%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUN062+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 : Wed Oct 7 10:35:59 AM UTC 2026
% Result : Theorem 0.60s 0.42s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 8
% Syntax : Number of formulae : 230 ( 126 unt; 0 typ; 0 def)
% Number of atoms : 1317 ( 590 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 2674 (1085 ~; 376 |; 57 &;1156 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 4 con; 0-3 aty)
% Number of variables : 599 ( 0 ^; 539 !; 60 ?; 599 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_r1,type,
r1: $i > $o ).
thf(tp_r2,type,
r2: $i > $i > $o ).
thf(tp_r3,type,
r3: $i > $i > $i > $o ).
thf(tp_r4,type,
r4: $i > $i > $i > $o ).
thf(tp_sK10_SY66,type,
sK10_SY66: $i > $i ).
thf(tp_sK11_SY36,type,
sK11_SY36: $i > $i ).
thf(tp_sK12_SY36,type,
sK12_SY36: $i > $i ).
thf(tp_sK13_SY67,type,
sK13_SY67: $i > $i > $i ).
thf(tp_sK14_SY69,type,
sK14_SY69: $i > $i > $i ).
thf(tp_sK15_SY71,type,
sK15_SY71: $i > $i > $i ).
thf(tp_sK16_SY73,type,
sK16_SY73: $i > $i ).
thf(tp_sK17_SY74,type,
sK17_SY74: $i > $i ).
thf(tp_sK18_SY75,type,
sK18_SY75: $i > $i > $i ).
thf(tp_sK1_X1,type,
sK1_X1: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY43,type,
sK3_SY43: $i > $i ).
thf(tp_sK4_SY50,type,
sK4_SY50: $i > $i ).
thf(tp_sK5_SY35,type,
sK5_SY35: $i > $i ).
thf(tp_sK6_SY53,type,
sK6_SY53: $i > $i > $i ).
thf(tp_sK7_SY59,type,
sK7_SY59: $i > $i > $i ).
thf(tp_sK8_SY64,type,
sK8_SY64: $i > $i ).
thf(tp_sK9_SY65,type,
sK9_SY65: $i > $i ).
thf(1,axiom,
! [X7: $i,Y10: $i] :
( ! [Y20: $i] :
( ~ ( r1 @ Y20 )
| ( Y20 != Y10 ) )
| ~ ( r2 @ X7 @ Y10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7a) ).
thf(2,axiom,
! [X6: $i] :
( ? [Y19: $i] :
( ( r1 @ Y19 )
& ( X6 = Y19 ) )
| ? [Y1: $i,Y11: $i] :
( ( r2 @ Y1 @ Y11 )
& ( X6 = Y11 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6a) ).
thf(3,axiom,
! [X5: $i] :
? [Y8: $i] :
( ? [Y17: $i] :
( ( r1 @ Y17 )
& ( r4 @ X5 @ Y17 @ Y8 ) )
& ? [Y18: $i] :
( ( r1 @ Y18 )
& ( Y8 = Y18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5a) ).
thf(4,axiom,
! [X4: $i] :
? [Y9: $i] :
( ? [Y16: $i] :
( ( r1 @ Y16 )
& ( r3 @ X4 @ Y16 @ Y9 ) )
& ( Y9 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4a) ).
thf(7,axiom,
! [X1: $i,X8: $i] :
? [Y4: $i] :
( ? [Y5: $i] :
( ? [Y15: $i] :
( ( r2 @ X8 @ Y15 )
& ( r3 @ X1 @ Y15 @ Y5 ) )
& ( Y5 = Y4 ) )
& ? [Y7: $i] :
( ( r2 @ Y7 @ Y4 )
& ( r3 @ X1 @ X8 @ Y7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1a) ).
thf(9,axiom,
! [X13: $i,X14: $i] :
? [Y22: $i] :
! [X15: $i] :
( ( ~ ( r3 @ X13 @ X14 @ X15 )
& ( X15 != Y22 ) )
| ( ( r3 @ X13 @ X14 @ X15 )
& ( X15 = Y22 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(11,axiom,
? [Y24: $i] :
! [X19: $i] :
( ( ~ ( r1 @ X19 )
& ( X19 != Y24 ) )
| ( ( r1 @ X19 )
& ( X19 = Y24 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(12,conjecture,
! [X1: $i] :
? [Y2: $i,Y1: $i] :
( ! [Y4: $i] :
( ~ ( r1 @ Y4 )
| ( Y1 != Y4 ) )
& ? [Y3: $i] :
( ( r3 @ X1 @ Y1 @ Y3 )
& ( Y3 = Y2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infiniteNumbers) ).
thf(13,negated_conjecture,
( ( ! [X1: $i] :
? [Y2: $i,Y1: $i] :
( ! [Y4: $i] :
( ~ ( r1 @ Y4 )
| ( Y1 != Y4 ) )
& ? [Y3: $i] :
( ( r3 @ X1 @ Y1 @ Y3 )
& ( Y3 = Y2 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[12]) ).
thf(14,plain,
( ( ! [X1: $i] :
? [Y2: $i,Y1: $i] :
( ! [Y4: $i] :
( ~ ( r1 @ Y4 )
| ( Y1 != Y4 ) )
& ? [Y3: $i] :
( ( r3 @ X1 @ Y1 @ Y3 )
& ( Y3 = Y2 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [X7: $i,Y10: $i] :
( ! [Y20: $i] :
( ~ ( r1 @ Y20 )
| ( Y20 != Y10 ) )
| ~ ( r2 @ X7 @ Y10 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(16,plain,
( ( ! [X6: $i] :
( ? [Y19: $i] :
( ( r1 @ Y19 )
& ( X6 = Y19 ) )
| ? [Y1: $i,Y11: $i] :
( ( r2 @ Y1 @ Y11 )
& ( X6 = Y11 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(17,plain,
( ( ! [X5: $i] :
? [Y8: $i] :
( ? [Y17: $i] :
( ( r1 @ Y17 )
& ( r4 @ X5 @ Y17 @ Y8 ) )
& ? [Y18: $i] :
( ( r1 @ Y18 )
& ( Y8 = Y18 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [X4: $i] :
? [Y9: $i] :
( ? [Y16: $i] :
( ( r1 @ Y16 )
& ( r3 @ X4 @ Y16 @ Y9 ) )
& ( Y9 = X4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(19,plain,
( ( ! [X1: $i,X8: $i] :
? [Y4: $i] :
( ? [Y5: $i] :
( ? [Y15: $i] :
( ( r2 @ X8 @ Y15 )
& ( r3 @ X1 @ Y15 @ Y5 ) )
& ( Y5 = Y4 ) )
& ? [Y7: $i] :
( ( r2 @ Y7 @ Y4 )
& ( r3 @ X1 @ X8 @ Y7 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(20,plain,
( ( ! [X13: $i,X14: $i] :
? [Y22: $i] :
! [X15: $i] :
( ( ~ ( r3 @ X13 @ X14 @ X15 )
& ( X15 != Y22 ) )
| ( ( r3 @ X13 @ X14 @ X15 )
& ( X15 = Y22 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(21,plain,
( ( ? [Y24: $i] :
! [X19: $i] :
( ( ~ ( r1 @ X19 )
& ( X19 != Y24 ) )
| ( ( r1 @ X19 )
& ( X19 = Y24 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(22,plain,
( ( ? [SY31: $i,SY32: $i] :
( ! [Y4: $i] :
( ~ ( r1 @ Y4 )
| ( SY32 != Y4 ) )
& ? [SY34: $i] :
( ( r3 @ sK1_X1 @ SY32 @ SY34 )
& ( SY34 = SY31 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(23,plain,
( ( ~ ? [SY31: $i,SY32: $i] :
( ! [Y4: $i] :
( ~ ( r1 @ Y4 )
| ( SY32 != Y4 ) )
& ? [SY34: $i] :
( ( r3 @ sK1_X1 @ SY32 @ SY34 )
& ( SY34 = SY31 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(24,plain,
( ( ? [Y24: $i] :
! [X19: $i] :
( ( ~ ( r1 @ X19 )
& ( X19 != Y24 ) )
| ( ( r1 @ X19 )
& ( X19 = Y24 ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(25,plain,
( ( ! [X13: $i,X14: $i] :
? [Y22: $i] :
! [X15: $i] :
( ( ~ ( r3 @ X13 @ X14 @ X15 )
& ( X15 != Y22 ) )
| ( ( r3 @ X13 @ X14 @ X15 )
& ( X15 = Y22 ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(26,plain,
( ( ! [X1: $i,X8: $i] :
? [Y4: $i] :
( ? [Y5: $i] :
( ? [Y15: $i] :
( ( r2 @ X8 @ Y15 )
& ( r3 @ X1 @ Y15 @ Y5 ) )
& ( Y5 = Y4 ) )
& ? [Y7: $i] :
( ( r2 @ Y7 @ Y4 )
& ( r3 @ X1 @ X8 @ Y7 ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(27,plain,
( ( ! [X4: $i] :
? [Y9: $i] :
( ? [Y16: $i] :
( ( r1 @ Y16 )
& ( r3 @ X4 @ Y16 @ Y9 ) )
& ( Y9 = X4 ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(28,plain,
( ( ! [X5: $i] :
? [Y8: $i] :
( ? [Y17: $i] :
( ( r1 @ Y17 )
& ( r4 @ X5 @ Y17 @ Y8 ) )
& ? [Y18: $i] :
( ( r1 @ Y18 )
& ( Y8 = Y18 ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(29,plain,
( ( ! [X6: $i] :
( ? [Y19: $i] :
( ( r1 @ Y19 )
& ( X6 = Y19 ) )
| ? [Y1: $i,Y11: $i] :
( ( r2 @ Y1 @ Y11 )
& ( X6 = Y11 ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(30,plain,
( ( ! [X7: $i,Y10: $i] :
( ! [Y20: $i] :
( ~ ( r1 @ Y20 )
| ( Y20 != Y10 ) )
| ~ ( r2 @ X7 @ Y10 ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(31,plain,
( ( ~ ? [SY31: $i,SY32: $i] :
( ! [Y4: $i] :
( ~ ( r1 @ Y4 )
| ( SY32 != Y4 ) )
& ? [SY34: $i] :
( ( r3 @ sK1_X1 @ SY32 @ SY34 )
& ( SY34 = SY31 ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(32,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ~ ( ~ ( r1 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ( r2 @ SX1 @ SX2 )
| ( SX0 != SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(33,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ! [SX2: $i] :
( ~ ( r1 @ SX2 )
| ( SX1 != SX2 ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( r3 @ sK1_X1 @ SX1 @ SX2 )
| ( SX2 != SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(34,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ! [SX2: $i] :
~ ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( r2 @ SX1 @ SX4 )
| ~ ( r3 @ SX0 @ SX4 @ SX3 ) )
| ( SX3 != SX2 ) )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( r2 @ SX3 @ SX2 )
| ~ ( r3 @ SX0 @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(35,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( r1 @ SX2 )
| ~ ( r3 @ SX0 @ SX2 @ SX1 ) )
| ( SX1 != SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(36,plain,
( ( ~ ! [SX0: $i] :
~ ! [SX1: $i] :
( ~ ( ~ ~ ( r1 @ SX1 )
| ~ ( ( SX1 != SX0 ) ) )
| ~ ( ~ ( r1 @ SX1 )
| ( SX1 != SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(37,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( r1 @ SX2 )
| ( SX2 != SX1 ) )
| ~ ( r2 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(38,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ! [SX2: $i] :
~ ! [SX3: $i] :
( ~ ( ~ ~ ( r3 @ SX0 @ SX1 @ SX3 )
| ~ ( ( SX3 != SX2 ) ) )
| ~ ( ~ ( r3 @ SX0 @ SX1 @ SX3 )
| ( SX3 != SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(39,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( r1 @ SX2 )
| ~ ( r4 @ SX0 @ SX2 @ SX1 ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( r1 @ SX2 )
| ( SX1 != SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(40,plain,
! [SV1: $i] :
( ( ~ ! [SY35: $i] :
~ ~ ( ~ ( r1 @ SY35 )
| ( SV1 != SY35 ) )
| ~ ! [SY36: $i] :
~ ~ ! [SY37: $i] :
~ ~ ( ~ ( r2 @ SY36 @ SY37 )
| ( SV1 != SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(41,plain,
( ( ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ! [SX2: $i] :
( ~ ( r1 @ SX2 )
| ( SX1 != SX2 ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( r3 @ sK1_X1 @ SX1 @ SX2 )
| ( SX2 != SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(42,plain,
! [SV2: $i] :
( ( ! [SY38: $i] :
~ ! [SY39: $i] :
~ ~ ( ~ ~ ! [SY40: $i] :
~ ~ ( ~ ~ ! [SY41: $i] :
~ ~ ( ~ ( r2 @ SY38 @ SY41 )
| ~ ( r3 @ SV2 @ SY41 @ SY40 ) )
| ( SY40 != SY39 ) )
| ~ ~ ! [SY42: $i] :
~ ~ ( ~ ( r2 @ SY42 @ SY39 )
| ~ ( r3 @ SV2 @ SY38 @ SY42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(43,plain,
! [SV3: $i] :
( ( ~ ! [SY43: $i] :
~ ~ ( ~ ~ ! [SY44: $i] :
~ ~ ( ~ ( r1 @ SY44 )
| ~ ( r3 @ SV3 @ SY44 @ SY43 ) )
| ( SY43 != SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(44,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
( ~ ( ~ ~ ( r1 @ SX1 )
| ~ ( ( SX1 != SX0 ) ) )
| ~ ( ~ ( r1 @ SX1 )
| ( SX1 != SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(45,plain,
! [SV4: $i] :
( ( ! [SY45: $i] :
( ! [SX2: $i] :
( ~ ( r1 @ SX2 )
| ( SX2 != SY45 ) )
| ~ ( r2 @ SV4 @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(46,plain,
! [SV5: $i] :
( ( ! [SY47: $i] :
~ ! [SY48: $i] :
~ ! [SY49: $i] :
( ~ ( ~ ~ ( r3 @ SV5 @ SY47 @ SY49 )
| ~ ( ( SY49 != SY48 ) ) )
| ~ ( ~ ( r3 @ SV5 @ SY47 @ SY49 )
| ( SY49 != SY48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(47,plain,
! [SV6: $i] :
( ( ~ ! [SY50: $i] :
~ ~ ( ~ ~ ! [SY51: $i] :
~ ~ ( ~ ( r1 @ SY51 )
| ~ ( r4 @ SV6 @ SY51 @ SY50 ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( r1 @ SX2 )
| ( SY50 != SX2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(48,plain,
! [SV1: $i] :
( ( ( ~ ! [SY35: $i] :
~ ~ ( ~ ( r1 @ SY35 )
| ( SV1 != SY35 ) ) )
= $true )
| ( ( ~ ! [SY36: $i] :
~ ~ ! [SY37: $i] :
~ ~ ( ~ ( r2 @ SY36 @ SY37 )
| ( SV1 != SY37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(49,plain,
( ( ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ! [SX2: $i] :
( ~ ( r1 @ SX2 )
| ( SX1 != SX2 ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( r3 @ sK1_X1 @ SX1 @ SX2 )
| ( SX2 != SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(50,plain,
! [SV2: $i,SV7: $i] :
( ( ~ ! [SY53: $i] :
~ ~ ( ~ ~ ! [SY54: $i] :
~ ~ ( ~ ~ ! [SY55: $i] :
~ ~ ( ~ ( r2 @ SV7 @ SY55 )
| ~ ( r3 @ SV2 @ SY55 @ SY54 ) )
| ( SY54 != SY53 ) )
| ~ ~ ! [SY56: $i] :
~ ~ ( ~ ( r2 @ SY56 @ SY53 )
| ~ ( r3 @ SV2 @ SV7 @ SY56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(51,plain,
! [SV3: $i] :
( ( ! [SY43: $i] :
~ ~ ( ~ ~ ! [SY44: $i] :
~ ~ ( ~ ( r1 @ SY44 )
| ~ ( r3 @ SV3 @ SY44 @ SY43 ) )
| ( SY43 != SV3 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(52,plain,
( ( ~ ! [SY57: $i] :
( ~ ( ~ ~ ( r1 @ SY57 )
| ~ ( ( SY57 != sK2_SX0 ) ) )
| ~ ( ~ ( r1 @ SY57 )
| ( SY57 != sK2_SX0 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(53,plain,
! [SV4: $i,SV8: $i] :
( ( ! [SY58: $i] :
( ~ ( r1 @ SY58 )
| ( SY58 != SV8 ) )
| ~ ( r2 @ SV4 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(54,plain,
! [SV9: $i,SV5: $i] :
( ( ~ ! [SY59: $i] :
~ ! [SY60: $i] :
( ~ ( ~ ~ ( r3 @ SV5 @ SV9 @ SY60 )
| ~ ( ( SY60 != SY59 ) ) )
| ~ ( ~ ( r3 @ SV5 @ SV9 @ SY60 )
| ( SY60 != SY59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(55,plain,
! [SV6: $i] :
( ( ! [SY50: $i] :
~ ~ ( ~ ~ ! [SY51: $i] :
~ ~ ( ~ ( r1 @ SY51 )
| ~ ( r4 @ SV6 @ SY51 @ SY50 ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( r1 @ SX2 )
| ( SY50 != SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(56,plain,
! [SV1: $i] :
( ( ( ! [SY35: $i] :
~ ~ ( ~ ( r1 @ SY35 )
| ( SV1 != SY35 ) ) )
= $false )
| ( ( ~ ! [SY36: $i] :
~ ~ ! [SY37: $i] :
~ ~ ( ~ ( r2 @ SY36 @ SY37 )
| ( SV1 != SY37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(57,plain,
! [SV10: $i] :
( ( ~ ~ ! [SY61: $i] :
~ ~ ( ~ ! [SX2: $i] :
( ~ ( r1 @ SX2 )
| ( SY61 != SX2 ) )
| ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( r3 @ sK1_X1 @ SY61 @ SY63 )
| ( SY63 != SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(58,plain,
! [SV2: $i,SV7: $i] :
( ( ! [SY53: $i] :
~ ~ ( ~ ~ ! [SY54: $i] :
~ ~ ( ~ ~ ! [SY55: $i] :
~ ~ ( ~ ( r2 @ SV7 @ SY55 )
| ~ ( r3 @ SV2 @ SY55 @ SY54 ) )
| ( SY54 != SY53 ) )
| ~ ~ ! [SY56: $i] :
~ ~ ( ~ ( r2 @ SY56 @ SY53 )
| ~ ( r3 @ SV2 @ SV7 @ SY56 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(59,plain,
! [SV3: $i] :
( ( ~ ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( r1 @ SY64 )
| ~ ( r3 @ SV3 @ SY64 @ ( sK3_SY43 @ SV3 ) ) )
| ( ( sK3_SY43 @ SV3 )
!= SV3 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[51]) ).
thf(60,plain,
( ( ! [SY57: $i] :
( ~ ( ~ ~ ( r1 @ SY57 )
| ~ ( ( SY57 != sK2_SX0 ) ) )
| ~ ( ~ ( r1 @ SY57 )
| ( SY57 != sK2_SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(61,plain,
! [SV4: $i,SV8: $i] :
( ( ( ! [SY58: $i] :
( ~ ( r1 @ SY58 )
| ( SY58 != SV8 ) ) )
= $true )
| ( ( ~ ( r2 @ SV4 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(62,plain,
! [SV9: $i,SV5: $i] :
( ( ! [SY59: $i] :
~ ! [SY60: $i] :
( ~ ( ~ ~ ( r3 @ SV5 @ SV9 @ SY60 )
| ~ ( ( SY60 != SY59 ) ) )
| ~ ( ~ ( r3 @ SV5 @ SV9 @ SY60 )
| ( SY60 != SY59 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(63,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ( r1 @ SY65 )
| ~ ( r4 @ SV6 @ SY65 @ ( sK4_SY50 @ SV6 ) ) )
| ~ ~ ! [SY66: $i] :
~ ~ ( ~ ( r1 @ SY66 )
| ( ( sK4_SY50 @ SV6 )
!= SY66 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[55]) ).
thf(64,plain,
! [SV1: $i] :
( ( ( ~ ~ ( ~ ( r1 @ ( sK5_SY35 @ SV1 ) )
| ( SV1
!= ( sK5_SY35 @ SV1 ) ) ) )
= $false )
| ( ( ~ ! [SY36: $i] :
~ ~ ! [SY37: $i] :
~ ~ ( ~ ( r2 @ SY36 @ SY37 )
| ( SV1 != SY37 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[56]) ).
thf(65,plain,
! [SV10: $i] :
( ( ~ ! [SY61: $i] :
~ ~ ( ~ ! [SX2: $i] :
( ~ ( r1 @ SX2 )
| ( SY61 != SX2 ) )
| ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( r3 @ sK1_X1 @ SY61 @ SY63 )
| ( SY63 != SV10 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(66,plain,
! [SV2: $i,SV7: $i] :
( ( ~ ~ ( ~ ~ ! [SY67: $i] :
~ ~ ( ~ ~ ! [SY55: $i] :
~ ~ ( ~ ( r2 @ SV7 @ SY55 )
| ~ ( r3 @ SV2 @ SY55 @ SY67 ) )
| ( SY67
!= ( sK6_SY53 @ SV2 @ SV7 ) ) )
| ~ ~ ! [SY69: $i] :
~ ~ ( ~ ( r2 @ SY69 @ ( sK6_SY53 @ SV2 @ SV7 ) )
| ~ ( r3 @ SV2 @ SV7 @ SY69 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[58]) ).
thf(67,plain,
! [SV3: $i] :
( ( ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( r1 @ SY64 )
| ~ ( r3 @ SV3 @ SY64 @ ( sK3_SY43 @ SV3 ) ) )
| ( ( sK3_SY43 @ SV3 )
!= SV3 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(68,plain,
! [SV11: $i] :
( ( ~ ( ~ ~ ( r1 @ SV11 )
| ~ ( ( SV11 != sK2_SX0 ) ) )
| ~ ( ~ ( r1 @ SV11 )
| ( SV11 != sK2_SX0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(69,plain,
! [SV4: $i,SV8: $i,SV12: $i] :
( ( ( ~ ( r1 @ SV12 )
| ( SV12 != SV8 ) )
= $true )
| ( ( ~ ( r2 @ SV4 @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(70,plain,
! [SV9: $i,SV5: $i] :
( ( ~ ! [SY70: $i] :
( ~ ( ~ ~ ( r3 @ SV5 @ SV9 @ SY70 )
| ~ ( ( SY70
!= ( sK7_SY59 @ SV9 @ SV5 ) ) ) )
| ~ ( ~ ( r3 @ SV5 @ SV9 @ SY70 )
| ( SY70
!= ( sK7_SY59 @ SV9 @ SV5 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[62]) ).
thf(71,plain,
! [SV6: $i] :
( ( ~ ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ( r1 @ SY65 )
| ~ ( r4 @ SV6 @ SY65 @ ( sK4_SY50 @ SV6 ) ) )
| ~ ~ ! [SY66: $i] :
~ ~ ( ~ ( r1 @ SY66 )
| ( ( sK4_SY50 @ SV6 )
!= SY66 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(72,plain,
! [SV1: $i] :
( ( ( ~ ( ~ ( r1 @ ( sK5_SY35 @ SV1 ) )
| ( SV1
!= ( sK5_SY35 @ SV1 ) ) ) )
= $true )
| ( ( ~ ! [SY36: $i] :
~ ~ ! [SY37: $i] :
~ ~ ( ~ ( r2 @ SY36 @ SY37 )
| ( SV1 != SY37 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(73,plain,
! [SV10: $i] :
( ( ! [SY61: $i] :
~ ~ ( ~ ! [SX2: $i] :
( ~ ( r1 @ SX2 )
| ( SY61 != SX2 ) )
| ~ ~ ! [SY63: $i] :
~ ~ ( ~ ( r3 @ sK1_X1 @ SY61 @ SY63 )
| ( SY63 != SV10 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(74,plain,
! [SV2: $i,SV7: $i] :
( ( ~ ( ~ ~ ! [SY67: $i] :
~ ~ ( ~ ~ ! [SY55: $i] :
~ ~ ( ~ ( r2 @ SV7 @ SY55 )
| ~ ( r3 @ SV2 @ SY55 @ SY67 ) )
| ( SY67
!= ( sK6_SY53 @ SV2 @ SV7 ) ) )
| ~ ~ ! [SY69: $i] :
~ ~ ( ~ ( r2 @ SY69 @ ( sK6_SY53 @ SV2 @ SV7 ) )
| ~ ( r3 @ SV2 @ SV7 @ SY69 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(75,plain,
! [SV3: $i] :
( ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( r1 @ SY64 )
| ~ ( r3 @ SV3 @ SY64 @ ( sK3_SY43 @ SV3 ) ) )
| ( ( sK3_SY43 @ SV3 )
!= SV3 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(76,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ~ ( r1 @ SV11 )
| ~ ( ( SV11 != sK2_SX0 ) ) ) )
= $true )
| ( ( ~ ( ~ ( r1 @ SV11 )
| ( SV11 != sK2_SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(77,plain,
! [SV4: $i,SV8: $i,SV12: $i] :
( ( ( ~ ( r1 @ SV12 ) )
= $true )
| ( ( SV12 != SV8 )
= $true )
| ( ( ~ ( r2 @ SV4 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(78,plain,
! [SV9: $i,SV5: $i] :
( ( ! [SY70: $i] :
( ~ ( ~ ~ ( r3 @ SV5 @ SV9 @ SY70 )
| ~ ( ( SY70
!= ( sK7_SY59 @ SV9 @ SV5 ) ) ) )
| ~ ( ~ ( r3 @ SV5 @ SV9 @ SY70 )
| ( SY70
!= ( sK7_SY59 @ SV9 @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(79,plain,
! [SV6: $i] :
( ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ( r1 @ SY65 )
| ~ ( r4 @ SV6 @ SY65 @ ( sK4_SY50 @ SV6 ) ) )
| ~ ~ ! [SY66: $i] :
~ ~ ( ~ ( r1 @ SY66 )
| ( ( sK4_SY50 @ SV6 )
!= SY66 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(80,plain,
! [SV1: $i] :
( ( ( ~ ( r1 @ ( sK5_SY35 @ SV1 ) )
| ( SV1
!= ( sK5_SY35 @ SV1 ) ) )
= $false )
| ( ( ~ ! [SY36: $i] :
~ ~ ! [SY37: $i] :
~ ~ ( ~ ( r2 @ SY36 @ SY37 )
| ( SV1 != SY37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(81,plain,
! [SV10: $i,SV13: $i] :
( ( ~ ~ ( ~ ! [SY71: $i] :
( ~ ( r1 @ SY71 )
| ( SV13 != SY71 ) )
| ~ ~ ! [SY72: $i] :
~ ~ ( ~ ( r3 @ sK1_X1 @ SV13 @ SY72 )
| ( SY72 != SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(82,plain,
! [SV2: $i,SV7: $i] :
( ( ~ ~ ! [SY67: $i] :
~ ~ ( ~ ~ ! [SY55: $i] :
~ ~ ( ~ ( r2 @ SV7 @ SY55 )
| ~ ( r3 @ SV2 @ SY55 @ SY67 ) )
| ( SY67
!= ( sK6_SY53 @ SV2 @ SV7 ) ) )
| ~ ~ ! [SY69: $i] :
~ ~ ( ~ ( r2 @ SY69 @ ( sK6_SY53 @ SV2 @ SV7 ) )
| ~ ( r3 @ SV2 @ SV7 @ SY69 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(83,plain,
! [SV3: $i] :
( ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ( r1 @ SY64 )
| ~ ( r3 @ SV3 @ SY64 @ ( sK3_SY43 @ SV3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(84,plain,
! [SV3: $i] :
( ( ( sK3_SY43 @ SV3 )
!= SV3 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(85,plain,
! [SV11: $i] :
( ( ( ~ ~ ( r1 @ SV11 )
| ~ ( ( SV11 != sK2_SX0 ) ) )
= $false )
| ( ( ~ ( ~ ( r1 @ SV11 )
| ( SV11 != sK2_SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(86,plain,
! [SV4: $i,SV8: $i,SV12: $i] :
( ( ( r1 @ SV12 )
= $false )
| ( ( SV12 != SV8 )
= $true )
| ( ( ~ ( r2 @ SV4 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(87,plain,
! [SV14: $i,SV9: $i,SV5: $i] :
( ( ~ ( ~ ~ ( r3 @ SV5 @ SV9 @ SV14 )
| ~ ( ( SV14
!= ( sK7_SY59 @ SV9 @ SV5 ) ) ) )
| ~ ( ~ ( r3 @ SV5 @ SV9 @ SV14 )
| ( SV14
!= ( sK7_SY59 @ SV9 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(88,plain,
! [SV6: $i] :
( ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ( r1 @ SY65 )
| ~ ( r4 @ SV6 @ SY65 @ ( sK4_SY50 @ SV6 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(89,plain,
! [SV6: $i] :
( ( ~ ~ ! [SY66: $i] :
~ ~ ( ~ ( r1 @ SY66 )
| ( ( sK4_SY50 @ SV6 )
!= SY66 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(90,plain,
! [SV1: $i] :
( ( ( ~ ( r1 @ ( sK5_SY35 @ SV1 ) ) )
= $false )
| ( ( ~ ! [SY36: $i] :
~ ~ ! [SY37: $i] :
~ ~ ( ~ ( r2 @ SY36 @ SY37 )
| ( SV1 != SY37 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(91,plain,
! [SV1: $i] :
( ( ( SV1
!= ( sK5_SY35 @ SV1 ) )
= $false )
| ( ( ~ ! [SY36: $i] :
~ ~ ! [SY37: $i] :
~ ~ ( ~ ( r2 @ SY36 @ SY37 )
| ( SV1 != SY37 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(92,plain,
! [SV10: $i,SV13: $i] :
( ( ~ ( ~ ! [SY71: $i] :
( ~ ( r1 @ SY71 )
| ( SV13 != SY71 ) )
| ~ ~ ! [SY72: $i] :
~ ~ ( ~ ( r3 @ sK1_X1 @ SV13 @ SY72 )
| ( SY72 != SV10 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(93,plain,
! [SV2: $i,SV7: $i] :
( ( ~ ~ ! [SY67: $i] :
~ ~ ( ~ ~ ! [SY55: $i] :
~ ~ ( ~ ( r2 @ SV7 @ SY55 )
| ~ ( r3 @ SV2 @ SY55 @ SY67 ) )
| ( SY67
!= ( sK6_SY53 @ SV2 @ SV7 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(94,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ~ ! [SY69: $i] :
~ ~ ( ~ ( r2 @ SY69 @ ( sK6_SY53 @ SV2 @ SV7 ) )
| ~ ( r3 @ SV2 @ SV7 @ SY69 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(95,plain,
! [SV3: $i] :
( ( ~ ! [SY64: $i] :
~ ~ ( ~ ( r1 @ SY64 )
| ~ ( r3 @ SV3 @ SY64 @ ( sK3_SY43 @ SV3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(96,plain,
! [SV3: $i] :
( ( ( sK3_SY43 @ SV3 )
= SV3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(97,plain,
! [SV11: $i] :
( ( ( ~ ~ ( r1 @ SV11 ) )
= $false )
| ( ( ~ ( ~ ( r1 @ SV11 )
| ( SV11 != sK2_SX0 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(98,plain,
! [SV11: $i] :
( ( ( ~ ( ( SV11 != sK2_SX0 ) ) )
= $false )
| ( ( ~ ( ~ ( r1 @ SV11 )
| ( SV11 != sK2_SX0 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(99,plain,
! [SV4: $i,SV8: $i,SV12: $i] :
( ( ( SV12 = SV8 )
= $false )
| ( ( r1 @ SV12 )
= $false )
| ( ( ~ ( r2 @ SV4 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(100,plain,
! [SV14: $i,SV9: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( r3 @ SV5 @ SV9 @ SV14 )
| ~ ( ( SV14
!= ( sK7_SY59 @ SV9 @ SV5 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( r3 @ SV5 @ SV9 @ SV14 )
| ( SV14
!= ( sK7_SY59 @ SV9 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(101,plain,
! [SV6: $i] :
( ( ~ ! [SY65: $i] :
~ ~ ( ~ ( r1 @ SY65 )
| ~ ( r4 @ SV6 @ SY65 @ ( sK4_SY50 @ SV6 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(102,plain,
! [SV6: $i] :
( ( ~ ! [SY66: $i] :
~ ~ ( ~ ( r1 @ SY66 )
| ( ( sK4_SY50 @ SV6 )
!= SY66 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(103,plain,
! [SV1: $i] :
( ( ( r1 @ ( sK5_SY35 @ SV1 ) )
= $true )
| ( ( ~ ! [SY36: $i] :
~ ~ ! [SY37: $i] :
~ ~ ( ~ ( r2 @ SY36 @ SY37 )
| ( SV1 != SY37 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(104,plain,
! [SV1: $i] :
( ( ( SV1
= ( sK5_SY35 @ SV1 ) )
= $true )
| ( ( ~ ! [SY36: $i] :
~ ~ ! [SY37: $i] :
~ ~ ( ~ ( r2 @ SY36 @ SY37 )
| ( SV1 != SY37 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(105,plain,
! [SV10: $i,SV13: $i] :
( ( ~ ! [SY71: $i] :
( ~ ( r1 @ SY71 )
| ( SV13 != SY71 ) )
| ~ ~ ! [SY72: $i] :
~ ~ ( ~ ( r3 @ sK1_X1 @ SV13 @ SY72 )
| ( SY72 != SV10 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(106,plain,
! [SV2: $i,SV7: $i] :
( ( ~ ! [SY67: $i] :
~ ~ ( ~ ~ ! [SY55: $i] :
~ ~ ( ~ ( r2 @ SV7 @ SY55 )
| ~ ( r3 @ SV2 @ SY55 @ SY67 ) )
| ( SY67
!= ( sK6_SY53 @ SV2 @ SV7 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(107,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ! [SY69: $i] :
~ ~ ( ~ ( r2 @ SY69 @ ( sK6_SY53 @ SV2 @ SV7 ) )
| ~ ( r3 @ SV2 @ SV7 @ SY69 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(108,plain,
! [SV3: $i] :
( ( ! [SY64: $i] :
~ ~ ( ~ ( r1 @ SY64 )
| ~ ( r3 @ SV3 @ SY64 @ ( sK3_SY43 @ SV3 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(109,plain,
! [SV11: $i] :
( ( ( ~ ( r1 @ SV11 ) )
= $true )
| ( ( ~ ( ~ ( r1 @ SV11 )
| ( SV11 != sK2_SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(110,plain,
! [SV11: $i] :
( ( ( SV11 != sK2_SX0 )
= $true )
| ( ( ~ ( ~ ( r1 @ SV11 )
| ( SV11 != sK2_SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(111,plain,
! [SV12: $i,SV8: $i,SV4: $i] :
( ( ( r2 @ SV4 @ SV8 )
= $false )
| ( ( r1 @ SV12 )
= $false )
| ( ( SV12 = SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(112,plain,
! [SV14: $i,SV9: $i,SV5: $i] :
( ( ( ~ ~ ( r3 @ SV5 @ SV9 @ SV14 )
| ~ ( ( SV14
!= ( sK7_SY59 @ SV9 @ SV5 ) ) ) )
= $false )
| ( ( ~ ( ~ ( r3 @ SV5 @ SV9 @ SV14 )
| ( SV14
!= ( sK7_SY59 @ SV9 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(113,plain,
! [SV6: $i] :
( ( ! [SY65: $i] :
~ ~ ( ~ ( r1 @ SY65 )
| ~ ( r4 @ SV6 @ SY65 @ ( sK4_SY50 @ SV6 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(114,plain,
! [SV6: $i] :
( ( ! [SY66: $i] :
~ ~ ( ~ ( r1 @ SY66 )
| ( ( sK4_SY50 @ SV6 )
!= SY66 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(115,plain,
! [SV1: $i] :
( ( ( ! [SY36: $i] :
~ ~ ! [SY37: $i] :
~ ~ ( ~ ( r2 @ SY36 @ SY37 )
| ( SV1 != SY37 ) ) )
= $false )
| ( ( r1 @ ( sK5_SY35 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(116,plain,
! [SV1: $i] :
( ( ( ! [SY36: $i] :
~ ~ ! [SY37: $i] :
~ ~ ( ~ ( r2 @ SY36 @ SY37 )
| ( SV1 != SY37 ) ) )
= $false )
| ( ( SV1
= ( sK5_SY35 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(117,plain,
! [SV10: $i,SV13: $i] :
( ( ( ~ ! [SY71: $i] :
( ~ ( r1 @ SY71 )
| ( SV13 != SY71 ) ) )
= $true )
| ( ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ( r3 @ sK1_X1 @ SV13 @ SY72 )
| ( SY72 != SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(118,plain,
! [SV2: $i,SV7: $i] :
( ( ! [SY67: $i] :
~ ~ ( ~ ~ ! [SY55: $i] :
~ ~ ( ~ ( r2 @ SV7 @ SY55 )
| ~ ( r3 @ SV2 @ SY55 @ SY67 ) )
| ( SY67
!= ( sK6_SY53 @ SV2 @ SV7 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(119,plain,
! [SV7: $i,SV2: $i] :
( ( ! [SY69: $i] :
~ ~ ( ~ ( r2 @ SY69 @ ( sK6_SY53 @ SV2 @ SV7 ) )
| ~ ( r3 @ SV2 @ SV7 @ SY69 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(120,plain,
! [SV3: $i] :
( ( ~ ~ ( ~ ( r1 @ ( sK8_SY64 @ SV3 ) )
| ~ ( r3 @ SV3 @ ( sK8_SY64 @ SV3 ) @ ( sK3_SY43 @ SV3 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[108]) ).
thf(121,plain,
! [SV11: $i] :
( ( ( r1 @ SV11 )
= $false )
| ( ( ~ ( ~ ( r1 @ SV11 )
| ( SV11 != sK2_SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(122,plain,
! [SV11: $i] :
( ( ( SV11 = sK2_SX0 )
= $false )
| ( ( ~ ( ~ ( r1 @ SV11 )
| ( SV11 != sK2_SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(123,plain,
! [SV14: $i,SV9: $i,SV5: $i] :
( ( ( ~ ~ ( r3 @ SV5 @ SV9 @ SV14 ) )
= $false )
| ( ( ~ ( ~ ( r3 @ SV5 @ SV9 @ SV14 )
| ( SV14
!= ( sK7_SY59 @ SV9 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(124,plain,
! [SV5: $i,SV9: $i,SV14: $i] :
( ( ( ~ ( ( SV14
!= ( sK7_SY59 @ SV9 @ SV5 ) ) ) )
= $false )
| ( ( ~ ( ~ ( r3 @ SV5 @ SV9 @ SV14 )
| ( SV14
!= ( sK7_SY59 @ SV9 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(125,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ( r1 @ ( sK9_SY65 @ SV6 ) )
| ~ ( r4 @ SV6 @ ( sK9_SY65 @ SV6 ) @ ( sK4_SY50 @ SV6 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[113]) ).
thf(126,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ( r1 @ ( sK10_SY66 @ SV6 ) )
| ( ( sK4_SY50 @ SV6 )
!= ( sK10_SY66 @ SV6 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[114]) ).
thf(127,plain,
! [SV1: $i] :
( ( ( ~ ~ ! [SY73: $i] :
~ ~ ( ~ ( r2 @ ( sK11_SY36 @ SV1 ) @ SY73 )
| ( SV1 != SY73 ) ) )
= $false )
| ( ( r1 @ ( sK5_SY35 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[115]) ).
thf(128,plain,
! [SV1: $i] :
( ( ( ~ ~ ! [SY74: $i] :
~ ~ ( ~ ( r2 @ ( sK12_SY36 @ SV1 ) @ SY74 )
| ( SV1 != SY74 ) ) )
= $false )
| ( ( SV1
= ( sK5_SY35 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[116]) ).
thf(129,plain,
! [SV10: $i,SV13: $i] :
( ( ( ! [SY71: $i] :
( ~ ( r1 @ SY71 )
| ( SV13 != SY71 ) ) )
= $false )
| ( ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ( r3 @ sK1_X1 @ SV13 @ SY72 )
| ( SY72 != SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(130,plain,
! [SV2: $i,SV7: $i] :
( ( ~ ~ ( ~ ~ ! [SY75: $i] :
~ ~ ( ~ ( r2 @ SV7 @ SY75 )
| ~ ( r3 @ SV2 @ SY75 @ ( sK13_SY67 @ SV2 @ SV7 ) ) )
| ( ( sK13_SY67 @ SV2 @ SV7 )
!= ( sK6_SY53 @ SV2 @ SV7 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[118]) ).
thf(131,plain,
! [SV2: $i,SV7: $i] :
( ( ~ ~ ( ~ ( r2 @ ( sK14_SY69 @ SV7 @ SV2 ) @ ( sK6_SY53 @ SV2 @ SV7 ) )
| ~ ( r3 @ SV2 @ SV7 @ ( sK14_SY69 @ SV7 @ SV2 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[119]) ).
thf(132,plain,
! [SV3: $i] :
( ( ~ ( ~ ( r1 @ ( sK8_SY64 @ SV3 ) )
| ~ ( r3 @ SV3 @ ( sK8_SY64 @ SV3 ) @ ( sK3_SY43 @ SV3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(133,plain,
! [SV11: $i] :
( ( ( ~ ( r1 @ SV11 )
| ( SV11 != sK2_SX0 ) )
= $false )
| ( ( r1 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(134,plain,
! [SV11: $i] :
( ( ( ~ ( r1 @ SV11 )
| ( SV11 != sK2_SX0 ) )
= $false )
| ( ( SV11 = sK2_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(135,plain,
! [SV14: $i,SV9: $i,SV5: $i] :
( ( ( ~ ( r3 @ SV5 @ SV9 @ SV14 ) )
= $true )
| ( ( ~ ( ~ ( r3 @ SV5 @ SV9 @ SV14 )
| ( SV14
!= ( sK7_SY59 @ SV9 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(136,plain,
! [SV5: $i,SV9: $i,SV14: $i] :
( ( ( SV14
!= ( sK7_SY59 @ SV9 @ SV5 ) )
= $true )
| ( ( ~ ( ~ ( r3 @ SV5 @ SV9 @ SV14 )
| ( SV14
!= ( sK7_SY59 @ SV9 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(137,plain,
! [SV6: $i] :
( ( ~ ( ~ ( r1 @ ( sK9_SY65 @ SV6 ) )
| ~ ( r4 @ SV6 @ ( sK9_SY65 @ SV6 ) @ ( sK4_SY50 @ SV6 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(138,plain,
! [SV6: $i] :
( ( ~ ( ~ ( r1 @ ( sK10_SY66 @ SV6 ) )
| ( ( sK4_SY50 @ SV6 )
!= ( sK10_SY66 @ SV6 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(139,plain,
! [SV1: $i] :
( ( ( ~ ! [SY73: $i] :
~ ~ ( ~ ( r2 @ ( sK11_SY36 @ SV1 ) @ SY73 )
| ( SV1 != SY73 ) ) )
= $true )
| ( ( r1 @ ( sK5_SY35 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(140,plain,
! [SV1: $i] :
( ( ( ~ ! [SY74: $i] :
~ ~ ( ~ ( r2 @ ( sK12_SY36 @ SV1 ) @ SY74 )
| ( SV1 != SY74 ) ) )
= $true )
| ( ( SV1
= ( sK5_SY35 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(141,plain,
! [SV13: $i,SV10: $i] :
( ( ( ~ ( r1 @ ( sK15_SY71 @ SV10 @ SV13 ) )
| ( SV13
!= ( sK15_SY71 @ SV10 @ SV13 ) ) )
= $false )
| ( ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ( r3 @ sK1_X1 @ SV13 @ SY72 )
| ( SY72 != SV10 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[129]) ).
thf(142,plain,
! [SV2: $i,SV7: $i] :
( ( ~ ( ~ ~ ! [SY75: $i] :
~ ~ ( ~ ( r2 @ SV7 @ SY75 )
| ~ ( r3 @ SV2 @ SY75 @ ( sK13_SY67 @ SV2 @ SV7 ) ) )
| ( ( sK13_SY67 @ SV2 @ SV7 )
!= ( sK6_SY53 @ SV2 @ SV7 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(143,plain,
! [SV2: $i,SV7: $i] :
( ( ~ ( ~ ( r2 @ ( sK14_SY69 @ SV7 @ SV2 ) @ ( sK6_SY53 @ SV2 @ SV7 ) )
| ~ ( r3 @ SV2 @ SV7 @ ( sK14_SY69 @ SV7 @ SV2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(144,plain,
! [SV3: $i] :
( ( ~ ( r1 @ ( sK8_SY64 @ SV3 ) )
| ~ ( r3 @ SV3 @ ( sK8_SY64 @ SV3 ) @ ( sK3_SY43 @ SV3 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(145,plain,
! [SV11: $i] :
( ( ( ~ ( r1 @ SV11 ) )
= $false )
| ( ( r1 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(146,plain,
! [SV11: $i] :
( ( ( SV11 != sK2_SX0 )
= $false )
| ( ( r1 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(147,plain,
! [SV11: $i] :
( ( ( ~ ( r1 @ SV11 ) )
= $false )
| ( ( SV11 = sK2_SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(148,plain,
! [SV11: $i] :
( ( ( SV11 != sK2_SX0 )
= $false )
| ( ( SV11 = sK2_SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(149,plain,
! [SV14: $i,SV9: $i,SV5: $i] :
( ( ( r3 @ SV5 @ SV9 @ SV14 )
= $false )
| ( ( ~ ( ~ ( r3 @ SV5 @ SV9 @ SV14 )
| ( SV14
!= ( sK7_SY59 @ SV9 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(150,plain,
! [SV5: $i,SV9: $i,SV14: $i] :
( ( ( SV14
= ( sK7_SY59 @ SV9 @ SV5 ) )
= $false )
| ( ( ~ ( ~ ( r3 @ SV5 @ SV9 @ SV14 )
| ( SV14
!= ( sK7_SY59 @ SV9 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(151,plain,
! [SV6: $i] :
( ( ~ ( r1 @ ( sK9_SY65 @ SV6 ) )
| ~ ( r4 @ SV6 @ ( sK9_SY65 @ SV6 ) @ ( sK4_SY50 @ SV6 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(152,plain,
! [SV6: $i] :
( ( ~ ( r1 @ ( sK10_SY66 @ SV6 ) )
| ( ( sK4_SY50 @ SV6 )
!= ( sK10_SY66 @ SV6 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(153,plain,
! [SV1: $i] :
( ( ( ! [SY73: $i] :
~ ~ ( ~ ( r2 @ ( sK11_SY36 @ SV1 ) @ SY73 )
| ( SV1 != SY73 ) ) )
= $false )
| ( ( r1 @ ( sK5_SY35 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(154,plain,
! [SV1: $i] :
( ( ( ! [SY74: $i] :
~ ~ ( ~ ( r2 @ ( sK12_SY36 @ SV1 ) @ SY74 )
| ( SV1 != SY74 ) ) )
= $false )
| ( ( SV1
= ( sK5_SY35 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(155,plain,
! [SV13: $i,SV10: $i] :
( ( ( ~ ( r1 @ ( sK15_SY71 @ SV10 @ SV13 ) ) )
= $false )
| ( ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ( r3 @ sK1_X1 @ SV13 @ SY72 )
| ( SY72 != SV10 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(156,plain,
! [SV10: $i,SV13: $i] :
( ( ( SV13
!= ( sK15_SY71 @ SV10 @ SV13 ) )
= $false )
| ( ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ( r3 @ sK1_X1 @ SV13 @ SY72 )
| ( SY72 != SV10 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(157,plain,
! [SV2: $i,SV7: $i] :
( ( ~ ~ ! [SY75: $i] :
~ ~ ( ~ ( r2 @ SV7 @ SY75 )
| ~ ( r3 @ SV2 @ SY75 @ ( sK13_SY67 @ SV2 @ SV7 ) ) )
| ( ( sK13_SY67 @ SV2 @ SV7 )
!= ( sK6_SY53 @ SV2 @ SV7 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(158,plain,
! [SV2: $i,SV7: $i] :
( ( ~ ( r2 @ ( sK14_SY69 @ SV7 @ SV2 ) @ ( sK6_SY53 @ SV2 @ SV7 ) )
| ~ ( r3 @ SV2 @ SV7 @ ( sK14_SY69 @ SV7 @ SV2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(159,plain,
! [SV3: $i] :
( ( ~ ( r1 @ ( sK8_SY64 @ SV3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(160,plain,
! [SV3: $i] :
( ( ~ ( r3 @ SV3 @ ( sK8_SY64 @ SV3 ) @ ( sK3_SY43 @ SV3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(161,plain,
! [SV11: $i] :
( ( ( r1 @ SV11 )
= $true )
| ( ( r1 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(162,plain,
! [SV11: $i] :
( ( ( SV11 = sK2_SX0 )
= $true )
| ( ( r1 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(163,plain,
! [SV11: $i] :
( ( ( r1 @ SV11 )
= $true )
| ( ( SV11 = sK2_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(164,plain,
! [SV11: $i] :
( ( ( SV11 = sK2_SX0 )
= $true )
| ( ( SV11 = sK2_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(165,plain,
! [SV14: $i,SV9: $i,SV5: $i] :
( ( ( ~ ( r3 @ SV5 @ SV9 @ SV14 )
| ( SV14
!= ( sK7_SY59 @ SV9 @ SV5 ) ) )
= $false )
| ( ( r3 @ SV5 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(166,plain,
! [SV14: $i,SV9: $i,SV5: $i] :
( ( ( ~ ( r3 @ SV5 @ SV9 @ SV14 )
| ( SV14
!= ( sK7_SY59 @ SV9 @ SV5 ) ) )
= $false )
| ( ( SV14
= ( sK7_SY59 @ SV9 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(167,plain,
! [SV6: $i] :
( ( ~ ( r1 @ ( sK9_SY65 @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(168,plain,
! [SV6: $i] :
( ( ~ ( r4 @ SV6 @ ( sK9_SY65 @ SV6 ) @ ( sK4_SY50 @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(169,plain,
! [SV6: $i] :
( ( ~ ( r1 @ ( sK10_SY66 @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(170,plain,
! [SV6: $i] :
( ( ( sK4_SY50 @ SV6 )
!= ( sK10_SY66 @ SV6 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(171,plain,
! [SV1: $i] :
( ( ( ~ ~ ( ~ ( r2 @ ( sK11_SY36 @ SV1 ) @ ( sK16_SY73 @ SV1 ) )
| ( SV1
!= ( sK16_SY73 @ SV1 ) ) ) )
= $false )
| ( ( r1 @ ( sK5_SY35 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[153]) ).
thf(172,plain,
! [SV1: $i] :
( ( ( ~ ~ ( ~ ( r2 @ ( sK12_SY36 @ SV1 ) @ ( sK17_SY74 @ SV1 ) )
| ( SV1
!= ( sK17_SY74 @ SV1 ) ) ) )
= $false )
| ( ( SV1
= ( sK5_SY35 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[154]) ).
thf(173,plain,
! [SV13: $i,SV10: $i] :
( ( ( r1 @ ( sK15_SY71 @ SV10 @ SV13 ) )
= $true )
| ( ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ( r3 @ sK1_X1 @ SV13 @ SY72 )
| ( SY72 != SV10 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[155]) ).
thf(174,plain,
! [SV10: $i,SV13: $i] :
( ( ( SV13
= ( sK15_SY71 @ SV10 @ SV13 ) )
= $true )
| ( ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ( r3 @ sK1_X1 @ SV13 @ SY72 )
| ( SY72 != SV10 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(175,plain,
! [SV2: $i,SV7: $i] :
( ( ~ ~ ! [SY75: $i] :
~ ~ ( ~ ( r2 @ SV7 @ SY75 )
| ~ ( r3 @ SV2 @ SY75 @ ( sK13_SY67 @ SV2 @ SV7 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(176,plain,
! [SV7: $i,SV2: $i] :
( ( ( sK13_SY67 @ SV2 @ SV7 )
!= ( sK6_SY53 @ SV2 @ SV7 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(177,plain,
! [SV2: $i,SV7: $i] :
( ( ~ ( r2 @ ( sK14_SY69 @ SV7 @ SV2 ) @ ( sK6_SY53 @ SV2 @ SV7 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(178,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ( r3 @ SV2 @ SV7 @ ( sK14_SY69 @ SV7 @ SV2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(179,plain,
! [SV3: $i] :
( ( r1 @ ( sK8_SY64 @ SV3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(180,plain,
! [SV3: $i] :
( ( r3 @ SV3 @ ( sK8_SY64 @ SV3 ) @ ( sK3_SY43 @ SV3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(181,plain,
! [SV14: $i,SV9: $i,SV5: $i] :
( ( ( ~ ( r3 @ SV5 @ SV9 @ SV14 ) )
= $false )
| ( ( r3 @ SV5 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(182,plain,
! [SV5: $i,SV9: $i,SV14: $i] :
( ( ( SV14
!= ( sK7_SY59 @ SV9 @ SV5 ) )
= $false )
| ( ( r3 @ SV5 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(183,plain,
! [SV14: $i,SV9: $i,SV5: $i] :
( ( ( ~ ( r3 @ SV5 @ SV9 @ SV14 ) )
= $false )
| ( ( SV14
= ( sK7_SY59 @ SV9 @ SV5 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(184,plain,
! [SV5: $i,SV9: $i,SV14: $i] :
( ( ( SV14
!= ( sK7_SY59 @ SV9 @ SV5 ) )
= $false )
| ( ( SV14
= ( sK7_SY59 @ SV9 @ SV5 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(185,plain,
! [SV6: $i] :
( ( r1 @ ( sK9_SY65 @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(186,plain,
! [SV6: $i] :
( ( r4 @ SV6 @ ( sK9_SY65 @ SV6 ) @ ( sK4_SY50 @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(187,plain,
! [SV6: $i] :
( ( r1 @ ( sK10_SY66 @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(188,plain,
! [SV6: $i] :
( ( ( sK4_SY50 @ SV6 )
= ( sK10_SY66 @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(189,plain,
! [SV1: $i] :
( ( ( ~ ( ~ ( r2 @ ( sK11_SY36 @ SV1 ) @ ( sK16_SY73 @ SV1 ) )
| ( SV1
!= ( sK16_SY73 @ SV1 ) ) ) )
= $true )
| ( ( r1 @ ( sK5_SY35 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(190,plain,
! [SV1: $i] :
( ( ( ~ ( ~ ( r2 @ ( sK12_SY36 @ SV1 ) @ ( sK17_SY74 @ SV1 ) )
| ( SV1
!= ( sK17_SY74 @ SV1 ) ) ) )
= $true )
| ( ( SV1
= ( sK5_SY35 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(191,plain,
! [SV10: $i,SV13: $i] :
( ( ( ~ ! [SY72: $i] :
~ ~ ( ~ ( r3 @ sK1_X1 @ SV13 @ SY72 )
| ( SY72 != SV10 ) ) )
= $false )
| ( ( r1 @ ( sK15_SY71 @ SV10 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(192,plain,
! [SV10: $i,SV13: $i] :
( ( ( ~ ! [SY72: $i] :
~ ~ ( ~ ( r3 @ sK1_X1 @ SV13 @ SY72 )
| ( SY72 != SV10 ) ) )
= $false )
| ( ( SV13
= ( sK15_SY71 @ SV10 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(193,plain,
! [SV2: $i,SV7: $i] :
( ( ~ ! [SY75: $i] :
~ ~ ( ~ ( r2 @ SV7 @ SY75 )
| ~ ( r3 @ SV2 @ SY75 @ ( sK13_SY67 @ SV2 @ SV7 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(194,plain,
! [SV7: $i,SV2: $i] :
( ( ( sK13_SY67 @ SV2 @ SV7 )
= ( sK6_SY53 @ SV2 @ SV7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(195,plain,
! [SV2: $i,SV7: $i] :
( ( r2 @ ( sK14_SY69 @ SV7 @ SV2 ) @ ( sK6_SY53 @ SV2 @ SV7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(196,plain,
! [SV7: $i,SV2: $i] :
( ( r3 @ SV2 @ SV7 @ ( sK14_SY69 @ SV7 @ SV2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(197,plain,
! [SV14: $i,SV9: $i,SV5: $i] :
( ( ( r3 @ SV5 @ SV9 @ SV14 )
= $true )
| ( ( r3 @ SV5 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(198,plain,
! [SV5: $i,SV9: $i,SV14: $i] :
( ( ( SV14
= ( sK7_SY59 @ SV9 @ SV5 ) )
= $true )
| ( ( r3 @ SV5 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(199,plain,
! [SV14: $i,SV9: $i,SV5: $i] :
( ( ( r3 @ SV5 @ SV9 @ SV14 )
= $true )
| ( ( SV14
= ( sK7_SY59 @ SV9 @ SV5 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(200,plain,
! [SV5: $i,SV9: $i,SV14: $i] :
( ( ( SV14
= ( sK7_SY59 @ SV9 @ SV5 ) )
= $true )
| ( ( SV14
= ( sK7_SY59 @ SV9 @ SV5 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(201,plain,
! [SV1: $i] :
( ( ( ~ ( r2 @ ( sK11_SY36 @ SV1 ) @ ( sK16_SY73 @ SV1 ) )
| ( SV1
!= ( sK16_SY73 @ SV1 ) ) )
= $false )
| ( ( r1 @ ( sK5_SY35 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(202,plain,
! [SV1: $i] :
( ( ( ~ ( r2 @ ( sK12_SY36 @ SV1 ) @ ( sK17_SY74 @ SV1 ) )
| ( SV1
!= ( sK17_SY74 @ SV1 ) ) )
= $false )
| ( ( SV1
= ( sK5_SY35 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(203,plain,
! [SV10: $i,SV13: $i] :
( ( ( ! [SY72: $i] :
~ ~ ( ~ ( r3 @ sK1_X1 @ SV13 @ SY72 )
| ( SY72 != SV10 ) ) )
= $true )
| ( ( r1 @ ( sK15_SY71 @ SV10 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(204,plain,
! [SV10: $i,SV13: $i] :
( ( ( ! [SY72: $i] :
~ ~ ( ~ ( r3 @ sK1_X1 @ SV13 @ SY72 )
| ( SY72 != SV10 ) ) )
= $true )
| ( ( SV13
= ( sK15_SY71 @ SV10 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[192]) ).
thf(205,plain,
! [SV2: $i,SV7: $i] :
( ( ! [SY75: $i] :
~ ~ ( ~ ( r2 @ SV7 @ SY75 )
| ~ ( r3 @ SV2 @ SY75 @ ( sK13_SY67 @ SV2 @ SV7 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(206,plain,
! [SV1: $i] :
( ( ( ~ ( r2 @ ( sK11_SY36 @ SV1 ) @ ( sK16_SY73 @ SV1 ) ) )
= $false )
| ( ( r1 @ ( sK5_SY35 @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(207,plain,
! [SV1: $i] :
( ( ( SV1
!= ( sK16_SY73 @ SV1 ) )
= $false )
| ( ( r1 @ ( sK5_SY35 @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(208,plain,
! [SV1: $i] :
( ( ( ~ ( r2 @ ( sK12_SY36 @ SV1 ) @ ( sK17_SY74 @ SV1 ) ) )
= $false )
| ( ( SV1
= ( sK5_SY35 @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(209,plain,
! [SV1: $i] :
( ( ( SV1
!= ( sK17_SY74 @ SV1 ) )
= $false )
| ( ( SV1
= ( sK5_SY35 @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(210,plain,
! [SV10: $i,SV15: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( r3 @ sK1_X1 @ SV13 @ SV15 )
| ( SV15 != SV10 ) ) )
= $true )
| ( ( r1 @ ( sK15_SY71 @ SV10 @ SV13 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(211,plain,
! [SV10: $i,SV16: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( r3 @ sK1_X1 @ SV13 @ SV16 )
| ( SV16 != SV10 ) ) )
= $true )
| ( ( SV13
= ( sK15_SY71 @ SV10 @ SV13 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(212,plain,
! [SV2: $i,SV7: $i] :
( ( ~ ~ ( ~ ( r2 @ SV7 @ ( sK18_SY75 @ SV2 @ SV7 ) )
| ~ ( r3 @ SV2 @ ( sK18_SY75 @ SV2 @ SV7 ) @ ( sK13_SY67 @ SV2 @ SV7 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[205]) ).
thf(213,plain,
! [SV1: $i] :
( ( ( r2 @ ( sK11_SY36 @ SV1 ) @ ( sK16_SY73 @ SV1 ) )
= $true )
| ( ( r1 @ ( sK5_SY35 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(214,plain,
! [SV1: $i] :
( ( ( SV1
= ( sK16_SY73 @ SV1 ) )
= $true )
| ( ( r1 @ ( sK5_SY35 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(215,plain,
! [SV1: $i] :
( ( ( r2 @ ( sK12_SY36 @ SV1 ) @ ( sK17_SY74 @ SV1 ) )
= $true )
| ( ( SV1
= ( sK5_SY35 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(216,plain,
! [SV1: $i] :
( ( ( SV1
= ( sK17_SY74 @ SV1 ) )
= $true )
| ( ( SV1
= ( sK5_SY35 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(217,plain,
! [SV10: $i,SV15: $i,SV13: $i] :
( ( ( ~ ( ~ ( r3 @ sK1_X1 @ SV13 @ SV15 )
| ( SV15 != SV10 ) ) )
= $false )
| ( ( r1 @ ( sK15_SY71 @ SV10 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(218,plain,
! [SV10: $i,SV16: $i,SV13: $i] :
( ( ( ~ ( ~ ( r3 @ sK1_X1 @ SV13 @ SV16 )
| ( SV16 != SV10 ) ) )
= $false )
| ( ( SV13
= ( sK15_SY71 @ SV10 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(219,plain,
! [SV2: $i,SV7: $i] :
( ( ~ ( ~ ( r2 @ SV7 @ ( sK18_SY75 @ SV2 @ SV7 ) )
| ~ ( r3 @ SV2 @ ( sK18_SY75 @ SV2 @ SV7 ) @ ( sK13_SY67 @ SV2 @ SV7 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(220,plain,
! [SV10: $i,SV15: $i,SV13: $i] :
( ( ( ~ ( r3 @ sK1_X1 @ SV13 @ SV15 )
| ( SV15 != SV10 ) )
= $true )
| ( ( r1 @ ( sK15_SY71 @ SV10 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(221,plain,
! [SV10: $i,SV16: $i,SV13: $i] :
( ( ( ~ ( r3 @ sK1_X1 @ SV13 @ SV16 )
| ( SV16 != SV10 ) )
= $true )
| ( ( SV13
= ( sK15_SY71 @ SV10 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(222,plain,
! [SV2: $i,SV7: $i] :
( ( ~ ( r2 @ SV7 @ ( sK18_SY75 @ SV2 @ SV7 ) )
| ~ ( r3 @ SV2 @ ( sK18_SY75 @ SV2 @ SV7 ) @ ( sK13_SY67 @ SV2 @ SV7 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(223,plain,
! [SV10: $i,SV15: $i,SV13: $i] :
( ( ( ~ ( r3 @ sK1_X1 @ SV13 @ SV15 ) )
= $true )
| ( ( SV15 != SV10 )
= $true )
| ( ( r1 @ ( sK15_SY71 @ SV10 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(224,plain,
! [SV10: $i,SV16: $i,SV13: $i] :
( ( ( ~ ( r3 @ sK1_X1 @ SV13 @ SV16 ) )
= $true )
| ( ( SV16 != SV10 )
= $true )
| ( ( SV13
= ( sK15_SY71 @ SV10 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(225,plain,
! [SV2: $i,SV7: $i] :
( ( ~ ( r2 @ SV7 @ ( sK18_SY75 @ SV2 @ SV7 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(226,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ( r3 @ SV2 @ ( sK18_SY75 @ SV2 @ SV7 ) @ ( sK13_SY67 @ SV2 @ SV7 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(227,plain,
! [SV10: $i,SV15: $i,SV13: $i] :
( ( ( r3 @ sK1_X1 @ SV13 @ SV15 )
= $false )
| ( ( SV15 != SV10 )
= $true )
| ( ( r1 @ ( sK15_SY71 @ SV10 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(228,plain,
! [SV10: $i,SV16: $i,SV13: $i] :
( ( ( r3 @ sK1_X1 @ SV13 @ SV16 )
= $false )
| ( ( SV16 != SV10 )
= $true )
| ( ( SV13
= ( sK15_SY71 @ SV10 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(229,plain,
! [SV2: $i,SV7: $i] :
( ( r2 @ SV7 @ ( sK18_SY75 @ SV2 @ SV7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(230,plain,
! [SV7: $i,SV2: $i] :
( ( r3 @ SV2 @ ( sK18_SY75 @ SV2 @ SV7 ) @ ( sK13_SY67 @ SV2 @ SV7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(231,plain,
! [SV13: $i,SV10: $i,SV15: $i] :
( ( ( SV15 = SV10 )
= $false )
| ( ( r3 @ sK1_X1 @ SV13 @ SV15 )
= $false )
| ( ( r1 @ ( sK15_SY71 @ SV10 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(232,plain,
! [SV13: $i,SV10: $i,SV16: $i] :
( ( ( SV16 = SV10 )
= $false )
| ( ( r3 @ sK1_X1 @ SV13 @ SV16 )
= $false )
| ( ( SV13
= ( sK15_SY71 @ SV10 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(233,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[96,232,231,230,229,216,215,214,213,200,199,198,197,196,195,194,188,187,186,185,180,179,164,163,162,161,111]) ).
thf(234,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[233]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN062+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.20 % Computer : n004.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Oct 6 13:46:39 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.60/0.42
% 0.60/0.42 No.of.Axioms: 7
% 0.60/0.42
% 0.60/0.42 Length.of.Defs: 0
% 0.60/0.42
% 0.60/0.42 Contains.Choice.Funs: false
% 0.60/0.42 ......
% 0.60/0.42
% 0.60/0.42 ********************************
% 0.60/0.42 * All subproblems solved! *
% 0.60/0.42 ********************************
% 0.60/0.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:7,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:233,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.60/0.42
% 0.60/0.42 %**** Beginning of derivation protocol ****
% 0.60/0.42 % SZS output start CNFRefutation
% See solution above
% 0.60/0.43
% 0.60/0.43 %**** End of derivation protocol ****
% 0.60/0.43 %**** no. of clauses in derivation: 230 ****
% 0.60/0.43 %**** clause counter: 233 ****
% 0.60/0.43
% 0.60/0.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:7,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:233,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------