10)
| ! [X27] :
( ~ p102(X27)
| ~ p3(X27)
| ~ r1(X10,X27) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])],[predicate_definition_introduction]) ).
fof(f17,definition,
! [X10] :
( ~ sP8(X10)
| ~ p103(X10)
| ( ( ~ p4(X10)
| ! [X26] :
( ~ p103(X26)
| p4(X26)
| ~ r1(X10,X26) ) )
& ( p4(X10)
| ! [X25] :
( ~ p103(X25)
| ~ p4(X25)
| ~ r1(X10,X25) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f18,definition,
! [X10] :
( ~ sP9(X10)
| ~ p104(X10)
| ( ( ~ p5(X10)
| ! [X24] :
( ~ p104(X24)
| p5(X24)
| ~ r1(X10,X24) ) )
& ( p5(X10)
| ! [X23] :
( ~ p104(X23)
| ~ p5(X23)
| ~ r1(X10,X23) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])],[predicate_definition_introduction]) ).
fof(f19,definition,
! [X10] :
( ~ sP10(X10)
| ~ p105(X10)
| ( ( ~ p6(X10)
| ! [X22] :
( ~ p105(X22)
| p6(X22)
| ~ r1(X10,X22) ) )
& ( p6(X10)
| ! [X21] :
( ~ p105(X21)
| ~ p6(X21)
| ~ r1(X10,X21) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])],[predicate_definition_introduction]) ).
fof(f20,definition,
! [X10] :
( ~ sP11(X10)
| ( ( ~ p101(X10)
| p100(X10) )
& ( ~ p102(X10)
| p101(X10) )
& ( ~ p103(X10)
| p102(X10) )
& ( ~ p104(X10)
| p103(X10) )
& ( ~ p105(X10)
| p104(X10) )
& sP5(X10)
& sP6(X10)
& sP7(X10)
& sP8(X10)
& sP9(X10)
& sP10(X10)
& sP0(X10)
& sP1(X10)
& sP2(X10)
& sP3(X10)
& sP4(X10) ) ),
introduced(definition,[new_symbols(definition,[sP11])],[predicate_definition_introduction]) ).
fof(f21,plain,
? [X0] :
( p100(X0)
& ~ p101(X0)
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( sP11(X10)
| ~ r1(X9,X10) )
| ~ r1(X8,X9) )
| ~ r1(X7,X8) )
| ~ r1(X6,X7) )
| ~ r1(X0,X6) )
& ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( p3(X5)
| ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X2,X3) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) ) ),
inference(definition_folding,[],[f8,f20,f19,f18,f17,f16,f15,f14,f13,f12,f11,f10,f9]) ).
fof(f48,plain,
! [X10] :
( ~ sP0(X10)
| ~ p100(X10)
| p101(X10)
| ( ? [X20] :
( p101(X20)
& ~ p102(X20)
& p2(X20)
& r1(X10,X20) )
& ? [X19] :
( p101(X19)
& ~ p102(X19)
& ~ p2(X19)
& r1(X10,X19) ) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f49,plain,
! [X0] :
( ~ sP0(X0)
| ~ p100(X0)
| p101(X0)
| ( ? [X2] :
( p101(X2)
& ~ p102(X2)
& p2(X2)
& r1(X0,X2) )
& ? [X1] :
( p101(X1)
& ~ p102(X1)
& ~ p2(X1)
& r1(X0,X1) ) ) ),
inference(rectify,[],[f48]) ).
fof(f50,plain,
! [X0] :
( ~ sP0(X0)
| ~ p100(X0)
| p101(X0)
| ( p101(sK21(X0))
& ~ p102(sK21(X0))
& p2(sK21(X0))
& r1(X0,sK21(X0))
& p101(sK20(X0))
& ~ p102(sK20(X0))
& ~ p2(sK20(X0))
& r1(X0,sK20(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21]),skolemize(X1,sK20(X0)),skolemize(X2,sK21(X0))],[f49]) ).
fof(f111,plain,
! [X0] :
( ~ sP0(X0)
| ~ p100(X0)
| p101(X0)
| p101(sK21(X0)) ),
inference(cnf_transformation,[],[f50]) ).
fof(f112,plain,
! [X0] :
( ~ sP0(X0)
| ~ p100(X0)
| p101(X0)
| ~ p102(sK21(X0)) ),
inference(cnf_transformation,[],[f50]) ).
fof(f114,plain,
! [X0] :
( ~ sP0(X0)
| ~ p100(X0)
| p101(X0)
| r1(X0,sK21(X0)) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_112,plain,
! [X0: $i] :
( p101(X0)
| r1(X0,sK21(X0))
| ~ p100(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_114,plain,
! [X0: $i] :
( p101(X0)
| ~ p100(X0)
| ~ sP0(X0)
| ~ p102(sK21(X0)) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_115,plain,
! [X0: $i] :
( p101(X0)
| p101(sK21(X0))
| ~ p100(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_136,plain,
( p101(sK22)
| p101(sK21(sK22))
| ~ p100(sK22)
| ~ sP0(sK22) ),
inference(instantiation,[status(thm)],[c_115]) ).
tcf(c_148,plain,
( p101(sK22)
| ~ p100(sK22)
| ~ sP0(sK22)
| ~ p102(sK21(sK22)) ),
inference(instantiation,[status(thm)],[c_114]) ).
tcf(c_149,plain,
( p101(sK22)
| r1(sK22,sK21(sK22))
| ~ p100(sK22)
| ~ sP0(sK22) ),
inference(instantiation,[status(thm)],[c_112]) ).
tcf(c_1502,plain,
! [X0: $i] :
( p101(X0)
| p101(sK21(X0))
| ~ p100(X0)
| ~ sP11(X0) ),
inference(resolution,[status(thm)],[c_54,c_115]) ).
tcf(c_1516,plain,
! [X0: $i] :
( p101(X0)
| ~ p100(X0)
| ~ sP11(X0)
| ~ p102(sK21(X0)) ),
inference(resolution,[status(thm)],[c_54,c_114]) ).
tcf(c_1544,plain,
! [X0: $i] :
( p101(X0)
| r1(X0,sK21(X0))
| ~ p100(X0)
| ~ sP11(X0) ),
inference(resolution,[status(thm)],[c_54,c_112]) ).
tcf(c_1678,plain,
( p101(sK22)
| r1(sK22,sK21(sK22))
| ~ sP11(sK22) ),
inference(resolution,[status(thm)],[c_1544,c_119]) ).
tcf(c_1679,plain,
r1(sK22,sK21(sK22)),
inference(global_subsumption_just,[status(thm)],[c_1678,c_119,c_118,c_120,c_127,c_149,c_166]) ).
tcf(c_1690,plain,
( p101(sK22)
| ~ sP11(sK22)
| ~ p102(sK21(sK22)) ),
inference(resolution,[status(thm)],[c_1516,c_119]) ).
tcf(c_1691,plain,
~ p102(sK21(sK22)),
inference(global_subsumption_just,[status(thm)],[c_1690,c_119,c_118,c_120,c_127,c_148,c_166]) ).
tcf(c_1696,plain,
( p101(sK22)
| p101(sK21(sK22))
| ~ sP11(sK22) ),
inference(resolution,[status(thm)],[c_1502,c_119]) ).
tcf(c_1697,plain,
p101(sK21(sK22)),
inference(global_subsumption_just,[status(thm)],[c_1696,c_119,c_118,c_120,c_127,c_136,c_166]) ).
tcf(c_5118,plain,
p101(iPr_def_10),
inference(demodulation,[status(thm)],[c_1697,c_5116]) ).
tcf(c_5119,plain,
~ p102(iPr_def_10),
inference(demodulation,[status(thm)],[c_1691]) ).
tcf(c_5121,plain,
r1(sK22,iPr_def_10),
inference(demodulation,[status(thm)],[c_1679]) ).
tcf(c_6202,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP11(X2)
| ~ r1(sK22,sK22)
| ~ r1(iPr_def_10,X0)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(superposition,[status(thm)],[c_5121,c_5127]) ).
tcf(c_6279,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP11(X2)
| ~ r1(X0,X1)
| ~ r1(X1,X2)
| ~ r1(iPr_def_10,X0) ),
inference(global_subsumption_just,[status(thm)],[c_6202,c_120,c_6202]) ).
tcf(c_6280,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP11(X2)
| ~ r1(iPr_def_10,X0)
| ~ r1(X1,X2)
| ~ r1(X0,X1) ),
inference(renaming,[status(thm)],[c_6279]) ).
tcf(c_6289,plain,
! [X0: $i,X1: $i] :
( sP11(X1)
| ~ r1(iPr_def_10,X0)
| ~ r1(X0,X1) ),
inference(superposition,[status(thm)],[c_49,c_6280]) ).
tcf(c_6427,plain,
! [X0: $i] :
( sP11(X0)
| ~ r1(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_49,c_6289]) ).
tcf(c_6446,plain,
sP11(iPr_def_10),
inference(superposition,[status(thm)],[c_49,c_6427]) ).
tcf(c_8081,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_8080,c_7141,c_6996,c_6446,c_5121,c_5119,c_5118,c_120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL656+1.005 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.42 % Computer : n006.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Thu Sep 24 00:01:56 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.49 Running first-order theorem proving
% 0.17/0.49 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
% 0.17/0.50
% 0.17/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.17/0.50
% 0.17/0.50 % Detected problem language: tptp
% 0.24/0.52 % Proving...
% 4.04/1.31 % SZS status Started for theBenchmark.p
% 4.04/1.31 % SZS status Theorem for theBenchmark.p
% 4.04/1.31
% 4.04/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.04/1.31
% 4.04/1.31 % ------ iProver source info
% 4.04/1.31
% 4.04/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 4.04/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.04/1.31 % git: non_committed_changes: false
% 4.04/1.31
% 4.04/1.31 % ------ Parsing...
% 4.04/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.04/1.31
% 4.04/1.31 % ------ Preprocessing... sf_s rm: 3 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.04/1.31
% 4.04/1.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.04/1.31
% 4.04/1.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.04/1.31 % ------ Proving...
% 4.04/1.31 % ------ Problem Properties
% 4.04/1.31
% 4.04/1.31 %
% 4.04/1.31 % clauses 58
% 4.04/1.31 % conjectures 3
% 4.04/1.31 % EPR 26
% 4.04/1.31 % Horn 38
% 4.04/1.31 % unary 12
% 4.04/1.31 % binary 0
% 4.04/1.31 % lits 216
% 4.04/1.31 % lits eq 2
% 4.04/1.31 % fd_pure 0
% 4.04/1.31 % fd_pseudo 0
% 4.04/1.31 % fd_cond 0
% 4.04/1.31 % fd_pseudo_cond 0
% 4.04/1.31 % AC symbols 0
% 4.04/1.31
% 4.04/1.31 % ------ Schedule dynamic 5 is on
% 4.04/1.31
% 4.04/1.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.04/1.31
% 4.04/1.31
% 4.04/1.31 % ------
% 4.04/1.31 % Current options:
% 4.04/1.31 % ------
% 4.04/1.31
% 4.04/1.31
% 4.04/1.31 %
% 4.04/1.31
% 4.04/1.31 % ------ Proving...
% 4.04/1.31 %
% 4.04/1.31
% 4.04/1.31 % SZS status Theorem for theBenchmark.p
% 4.04/1.31
% 4.04/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.04/1.31
% 4.04/1.31
%------------------------------------------------------------------------------