%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : LCL686+1.005 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 07:52:00 EDT 2023
% Result : Theorem 1.06s 1.15s
% Output : CNFRefutation 1.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 48 ( 5 unt; 0 def)
% Number of atoms : 1417 ( 0 equ)
% Maximal formula atoms : 140 ( 29 avg)
% Number of connectives : 2297 ( 928 ~; 767 |; 596 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 57 ( 15 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 24 ( 23 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 303 ( 0 sgn; 222 !; 68 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : r1(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
fof(f3,conjecture,
~ ? [X0] :
~ ( ! [X1] :
( ~ ! [X0] :
( ~ ( ! [X1] :
( ( p1(X1)
& p2(X1) )
| ( ~ p2(X1)
& ~ p1(X1) )
| ( p2(X1)
& p3(X1) )
| ( ~ p3(X1)
& ~ p2(X1) )
| ( p3(X1)
& p4(X1) )
| ( ~ p4(X1)
& ~ p3(X1) )
| ( p4(X1)
& p5(X1) )
| ( ~ p5(X1)
& ~ p4(X1) )
| ( p5(X1)
& p6(X1) )
| ( ~ p6(X1)
& ~ p5(X1) )
| ( p6(X1)
& p7(X1) )
| ( ~ p7(X1)
& ~ p6(X1) )
| ( p7(X1)
& p8(X1) )
| ( ~ p8(X1)
& ~ p7(X1) )
| ( p8(X1)
& p9(X1) )
| ( ~ p9(X1)
& ~ p8(X1) )
| ( p9(X1)
& p10(X1) )
| ( ~ p10(X1)
& ~ p9(X1) )
| ( p10(X1)
& p11(X1) )
| ( ~ p11(X1)
& ~ p10(X1) )
| ( p11(X1)
& p12(X1) )
| ( ~ p12(X1)
& ~ p11(X1) )
| ( p12(X1)
& p13(X1) )
| ( ~ p13(X1)
& ~ p12(X1) )
| ( p13(X1)
& p14(X1) )
| ( ~ p14(X1)
& ~ p13(X1) )
| ~ r1(X0,X1) )
| ! [X1] :
( p15(X1)
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ( ( p1(X1)
& ~ p2(X1) )
| ( ~ p1(X1)
& p2(X1) ) )
| ~ r1(X0,X1) )
| ! [X1] :
( ~ ! [X0] :
( ~ ( ( p2(X0)
& ~ p3(X0) )
| ( ~ p2(X0)
& p3(X0) ) )
| ~ r1(X1,X0) )
| ! [X0] :
( ~ ! [X1] :
( ~ ( ( p3(X1)
& ~ p4(X1) )
| ( ~ p3(X1)
& p4(X1) ) )
| ~ r1(X0,X1) )
| ! [X1] :
( ~ ! [X0] :
( ~ ( ( p4(X0)
& ~ p5(X0) )
| ( ~ p4(X0)
& p5(X0) ) )
| ~ r1(X1,X0) )
| ! [X0] :
( ~ ! [X1] :
( ~ ( ( p5(X1)
& ~ p6(X1) )
| ( ~ p5(X1)
& p6(X1) ) )
| ~ r1(X0,X1) )
| ! [X1] :
( ~ ! [X0] :
( ~ ( ( p6(X0)
& ~ p7(X0) )
| ( ~ p6(X0)
& p7(X0) ) )
| ~ r1(X1,X0) )
| ! [X0] :
( ~ ! [X1] :
( ~ ( ( p7(X1)
& ~ p8(X1) )
| ( ~ p7(X1)
& p8(X1) ) )
| ~ r1(X0,X1) )
| ! [X1] :
( ~ ! [X0] :
( ~ ( ( p8(X0)
& ~ p9(X0) )
| ( ~ p8(X0)
& p9(X0) ) )
| ~ r1(X1,X0) )
| ! [X0] :
( ~ ! [X1] :
( ~ ( ( p9(X1)
& ~ p10(X1) )
| ( ~ p9(X1)
& p10(X1) ) )
| ~ r1(X0,X1) )
| ! [X1] :
( ~ ! [X0] :
( ~ ( ( p10(X0)
& ~ p11(X0) )
| ( ~ p10(X0)
& p11(X0) ) )
| ~ r1(X1,X0) )
| ! [X0] :
( ~ ! [X1] :
( ~ ( ( p11(X1)
& ~ p12(X1) )
| ( ~ p11(X1)
& p12(X1) ) )
| ~ r1(X0,X1) )
| ! [X1] :
( ~ ! [X0] :
( ~ ( ( p12(X0)
& ~ p13(X0) )
| ( ~ p12(X0)
& p13(X0) ) )
| ~ r1(X1,X0) )
| ! [X0] :
( ~ ! [X1] :
( ~ ( ( p13(X1)
& ~ p14(X1) )
| ( ~ p13(X1)
& p14(X1) ) )
| ~ r1(X0,X1) )
| ! [X1] :
( $false
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ 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] :
( ! [X0] :
( ~ p1(X0)
| ~ r1(X1,X0) )
| ~ p15(X1)
| ~ r1(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
fof(f4,negated_conjecture,
~ ~ ? [X0] :
~ ( ! [X1] :
( ~ ! [X0] :
( ~ ( ! [X1] :
( ( p1(X1)
& p2(X1) )
| ( ~ p2(X1)
& ~ p1(X1) )
| ( p2(X1)
& p3(X1) )
| ( ~ p3(X1)
& ~ p2(X1) )
| ( p3(X1)
& p4(X1) )
| ( ~ p4(X1)
& ~ p3(X1) )
| ( p4(X1)
& p5(X1) )
| ( ~ p5(X1)
& ~ p4(X1) )
| ( p5(X1)
& p6(X1) )
| ( ~ p6(X1)
& ~ p5(X1) )
| ( p6(X1)
& p7(X1) )
| ( ~ p7(X1)
& ~ p6(X1) )
| ( p7(X1)
& p8(X1) )
| ( ~ p8(X1)
& ~ p7(X1) )
| ( p8(X1)
& p9(X1) )
| ( ~ p9(X1)
& ~ p8(X1) )
| ( p9(X1)
& p10(X1) )
| ( ~ p10(X1)
& ~ p9(X1) )
| ( p10(X1)
& p11(X1) )
| ( ~ p11(X1)
& ~ p10(X1) )
| ( p11(X1)
& p12(X1) )
| ( ~ p12(X1)
& ~ p11(X1) )
| ( p12(X1)
& p13(X1) )
| ( ~ p13(X1)
& ~ p12(X1) )
| ( p13(X1)
& p14(X1) )
| ( ~ p14(X1)
& ~ p13(X1) )
| ~ r1(X0,X1) )
| ! [X1] :
( p15(X1)
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ( ( p1(X1)
& ~ p2(X1) )
| ( ~ p1(X1)
& p2(X1) ) )
| ~ r1(X0,X1) )
| ! [X1] :
( ~ ! [X0] :
( ~ ( ( p2(X0)
& ~ p3(X0) )
| ( ~ p2(X0)
& p3(X0) ) )
| ~ r1(X1,X0) )
| ! [X0] :
( ~ ! [X1] :
( ~ ( ( p3(X1)
& ~ p4(X1) )
| ( ~ p3(X1)
& p4(X1) ) )
| ~ r1(X0,X1) )
| ! [X1] :
( ~ ! [X0] :
( ~ ( ( p4(X0)
& ~ p5(X0) )
| ( ~ p4(X0)
& p5(X0) ) )
| ~ r1(X1,X0) )
| ! [X0] :
( ~ ! [X1] :
( ~ ( ( p5(X1)
& ~ p6(X1) )
| ( ~ p5(X1)
& p6(X1) ) )
| ~ r1(X0,X1) )
| ! [X1] :
( ~ ! [X0] :
( ~ ( ( p6(X0)
& ~ p7(X0) )
| ( ~ p6(X0)
& p7(X0) ) )
| ~ r1(X1,X0) )
| ! [X0] :
( ~ ! [X1] :
( ~ ( ( p7(X1)
& ~ p8(X1) )
| ( ~ p7(X1)
& p8(X1) ) )
| ~ r1(X0,X1) )
| ! [X1] :
( ~ ! [X0] :
( ~ ( ( p8(X0)
& ~ p9(X0) )
| ( ~ p8(X0)
& p9(X0) ) )
| ~ r1(X1,X0) )
| ! [X0] :
( ~ ! [X1] :
( ~ ( ( p9(X1)
& ~ p10(X1) )
| ( ~ p9(X1)
& p10(X1) ) )
| ~ r1(X0,X1) )
| ! [X1] :
( ~ ! [X0] :
( ~ ( ( p10(X0)
& ~ p11(X0) )
| ( ~ p10(X0)
& p11(X0) ) )
| ~ r1(X1,X0) )
| ! [X0] :
( ~ ! [X1] :
( ~ ( ( p11(X1)
& ~ p12(X1) )
| ( ~ p11(X1)
& p12(X1) ) )
| ~ r1(X0,X1) )
| ! [X1] :
( ~ ! [X0] :
( ~ ( ( p12(X0)
& ~ p13(X0) )
| ( ~ p12(X0)
& p13(X0) ) )
| ~ r1(X1,X0) )
| ! [X0] :
( ~ ! [X1] :
( ~ ( ( p13(X1)
& ~ p14(X1) )
| ( ~ p13(X1)
& p14(X1) ) )
| ~ r1(X0,X1) )
| ! [X1] :
( $false
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ 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] :
( ! [X0] :
( ~ p1(X0)
| ~ r1(X1,X0) )
| ~ p15(X1)
| ~ r1(X0,X1) ) ),
inference(negated_conjecture,[],[f3]) ).
fof(f5,plain,
~ ~ ? [X0] :
~ ( ! [X1] :
( ~ ! [X2] :
( ~ ( ! [X3] :
( ( p1(X3)
& p2(X3) )
| ( ~ p2(X3)
& ~ p1(X3) )
| ( p2(X3)
& p3(X3) )
| ( ~ p3(X3)
& ~ p2(X3) )
| ( p3(X3)
& p4(X3) )
| ( ~ p4(X3)
& ~ p3(X3) )
| ( p4(X3)
& p5(X3) )
| ( ~ p5(X3)
& ~ p4(X3) )
| ( p5(X3)
& p6(X3) )
| ( ~ p6(X3)
& ~ p5(X3) )
| ( p6(X3)
& p7(X3) )
| ( ~ p7(X3)
& ~ p6(X3) )
| ( p7(X3)
& p8(X3) )
| ( ~ p8(X3)
& ~ p7(X3) )
| ( p8(X3)
& p9(X3) )
| ( ~ p9(X3)
& ~ p8(X3) )
| ( p9(X3)
& p10(X3) )
| ( ~ p10(X3)
& ~ p9(X3) )
| ( p10(X3)
& p11(X3) )
| ( ~ p11(X3)
& ~ p10(X3) )
| ( p11(X3)
& p12(X3) )
| ( ~ p12(X3)
& ~ p11(X3) )
| ( p12(X3)
& p13(X3) )
| ( ~ p13(X3)
& ~ p12(X3) )
| ( p13(X3)
& p14(X3) )
| ( ~ p14(X3)
& ~ p13(X3) )
| ~ r1(X2,X3) )
| ! [X4] :
( p15(X4)
| ~ r1(X2,X4) )
| ~ ! [X5] :
( ~ ( ( p1(X5)
& ~ p2(X5) )
| ( ~ p1(X5)
& p2(X5) ) )
| ~ r1(X2,X5) )
| ! [X6] :
( ~ ! [X7] :
( ~ ( ( p2(X7)
& ~ p3(X7) )
| ( ~ p2(X7)
& p3(X7) ) )
| ~ r1(X6,X7) )
| ! [X8] :
( ~ ! [X9] :
( ~ ( ( p3(X9)
& ~ p4(X9) )
| ( ~ p3(X9)
& p4(X9) ) )
| ~ r1(X8,X9) )
| ! [X10] :
( ~ ! [X11] :
( ~ ( ( p4(X11)
& ~ p5(X11) )
| ( ~ p4(X11)
& p5(X11) ) )
| ~ r1(X10,X11) )
| ! [X12] :
( ~ ! [X13] :
( ~ ( ( p5(X13)
& ~ p6(X13) )
| ( ~ p5(X13)
& p6(X13) ) )
| ~ r1(X12,X13) )
| ! [X14] :
( ~ ! [X15] :
( ~ ( ( p6(X15)
& ~ p7(X15) )
| ( ~ p6(X15)
& p7(X15) ) )
| ~ r1(X14,X15) )
| ! [X16] :
( ~ ! [X17] :
( ~ ( ( p7(X17)
& ~ p8(X17) )
| ( ~ p7(X17)
& p8(X17) ) )
| ~ r1(X16,X17) )
| ! [X18] :
( ~ ! [X19] :
( ~ ( ( p8(X19)
& ~ p9(X19) )
| ( ~ p8(X19)
& p9(X19) ) )
| ~ r1(X18,X19) )
| ! [X20] :
( ~ ! [X21] :
( ~ ( ( p9(X21)
& ~ p10(X21) )
| ( ~ p9(X21)
& p10(X21) ) )
| ~ r1(X20,X21) )
| ! [X22] :
( ~ ! [X23] :
( ~ ( ( p10(X23)
& ~ p11(X23) )
| ( ~ p10(X23)
& p11(X23) ) )
| ~ r1(X22,X23) )
| ! [X24] :
( ~ ! [X25] :
( ~ ( ( p11(X25)
& ~ p12(X25) )
| ( ~ p11(X25)
& p12(X25) ) )
| ~ r1(X24,X25) )
| ! [X26] :
( ~ ! [X27] :
( ~ ( ( p12(X27)
& ~ p13(X27) )
| ( ~ p12(X27)
& p13(X27) ) )
| ~ r1(X26,X27) )
| ! [X28] :
( ~ ! [X29] :
( ~ ( ( p13(X29)
& ~ p14(X29) )
| ( ~ p13(X29)
& p14(X29) ) )
| ~ r1(X28,X29) )
| ! [X30] :
( $false
| ~ r1(X28,X30) )
| ~ r1(X26,X28) )
| ~ r1(X24,X26) )
| ~ r1(X22,X24) )
| ~ r1(X20,X22) )
| ~ r1(X18,X20) )
| ~ r1(X16,X18) )
| ~ r1(X14,X16) )
| ~ r1(X12,X14) )
| ~ r1(X10,X12) )
| ~ r1(X8,X10) )
| ~ r1(X6,X8) )
| ~ r1(X2,X6) ) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) )
| ! [X31] :
( ! [X32] :
( ~ p1(X32)
| ~ r1(X31,X32) )
| ~ p15(X31)
| ~ r1(X0,X31) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
~ ~ ? [X0] :
~ ( ! [X1] :
( ~ ! [X2] :
( ~ ( ! [X3] :
( ( p1(X3)
& p2(X3) )
| ( ~ p2(X3)
& ~ p1(X3) )
| ( p2(X3)
& p3(X3) )
| ( ~ p3(X3)
& ~ p2(X3) )
| ( p3(X3)
& p4(X3) )
| ( ~ p4(X3)
& ~ p3(X3) )
| ( p4(X3)
& p5(X3) )
| ( ~ p5(X3)
& ~ p4(X3) )
| ( p5(X3)
& p6(X3) )
| ( ~ p6(X3)
& ~ p5(X3) )
| ( p6(X3)
& p7(X3) )
| ( ~ p7(X3)
& ~ p6(X3) )
| ( p7(X3)
& p8(X3) )
| ( ~ p8(X3)
& ~ p7(X3) )
| ( p8(X3)
& p9(X3) )
| ( ~ p9(X3)
& ~ p8(X3) )
| ( p9(X3)
& p10(X3) )
| ( ~ p10(X3)
& ~ p9(X3) )
| ( p10(X3)
& p11(X3) )
| ( ~ p11(X3)
& ~ p10(X3) )
| ( p11(X3)
& p12(X3) )
| ( ~ p12(X3)
& ~ p11(X3) )
| ( p12(X3)
& p13(X3) )
| ( ~ p13(X3)
& ~ p12(X3) )
| ( p13(X3)
& p14(X3) )
| ( ~ p14(X3)
& ~ p13(X3) )
| ~ r1(X2,X3) )
| ! [X4] :
( p15(X4)
| ~ r1(X2,X4) )
| ~ ! [X5] :
( ~ ( ( p1(X5)
& ~ p2(X5) )
| ( ~ p1(X5)
& p2(X5) ) )
| ~ r1(X2,X5) )
| ! [X6] :
( ~ ! [X7] :
( ~ ( ( p2(X7)
& ~ p3(X7) )
| ( ~ p2(X7)
& p3(X7) ) )
| ~ r1(X6,X7) )
| ! [X8] :
( ~ ! [X9] :
( ~ ( ( p3(X9)
& ~ p4(X9) )
| ( ~ p3(X9)
& p4(X9) ) )
| ~ r1(X8,X9) )
| ! [X10] :
( ~ ! [X11] :
( ~ ( ( p4(X11)
& ~ p5(X11) )
| ( ~ p4(X11)
& p5(X11) ) )
| ~ r1(X10,X11) )
| ! [X12] :
( ~ ! [X13] :
( ~ ( ( p5(X13)
& ~ p6(X13) )
| ( ~ p5(X13)
& p6(X13) ) )
| ~ r1(X12,X13) )
| ! [X14] :
( ~ ! [X15] :
( ~ ( ( p6(X15)
& ~ p7(X15) )
| ( ~ p6(X15)
& p7(X15) ) )
| ~ r1(X14,X15) )
| ! [X16] :
( ~ ! [X17] :
( ~ ( ( p7(X17)
& ~ p8(X17) )
| ( ~ p7(X17)
& p8(X17) ) )
| ~ r1(X16,X17) )
| ! [X18] :
( ~ ! [X19] :
( ~ ( ( p8(X19)
& ~ p9(X19) )
| ( ~ p8(X19)
& p9(X19) ) )
| ~ r1(X18,X19) )
| ! [X20] :
( ~ ! [X21] :
( ~ ( ( p9(X21)
& ~ p10(X21) )
| ( ~ p9(X21)
& p10(X21) ) )
| ~ r1(X20,X21) )
| ! [X22] :
( ~ ! [X23] :
( ~ ( ( p10(X23)
& ~ p11(X23) )
| ( ~ p10(X23)
& p11(X23) ) )
| ~ r1(X22,X23) )
| ! [X24] :
( ~ ! [X25] :
( ~ ( ( p11(X25)
& ~ p12(X25) )
| ( ~ p11(X25)
& p12(X25) ) )
| ~ r1(X24,X25) )
| ! [X26] :
( ~ ! [X27] :
( ~ ( ( p12(X27)
& ~ p13(X27) )
| ( ~ p12(X27)
& p13(X27) ) )
| ~ r1(X26,X27) )
| ! [X28] :
( ~ ! [X29] :
( ~ ( ( p13(X29)
& ~ p14(X29) )
| ( ~ p13(X29)
& p14(X29) ) )
| ~ r1(X28,X29) )
| ! [X30] : ~ r1(X28,X30)
| ~ r1(X26,X28) )
| ~ r1(X24,X26) )
| ~ r1(X22,X24) )
| ~ r1(X20,X22) )
| ~ r1(X18,X20) )
| ~ r1(X16,X18) )
| ~ r1(X14,X16) )
| ~ r1(X12,X14) )
| ~ r1(X10,X12) )
| ~ r1(X8,X10) )
| ~ r1(X6,X8) )
| ~ r1(X2,X6) ) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) )
| ! [X31] :
( ! [X32] :
( ~ p1(X32)
| ~ r1(X31,X32) )
| ~ p15(X31)
| ~ r1(X0,X31) ) ),
inference(true_and_false_elimination,[],[f5]) ).
fof(f7,plain,
? [X0] :
~ ( ! [X1] :
( ~ ! [X2] :
( ~ ( ! [X3] :
( ( p1(X3)
& p2(X3) )
| ( ~ p2(X3)
& ~ p1(X3) )
| ( p2(X3)
& p3(X3) )
| ( ~ p3(X3)
& ~ p2(X3) )
| ( p3(X3)
& p4(X3) )
| ( ~ p4(X3)
& ~ p3(X3) )
| ( p4(X3)
& p5(X3) )
| ( ~ p5(X3)
& ~ p4(X3) )
| ( p5(X3)
& p6(X3) )
| ( ~ p6(X3)
& ~ p5(X3) )
| ( p6(X3)
& p7(X3) )
| ( ~ p7(X3)
& ~ p6(X3) )
| ( p7(X3)
& p8(X3) )
| ( ~ p8(X3)
& ~ p7(X3) )
| ( p8(X3)
& p9(X3) )
| ( ~ p9(X3)
& ~ p8(X3) )
| ( p9(X3)
& p10(X3) )
| ( ~ p10(X3)
& ~ p9(X3) )
| ( p10(X3)
& p11(X3) )
| ( ~ p11(X3)
& ~ p10(X3) )
| ( p11(X3)
& p12(X3) )
| ( ~ p12(X3)
& ~ p11(X3) )
| ( p12(X3)
& p13(X3) )
| ( ~ p13(X3)
& ~ p12(X3) )
| ( p13(X3)
& p14(X3) )
| ( ~ p14(X3)
& ~ p13(X3) )
| ~ r1(X2,X3) )
| ! [X4] :
( p15(X4)
| ~ r1(X2,X4) )
| ~ ! [X5] :
( ~ ( ( p1(X5)
& ~ p2(X5) )
| ( ~ p1(X5)
& p2(X5) ) )
| ~ r1(X2,X5) )
| ! [X6] :
( ~ ! [X7] :
( ~ ( ( p2(X7)
& ~ p3(X7) )
| ( ~ p2(X7)
& p3(X7) ) )
| ~ r1(X6,X7) )
| ! [X8] :
( ~ ! [X9] :
( ~ ( ( p3(X9)
& ~ p4(X9) )
| ( ~ p3(X9)
& p4(X9) ) )
| ~ r1(X8,X9) )
| ! [X10] :
( ~ ! [X11] :
( ~ ( ( p4(X11)
& ~ p5(X11) )
| ( ~ p4(X11)
& p5(X11) ) )
| ~ r1(X10,X11) )
| ! [X12] :
( ~ ! [X13] :
( ~ ( ( p5(X13)
& ~ p6(X13) )
| ( ~ p5(X13)
& p6(X13) ) )
| ~ r1(X12,X13) )
| ! [X14] :
( ~ ! [X15] :
( ~ ( ( p6(X15)
& ~ p7(X15) )
| ( ~ p6(X15)
& p7(X15) ) )
| ~ r1(X14,X15) )
| ! [X16] :
( ~ ! [X17] :
( ~ ( ( p7(X17)
& ~ p8(X17) )
| ( ~ p7(X17)
& p8(X17) ) )
| ~ r1(X16,X17) )
| ! [X18] :
( ~ ! [X19] :
( ~ ( ( p8(X19)
& ~ p9(X19) )
| ( ~ p8(X19)
& p9(X19) ) )
| ~ r1(X18,X19) )
| ! [X20] :
( ~ ! [X21] :
( ~ ( ( p9(X21)
& ~ p10(X21) )
| ( ~ p9(X21)
& p10(X21) ) )
| ~ r1(X20,X21) )
| ! [X22] :
( ~ ! [X23] :
( ~ ( ( p10(X23)
& ~ p11(X23) )
| ( ~ p10(X23)
& p11(X23) ) )
| ~ r1(X22,X23) )
| ! [X24] :
( ~ ! [X25] :
( ~ ( ( p11(X25)
& ~ p12(X25) )
| ( ~ p11(X25)
& p12(X25) ) )
| ~ r1(X24,X25) )
| ! [X26] :
( ~ ! [X27] :
( ~ ( ( p12(X27)
& ~ p13(X27) )
| ( ~ p12(X27)
& p13(X27) ) )
| ~ r1(X26,X27) )
| ! [X28] :
( ~ ! [X29] :
( ~ ( ( p13(X29)
& ~ p14(X29) )
| ( ~ p13(X29)
& p14(X29) ) )
| ~ r1(X28,X29) )
| ! [X30] : ~ r1(X28,X30)
| ~ r1(X26,X28) )
| ~ r1(X24,X26) )
| ~ r1(X22,X24) )
| ~ r1(X20,X22) )
| ~ r1(X18,X20) )
| ~ r1(X16,X18) )
| ~ r1(X14,X16) )
| ~ r1(X12,X14) )
| ~ r1(X10,X12) )
| ~ r1(X8,X10) )
| ~ r1(X6,X8) )
| ~ r1(X2,X6) ) )
| ~ r1(X1,X2) )
| ~ r1(X0,X1) )
| ! [X31] :
( ! [X32] :
( ~ p1(X32)
| ~ r1(X31,X32) )
| ~ p15(X31)
| ~ r1(X0,X31) ) ),
inference(flattening,[],[f6]) ).
fof(f10,plain,
? [X0] :
( ? [X1] :
( ! [X2] :
( ( ? [X3] :
( ( ~ p1(X3)
| ~ p2(X3) )
& ( p2(X3)
| p1(X3) )
& ( ~ p2(X3)
| ~ p3(X3) )
& ( p3(X3)
| p2(X3) )
& ( ~ p3(X3)
| ~ p4(X3) )
& ( p4(X3)
| p3(X3) )
& ( ~ p4(X3)
| ~ p5(X3) )
& ( p5(X3)
| p4(X3) )
& ( ~ p5(X3)
| ~ p6(X3) )
& ( p6(X3)
| p5(X3) )
& ( ~ p6(X3)
| ~ p7(X3) )
& ( p7(X3)
| p6(X3) )
& ( ~ p7(X3)
| ~ p8(X3) )
& ( p8(X3)
| p7(X3) )
& ( ~ p8(X3)
| ~ p9(X3) )
& ( p9(X3)
| p8(X3) )
& ( ~ p9(X3)
| ~ p10(X3) )
& ( p10(X3)
| p9(X3) )
& ( ~ p10(X3)
| ~ p11(X3) )
& ( p11(X3)
| p10(X3) )
& ( ~ p11(X3)
| ~ p12(X3) )
& ( p12(X3)
| p11(X3) )
& ( ~ p12(X3)
| ~ p13(X3) )
& ( p13(X3)
| p12(X3) )
& ( ~ p13(X3)
| ~ p14(X3) )
& ( p14(X3)
| p13(X3) )
& r1(X2,X3) )
& ? [X4] :
( ~ p15(X4)
& r1(X2,X4) )
& ! [X5] :
( ( ( ~ p1(X5)
| p2(X5) )
& ( p1(X5)
| ~ p2(X5) ) )
| ~ r1(X2,X5) )
& ? [X6] :
( ! [X7] :
( ( ( ~ p2(X7)
| p3(X7) )
& ( p2(X7)
| ~ p3(X7) ) )
| ~ r1(X6,X7) )
& ? [X8] :
( ! [X9] :
( ( ( ~ p3(X9)
| p4(X9) )
& ( p3(X9)
| ~ p4(X9) ) )
| ~ r1(X8,X9) )
& ? [X10] :
( ! [X11] :
( ( ( ~ p4(X11)
| p5(X11) )
& ( p4(X11)
| ~ p5(X11) ) )
| ~ r1(X10,X11) )
& ? [X12] :
( ! [X13] :
( ( ( ~ p5(X13)
| p6(X13) )
& ( p5(X13)
| ~ p6(X13) ) )
| ~ r1(X12,X13) )
& ? [X14] :
( ! [X15] :
( ( ( ~ p6(X15)
| p7(X15) )
& ( p6(X15)
| ~ p7(X15) ) )
| ~ r1(X14,X15) )
& ? [X16] :
( ! [X17] :
( ( ( ~ p7(X17)
| p8(X17) )
& ( p7(X17)
| ~ p8(X17) ) )
| ~ r1(X16,X17) )
& ? [X18] :
( ! [X19] :
( ( ( ~ p8(X19)
| p9(X19) )
& ( p8(X19)
| ~ p9(X19) ) )
| ~ r1(X18,X19) )
& ? [X20] :
( ! [X21] :
( ( ( ~ p9(X21)
| p10(X21) )
& ( p9(X21)
| ~ p10(X21) ) )
| ~ r1(X20,X21) )
& ? [X22] :
( ! [X23] :
( ( ( ~ p10(X23)
| p11(X23) )
& ( p10(X23)
| ~ p11(X23) ) )
| ~ r1(X22,X23) )
& ? [X24] :
( ! [X25] :
( ( ( ~ p11(X25)
| p12(X25) )
& ( p11(X25)
| ~ p12(X25) ) )
| ~ r1(X24,X25) )
& ? [X26] :
( ! [X27] :
( ( ( ~ p12(X27)
| p13(X27) )
& ( p12(X27)
| ~ p13(X27) ) )
| ~ r1(X26,X27) )
& ? [X28] :
( ! [X29] :
( ( ( ~ p13(X29)
| p14(X29) )
& ( p13(X29)
| ~ p14(X29) ) )
| ~ r1(X28,X29) )
& ? [X30] : r1(X28,X30)
& r1(X26,X28) )
& r1(X24,X26) )
& r1(X22,X24) )
& r1(X20,X22) )
& r1(X18,X20) )
& r1(X16,X18) )
& r1(X14,X16) )
& r1(X12,X14) )
& r1(X10,X12) )
& r1(X8,X10) )
& r1(X6,X8) )
& r1(X2,X6) ) )
| ~ r1(X1,X2) )
& r1(X0,X1) )
& ? [X31] :
( ? [X32] :
( p1(X32)
& r1(X31,X32) )
& p15(X31)
& r1(X0,X31) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f11,plain,
! [X24] :
( ? [X26] :
( ! [X27] :
( ( ( ~ p12(X27)
| p13(X27) )
& ( p12(X27)
| ~ p13(X27) ) )
| ~ r1(X26,X27) )
& ? [X28] :
( ! [X29] :
( ( ( ~ p13(X29)
| p14(X29) )
& ( p13(X29)
| ~ p14(X29) ) )
| ~ r1(X28,X29) )
& ? [X30] : r1(X28,X30)
& r1(X26,X28) )
& r1(X24,X26) )
| ~ sP0(X24) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f12,plain,
! [X20] :
( ? [X22] :
( ! [X23] :
( ( ( ~ p10(X23)
| p11(X23) )
& ( p10(X23)
| ~ p11(X23) ) )
| ~ r1(X22,X23) )
& ? [X24] :
( ! [X25] :
( ( ( ~ p11(X25)
| p12(X25) )
& ( p11(X25)
| ~ p12(X25) ) )
| ~ r1(X24,X25) )
& sP0(X24)
& r1(X22,X24) )
& r1(X20,X22) )
| ~ sP1(X20) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f13,plain,
! [X16] :
( ? [X18] :
( ! [X19] :
( ( ( ~ p8(X19)
| p9(X19) )
& ( p8(X19)
| ~ p9(X19) ) )
| ~ r1(X18,X19) )
& ? [X20] :
( ! [X21] :
( ( ( ~ p9(X21)
| p10(X21) )
& ( p9(X21)
| ~ p10(X21) ) )
| ~ r1(X20,X21) )
& sP1(X20)
& r1(X18,X20) )
& r1(X16,X18) )
| ~ sP2(X16) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f14,plain,
! [X12] :
( ? [X14] :
( ! [X15] :
( ( ( ~ p6(X15)
| p7(X15) )
& ( p6(X15)
| ~ p7(X15) ) )
| ~ r1(X14,X15) )
& ? [X16] :
( ! [X17] :
( ( ( ~ p7(X17)
| p8(X17) )
& ( p7(X17)
| ~ p8(X17) ) )
| ~ r1(X16,X17) )
& sP2(X16)
& r1(X14,X16) )
& r1(X12,X14) )
| ~ sP3(X12) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f15,plain,
! [X8] :
( ? [X10] :
( ! [X11] :
( ( ( ~ p4(X11)
| p5(X11) )
& ( p4(X11)
| ~ p5(X11) ) )
| ~ r1(X10,X11) )
& ? [X12] :
( ! [X13] :
( ( ( ~ p5(X13)
| p6(X13) )
& ( p5(X13)
| ~ p6(X13) ) )
| ~ r1(X12,X13) )
& sP3(X12)
& r1(X10,X12) )
& r1(X8,X10) )
| ~ sP4(X8) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f16,plain,
! [X2] :
( ? [X3] :
( ( ~ p1(X3)
| ~ p2(X3) )
& ( p2(X3)
| p1(X3) )
& ( ~ p2(X3)
| ~ p3(X3) )
& ( p3(X3)
| p2(X3) )
& ( ~ p3(X3)
| ~ p4(X3) )
& ( p4(X3)
| p3(X3) )
& ( ~ p4(X3)
| ~ p5(X3) )
& ( p5(X3)
| p4(X3) )
& ( ~ p5(X3)
| ~ p6(X3) )
& ( p6(X3)
| p5(X3) )
& ( ~ p6(X3)
| ~ p7(X3) )
& ( p7(X3)
| p6(X3) )
& ( ~ p7(X3)
| ~ p8(X3) )
& ( p8(X3)
| p7(X3) )
& ( ~ p8(X3)
| ~ p9(X3) )
& ( p9(X3)
| p8(X3) )
& ( ~ p9(X3)
| ~ p10(X3) )
& ( p10(X3)
| p9(X3) )
& ( ~ p10(X3)
| ~ p11(X3) )
& ( p11(X3)
| p10(X3) )
& ( ~ p11(X3)
| ~ p12(X3) )
& ( p12(X3)
| p11(X3) )
& ( ~ p12(X3)
| ~ p13(X3) )
& ( p13(X3)
| p12(X3) )
& ( ~ p13(X3)
| ~ p14(X3) )
& ( p14(X3)
| p13(X3) )
& r1(X2,X3) )
| ~ sP5(X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f17,plain,
! [X2] :
( ? [X6] :
( ! [X7] :
( ( ( ~ p2(X7)
| p3(X7) )
& ( p2(X7)
| ~ p3(X7) ) )
| ~ r1(X6,X7) )
& ? [X8] :
( ! [X9] :
( ( ( ~ p3(X9)
| p4(X9) )
& ( p3(X9)
| ~ p4(X9) ) )
| ~ r1(X8,X9) )
& sP4(X8)
& r1(X6,X8) )
& r1(X2,X6) )
| ~ sP6(X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f18,plain,
? [X0] :
( ? [X1] :
( ! [X2] :
( ( sP5(X2)
& ? [X4] :
( ~ p15(X4)
& r1(X2,X4) )
& ! [X5] :
( ( ( ~ p1(X5)
| p2(X5) )
& ( p1(X5)
| ~ p2(X5) ) )
| ~ r1(X2,X5) )
& sP6(X2) )
| ~ r1(X1,X2) )
& r1(X0,X1) )
& ? [X31] :
( ? [X32] :
( p1(X32)
& r1(X31,X32) )
& p15(X31)
& r1(X0,X31) ) ),
inference(definition_folding,[],[f10,f17,f16,f15,f14,f13,f12,f11]) ).
fof(f24,plain,
! [X2] :
( ? [X3] :
( ( ~ p1(X3)
| ~ p2(X3) )
& ( p2(X3)
| p1(X3) )
& ( ~ p2(X3)
| ~ p3(X3) )
& ( p3(X3)
| p2(X3) )
& ( ~ p3(X3)
| ~ p4(X3) )
& ( p4(X3)
| p3(X3) )
& ( ~ p4(X3)
| ~ p5(X3) )
& ( p5(X3)
| p4(X3) )
& ( ~ p5(X3)
| ~ p6(X3) )
& ( p6(X3)
| p5(X3) )
& ( ~ p6(X3)
| ~ p7(X3) )
& ( p7(X3)
| p6(X3) )
& ( ~ p7(X3)
| ~ p8(X3) )
& ( p8(X3)
| p7(X3) )
& ( ~ p8(X3)
| ~ p9(X3) )
& ( p9(X3)
| p8(X3) )
& ( ~ p9(X3)
| ~ p10(X3) )
& ( p10(X3)
| p9(X3) )
& ( ~ p10(X3)
| ~ p11(X3) )
& ( p11(X3)
| p10(X3) )
& ( ~ p11(X3)
| ~ p12(X3) )
& ( p12(X3)
| p11(X3) )
& ( ~ p12(X3)
| ~ p13(X3) )
& ( p13(X3)
| p12(X3) )
& ( ~ p13(X3)
| ~ p14(X3) )
& ( p14(X3)
| p13(X3) )
& r1(X2,X3) )
| ~ sP5(X2) ),
inference(nnf_transformation,[],[f16]) ).
fof(f25,plain,
! [X0] :
( ? [X1] :
( ( ~ p1(X1)
| ~ p2(X1) )
& ( p2(X1)
| p1(X1) )
& ( ~ p2(X1)
| ~ p3(X1) )
& ( p3(X1)
| p2(X1) )
& ( ~ p3(X1)
| ~ p4(X1) )
& ( p4(X1)
| p3(X1) )
& ( ~ p4(X1)
| ~ p5(X1) )
& ( p5(X1)
| p4(X1) )
& ( ~ p5(X1)
| ~ p6(X1) )
& ( p6(X1)
| p5(X1) )
& ( ~ p6(X1)
| ~ p7(X1) )
& ( p7(X1)
| p6(X1) )
& ( ~ p7(X1)
| ~ p8(X1) )
& ( p8(X1)
| p7(X1) )
& ( ~ p8(X1)
| ~ p9(X1) )
& ( p9(X1)
| p8(X1) )
& ( ~ p9(X1)
| ~ p10(X1) )
& ( p10(X1)
| p9(X1) )
& ( ~ p10(X1)
| ~ p11(X1) )
& ( p11(X1)
| p10(X1) )
& ( ~ p11(X1)
| ~ p12(X1) )
& ( p12(X1)
| p11(X1) )
& ( ~ p12(X1)
| ~ p13(X1) )
& ( p13(X1)
| p12(X1) )
& ( ~ p13(X1)
| ~ p14(X1) )
& ( p14(X1)
| p13(X1) )
& r1(X0,X1) )
| ~ sP5(X0) ),
inference(rectify,[],[f24]) ).
fof(f26,plain,
! [X0] :
( ? [X1] :
( ( ~ p1(X1)
| ~ p2(X1) )
& ( p2(X1)
| p1(X1) )
& ( ~ p2(X1)
| ~ p3(X1) )
& ( p3(X1)
| p2(X1) )
& ( ~ p3(X1)
| ~ p4(X1) )
& ( p4(X1)
| p3(X1) )
& ( ~ p4(X1)
| ~ p5(X1) )
& ( p5(X1)
| p4(X1) )
& ( ~ p5(X1)
| ~ p6(X1) )
& ( p6(X1)
| p5(X1) )
& ( ~ p6(X1)
| ~ p7(X1) )
& ( p7(X1)
| p6(X1) )
& ( ~ p7(X1)
| ~ p8(X1) )
& ( p8(X1)
| p7(X1) )
& ( ~ p8(X1)
| ~ p9(X1) )
& ( p9(X1)
| p8(X1) )
& ( ~ p9(X1)
| ~ p10(X1) )
& ( p10(X1)
| p9(X1) )
& ( ~ p10(X1)
| ~ p11(X1) )
& ( p11(X1)
| p10(X1) )
& ( ~ p11(X1)
| ~ p12(X1) )
& ( p12(X1)
| p11(X1) )
& ( ~ p12(X1)
| ~ p13(X1) )
& ( p13(X1)
| p12(X1) )
& ( ~ p13(X1)
| ~ p14(X1) )
& ( p14(X1)
| p13(X1) )
& r1(X0,X1) )
=> ( ( ~ p1(sK9(X0))
| ~ p2(sK9(X0)) )
& ( p2(sK9(X0))
| p1(sK9(X0)) )
& ( ~ p2(sK9(X0))
| ~ p3(sK9(X0)) )
& ( p3(sK9(X0))
| p2(sK9(X0)) )
& ( ~ p3(sK9(X0))
| ~ p4(sK9(X0)) )
& ( p4(sK9(X0))
| p3(sK9(X0)) )
& ( ~ p4(sK9(X0))
| ~ p5(sK9(X0)) )
& ( p5(sK9(X0))
| p4(sK9(X0)) )
& ( ~ p5(sK9(X0))
| ~ p6(sK9(X0)) )
& ( p6(sK9(X0))
| p5(sK9(X0)) )
& ( ~ p6(sK9(X0))
| ~ p7(sK9(X0)) )
& ( p7(sK9(X0))
| p6(sK9(X0)) )
& ( ~ p7(sK9(X0))
| ~ p8(sK9(X0)) )
& ( p8(sK9(X0))
| p7(sK9(X0)) )
& ( ~ p8(sK9(X0))
| ~ p9(sK9(X0)) )
& ( p9(sK9(X0))
| p8(sK9(X0)) )
& ( ~ p9(sK9(X0))
| ~ p10(sK9(X0)) )
& ( p10(sK9(X0))
| p9(sK9(X0)) )
& ( ~ p10(sK9(X0))
| ~ p11(sK9(X0)) )
& ( p11(sK9(X0))
| p10(sK9(X0)) )
& ( ~ p11(sK9(X0))
| ~ p12(sK9(X0)) )
& ( p12(sK9(X0))
| p11(sK9(X0)) )
& ( ~ p12(sK9(X0))
| ~ p13(sK9(X0)) )
& ( p13(sK9(X0))
| p12(sK9(X0)) )
& ( ~ p13(sK9(X0))
| ~ p14(sK9(X0)) )
& ( p14(sK9(X0))
| p13(sK9(X0)) )
& r1(X0,sK9(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0] :
( ( ( ~ p1(sK9(X0))
| ~ p2(sK9(X0)) )
& ( p2(sK9(X0))
| p1(sK9(X0)) )
& ( ~ p2(sK9(X0))
| ~ p3(sK9(X0)) )
& ( p3(sK9(X0))
| p2(sK9(X0)) )
& ( ~ p3(sK9(X0))
| ~ p4(sK9(X0)) )
& ( p4(sK9(X0))
| p3(sK9(X0)) )
& ( ~ p4(sK9(X0))
| ~ p5(sK9(X0)) )
& ( p5(sK9(X0))
| p4(sK9(X0)) )
& ( ~ p5(sK9(X0))
| ~ p6(sK9(X0)) )
& ( p6(sK9(X0))
| p5(sK9(X0)) )
& ( ~ p6(sK9(X0))
| ~ p7(sK9(X0)) )
& ( p7(sK9(X0))
| p6(sK9(X0)) )
& ( ~ p7(sK9(X0))
| ~ p8(sK9(X0)) )
& ( p8(sK9(X0))
| p7(sK9(X0)) )
& ( ~ p8(sK9(X0))
| ~ p9(sK9(X0)) )
& ( p9(sK9(X0))
| p8(sK9(X0)) )
& ( ~ p9(sK9(X0))
| ~ p10(sK9(X0)) )
& ( p10(sK9(X0))
| p9(sK9(X0)) )
& ( ~ p10(sK9(X0))
| ~ p11(sK9(X0)) )
& ( p11(sK9(X0))
| p10(sK9(X0)) )
& ( ~ p11(sK9(X0))
| ~ p12(sK9(X0)) )
& ( p12(sK9(X0))
| p11(sK9(X0)) )
& ( ~ p12(sK9(X0))
| ~ p13(sK9(X0)) )
& ( p13(sK9(X0))
| p12(sK9(X0)) )
& ( ~ p13(sK9(X0))
| ~ p14(sK9(X0)) )
& ( p14(sK9(X0))
| p13(sK9(X0)) )
& r1(X0,sK9(X0)) )
| ~ sP5(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f25,f26]) ).
fof(f54,plain,
? [X0] :
( ? [X1] :
( ! [X2] :
( ( sP5(X2)
& ? [X3] :
( ~ p15(X3)
& r1(X2,X3) )
& ! [X4] :
( ( ( ~ p1(X4)
| p2(X4) )
& ( p1(X4)
| ~ p2(X4) ) )
| ~ r1(X2,X4) )
& sP6(X2) )
| ~ r1(X1,X2) )
& r1(X0,X1) )
& ? [X5] :
( ? [X6] :
( p1(X6)
& r1(X5,X6) )
& p15(X5)
& r1(X0,X5) ) ),
inference(rectify,[],[f18]) ).
fof(f55,plain,
( ? [X0] :
( ? [X1] :
( ! [X2] :
( ( sP5(X2)
& ? [X3] :
( ~ p15(X3)
& r1(X2,X3) )
& ! [X4] :
( ( ( ~ p1(X4)
| p2(X4) )
& ( p1(X4)
| ~ p2(X4) ) )
| ~ r1(X2,X4) )
& sP6(X2) )
| ~ r1(X1,X2) )
& r1(X0,X1) )
& ? [X5] :
( ? [X6] :
( p1(X6)
& r1(X5,X6) )
& p15(X5)
& r1(X0,X5) ) )
=> ( ? [X1] :
( ! [X2] :
( ( sP5(X2)
& ? [X3] :
( ~ p15(X3)
& r1(X2,X3) )
& ! [X4] :
( ( ( ~ p1(X4)
| p2(X4) )
& ( p1(X4)
| ~ p2(X4) ) )
| ~ r1(X2,X4) )
& sP6(X2) )
| ~ r1(X1,X2) )
& r1(sK21,X1) )
& ? [X5] :
( ? [X6] :
( p1(X6)
& r1(X5,X6) )
& p15(X5)
& r1(sK21,X5) ) ) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
( ? [X1] :
( ! [X2] :
( ( sP5(X2)
& ? [X3] :
( ~ p15(X3)
& r1(X2,X3) )
& ! [X4] :
( ( ( ~ p1(X4)
| p2(X4) )
& ( p1(X4)
| ~ p2(X4) ) )
| ~ r1(X2,X4) )
& sP6(X2) )
| ~ r1(X1,X2) )
& r1(sK21,X1) )
=> ( ! [X2] :
( ( sP5(X2)
& ? [X3] :
( ~ p15(X3)
& r1(X2,X3) )
& ! [X4] :
( ( ( ~ p1(X4)
| p2(X4) )
& ( p1(X4)
| ~ p2(X4) ) )
| ~ r1(X2,X4) )
& sP6(X2) )
| ~ r1(sK22,X2) )
& r1(sK21,sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
! [X2] :
( ? [X3] :
( ~ p15(X3)
& r1(X2,X3) )
=> ( ~ p15(sK23(X2))
& r1(X2,sK23(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
( ? [X5] :
( ? [X6] :
( p1(X6)
& r1(X5,X6) )
& p15(X5)
& r1(sK21,X5) )
=> ( ? [X6] :
( p1(X6)
& r1(sK24,X6) )
& p15(sK24)
& r1(sK21,sK24) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
( ? [X6] :
( p1(X6)
& r1(sK24,X6) )
=> ( p1(sK25)
& r1(sK24,sK25) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
( ! [X2] :
( ( sP5(X2)
& ~ p15(sK23(X2))
& r1(X2,sK23(X2))
& ! [X4] :
( ( ( ~ p1(X4)
| p2(X4) )
& ( p1(X4)
| ~ p2(X4) ) )
| ~ r1(X2,X4) )
& sP6(X2) )
| ~ r1(sK22,X2) )
& r1(sK21,sK22)
& p1(sK25)
& r1(sK24,sK25)
& p15(sK24)
& r1(sK21,sK24) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22,sK23,sK24,sK25])],[f54,f59,f58,f57,f56,f55]) ).
fof(f61,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f70,plain,
! [X0] :
( r1(X0,sK9(X0))
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f95,plain,
! [X0] :
( p2(sK9(X0))
| p1(sK9(X0))
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f96,plain,
! [X0] :
( ~ p1(sK9(X0))
| ~ p2(sK9(X0))
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f138,plain,
! [X2,X4] :
( p1(X4)
| ~ p2(X4)
| ~ r1(X2,X4)
| ~ r1(sK22,X2) ),
inference(cnf_transformation,[],[f60]) ).
fof(f139,plain,
! [X2,X4] :
( ~ p1(X4)
| p2(X4)
| ~ r1(X2,X4)
| ~ r1(sK22,X2) ),
inference(cnf_transformation,[],[f60]) ).
fof(f142,plain,
! [X2] :
( sP5(X2)
| ~ r1(sK22,X2) ),
inference(cnf_transformation,[],[f60]) ).
cnf(c_49,plain,
r1(X0,X0),
inference(cnf_transformation,[],[f61]) ).
cnf(c_58,plain,
( ~ p2(sK9(X0))
| ~ p1(sK9(X0))
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f96]) ).
cnf(c_59,plain,
( ~ sP5(X0)
| p2(sK9(X0))
| p1(sK9(X0)) ),
inference(cnf_transformation,[],[f95]) ).
cnf(c_84,plain,
( ~ sP5(X0)
| r1(X0,sK9(X0)) ),
inference(cnf_transformation,[],[f70]) ).
cnf(c_120,negated_conjecture,
( ~ r1(sK22,X0)
| sP5(X0) ),
inference(cnf_transformation,[],[f142]) ).
cnf(c_123,negated_conjecture,
( ~ r1(X0,X1)
| ~ r1(sK22,X0)
| ~ p1(X1)
| p2(X1) ),
inference(cnf_transformation,[],[f139]) ).
cnf(c_124,negated_conjecture,
( ~ r1(X0,X1)
| ~ r1(sK22,X0)
| ~ p2(X1)
| p1(X1) ),
inference(cnf_transformation,[],[f138]) ).
cnf(c_131,plain,
r1(sK22,sK22),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_133,plain,
( ~ r1(sK22,sK22)
| sP5(sK22) ),
inference(instantiation,[status(thm)],[c_120]) ).
cnf(c_144,plain,
( ~ sP5(sK22)
| r1(sK22,sK9(sK22)) ),
inference(instantiation,[status(thm)],[c_84]) ).
cnf(c_1319,plain,
( ~ r1(X0,sK9(X1))
| ~ r1(sK22,X0)
| ~ p1(sK9(X1))
| ~ sP5(X1) ),
inference(resolution,[status(thm)],[c_123,c_58]) ).
cnf(c_1320,plain,
( ~ r1(sK22,sK9(sK22))
| ~ r1(sK22,sK22)
| ~ p1(sK9(sK22))
| ~ sP5(sK22) ),
inference(instantiation,[status(thm)],[c_1319]) ).
cnf(c_1333,plain,
( ~ r1(X0,sK9(X1))
| ~ r1(sK22,X0)
| ~ sP5(X1)
| p1(sK9(X1)) ),
inference(resolution,[status(thm)],[c_124,c_59]) ).
cnf(c_1334,plain,
( ~ r1(sK22,sK9(sK22))
| ~ r1(sK22,sK22)
| ~ sP5(sK22)
| p1(sK9(sK22)) ),
inference(instantiation,[status(thm)],[c_1333]) ).
cnf(c_1335,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1334,c_1320,c_144,c_133,c_131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL686+1.005 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n028.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 05:40:36 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 1.06/1.15 % SZS status Started for theBenchmark.p
% 1.06/1.15 % SZS status Theorem for theBenchmark.p
% 1.06/1.15
% 1.06/1.15 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.06/1.15
% 1.06/1.15 ------ iProver source info
% 1.06/1.15
% 1.06/1.15 git: date: 2023-05-31 18:12:56 +0000
% 1.06/1.15 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.06/1.15 git: non_committed_changes: false
% 1.06/1.15 git: last_make_outside_of_git: false
% 1.06/1.15
% 1.06/1.15 ------ Parsing...
% 1.06/1.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.06/1.15
% 1.06/1.15 ------ Preprocessing... sf_s rm: 2 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s
% 1.06/1.15
% 1.06/1.15 % SZS status Theorem for theBenchmark.p
% 1.06/1.15
% 1.06/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.06/1.16
% 1.06/1.16
%------------------------------------------------------------------------------