%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : QUA012^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 10:37:04 AM UTC 2026
% Result : Theorem 180.68s 30.50s
% Output : CNFRefutation 180.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 15
% Syntax : Number of formulae : 210 ( 96 unt; 0 typ; 7 def)
% Number of atoms : 1543 ( 824 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 2576 ( 696 ~; 390 |; 6 &;1483 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 272 ( 272 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 30 usr; 7 con; 0-3 aty)
% Number of variables : 488 ( 137 ^; 347 !; 4 ?; 488 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_addition,type,
addition: $i > $i > $i ).
thf(tp_crossmult,type,
crossmult: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_emptyset,type,
emptyset: $i > $o ).
thf(tp_leq,type,
leq: $i > $i > $o ).
thf(tp_multiplication,type,
multiplication: $i > $i > $i ).
thf(tp_one,type,
one: $i ).
thf(tp_sK10_E,type,
sK10_E: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK11_SY22,type,
sK11_SY22: ( ( $i > $o ) > $o ) > $i > $o ).
thf(tp_sK12_SY21,type,
sK12_SY21: ( ( $i > $o ) > $o ) > $i > $o ).
thf(tp_sK13_SY27,type,
sK13_SY27: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK14_SY25,type,
sK14_SY25: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK15_SY23,type,
sK15_SY23: ( $i > $o ) > $i ).
thf(tp_sK16_SY30,type,
sK16_SY30: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK17_SY32,type,
sK17_SY32: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK18_SY34,type,
sK18_SY34: ( $i > $o ) > $i ).
thf(tp_sK1_X,type,
sK1_X: $i > $o ).
thf(tp_sK2_E,type,
sK2_E: $i ).
thf(tp_sK3_E,type,
sK3_E: $i ).
thf(tp_sK4_E,type,
sK4_E: $i ).
thf(tp_sK5_E,type,
sK5_E: ( ( $i > $o ) > $o ) > $i ).
thf(tp_sK6_E,type,
sK6_E: ( ( $i > $o ) > $o ) > $i ).
thf(tp_sK7_E,type,
sK7_E: $i > $i ).
thf(tp_sK8_E,type,
sK8_E: ( $i > $o ) > $i ).
thf(tp_sK9_E,type,
sK9_E: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_singleton,type,
singleton: $i > $i > $o ).
thf(tp_sup,type,
sup: ( $i > $o ) > $i ).
thf(tp_supset,type,
supset: ( ( $i > $o ) > $o ) > $i > $o ).
thf(tp_union,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_unionset,type,
unionset: ( ( $i > $o ) > $o ) > $i > $o ).
thf(tp_zero,type,
zero: $i ).
thf(addition,definition,
( addition
= ( ^ [X: $i,Y: $i] : ( sup @ ( union @ ( singleton @ X ) @ ( singleton @ Y ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_def) ).
thf(crossmult,definition,
( crossmult
= ( ^ [X: $i > $o,Y: $i > $o,A: $i] :
? [X1: $i,Y1: $i] :
( ( X @ X1 )
& ( Y @ Y1 )
& ( A
= ( multiplication @ X1 @ Y1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',crossmult_def) ).
thf(emptyset,definition,
( emptyset
= ( ^ [X: $i] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset_def) ).
thf(singleton,definition,
( singleton
= ( ^ [X: $i,U: $i] : ( U = X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_def) ).
thf(supset,definition,
( supset
= ( ^ [F: ( $i > $o ) > $o,X: $i] :
? [Y: $i > $o] :
( ( F @ Y )
& ( ( sup @ Y )
= X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',supset) ).
thf(union,definition,
( union
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_def) ).
thf(unionset,definition,
( unionset
= ( ^ [F: ( $i > $o ) > $o,X: $i] :
? [Y: $i > $o] :
( ( F @ Y )
& ( Y @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unionset) ).
thf(1,axiom,
! [X: $i] :
( ( multiplication @ one @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_neutral_left) ).
thf(2,axiom,
! [X: $i] :
( ( multiplication @ X @ one )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_neutral_right) ).
thf(3,axiom,
! [X: $i > $o,Y: $i > $o] :
( ( multiplication @ ( sup @ X ) @ ( sup @ Y ) )
= ( sup @ ( crossmult @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_def) ).
thf(4,axiom,
! [X1: $i,X2: $i] :
( ( leq @ X1 @ X2 )
<=> ( ( addition @ X1 @ X2 )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order_def) ).
thf(5,axiom,
! [X: ( $i > $o ) > $o] :
( ( sup @ ( supset @ X ) )
= ( sup @ ( unionset @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sup_set) ).
thf(6,axiom,
! [X: $i] :
( ( sup @ ( singleton @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sup_singleset) ).
thf(7,axiom,
( ( sup @ emptyset )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sup_es) ).
thf(8,conjecture,
! [X: $i > $o] :
( ( multiplication @ zero @ ( sup @ X ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_anni) ).
thf(9,negated_conjecture,
( ( ! [X: $i > $o] :
( ( multiplication @ zero @ ( sup @ X ) )
= zero ) )
= $false ),
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,plain,
( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= zero )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(11,plain,
( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
!= zero )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [X1: $i,X2: $i] :
( ( ( addition @ X1 @ X2 )
!= X2 )
| ( leq @ X1 @ X2 ) )
& ! [X1: $i,X2: $i] :
( ~ ( leq @ X1 @ X2 )
| ( ( addition @ X1 @ X2 )
= X2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(13,plain,
( ( ( sup @ emptyset )
= zero )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(14,plain,
( ( ! [X: $i] :
( ( sup @ ( singleton @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(15,plain,
( ( ! [X: ( $i > $o ) > $o] :
( ( sup @ ( supset @ X ) )
= ( sup @ ( unionset @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(16,plain,
( ( ! [X1: $i,X2: $i] :
( ( ( addition @ X1 @ X2 )
!= X2 )
| ( leq @ X1 @ X2 ) )
& ! [X1: $i,X2: $i] :
( ~ ( leq @ X1 @ X2 )
| ( ( addition @ X1 @ X2 )
= X2 ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(17,plain,
( ( ! [X: $i > $o,Y: $i > $o] :
( ( multiplication @ ( sup @ X ) @ ( sup @ Y ) )
= ( sup @ ( crossmult @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [X: $i] :
( ( multiplication @ X @ one )
= X ) )
= $true ),
inference(copy,[status(thm)],[2]) ).
thf(19,plain,
( ( ! [X: $i] :
( ( multiplication @ one @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[1]) ).
thf(20,plain,
( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
!= zero )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(21,plain,
( ( ( sup
@ ^ [SX0: $i] : $false )
= zero )
= $true ),
inference(unfold_def,[status(thm)],[13,addition,crossmult,emptyset,singleton,supset,union,unionset]) ).
thf(22,plain,
( ( ! [SX0: ( $i > $o ) > $o] :
( ( sup
@ ^ [SX1: $i] :
~ ! [SX2: $i > $o] :
~ ~ ( ~ ( SX0 @ SX2 )
| ( ( sup @ SX2 )
!= SX1 ) ) )
= ( sup
@ ^ [SX1: $i] :
~ ! [SX2: $i > $o] :
~ ~ ( ~ ( SX0 @ SX2 )
| ~ ( SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,addition,crossmult,emptyset,singleton,supset,union,unionset]) ).
thf(23,plain,
( ( ! [SX0: $i] :
( ( sup
@ ^ [SX1: $i] : ( SX1 = SX0 ) )
= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[14,addition,crossmult,emptyset,singleton,supset,union,unionset]) ).
thf(24,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( sup
@ ^ [SX2: $i] :
( ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
!= SX1 )
| ( leq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( sup
@ ^ [SX2: $i] :
( ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,addition,crossmult,emptyset,singleton,supset,union,unionset]) ).
thf(25,plain,
( ( ! [SX0: $i > $o,SX1: $i > $o] :
( ( multiplication @ ( sup @ SX0 ) @ ( sup @ SX1 ) )
= ( sup
@ ^ [SX2: $i] :
~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ( SX0 @ SX3 )
| ~ ( SX1 @ SX4 ) )
| ( SX2
!= ( multiplication @ SX3 @ SX4 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17,addition,crossmult,emptyset,singleton,supset,union,unionset]) ).
thf(26,plain,
! [SV1: $i] :
( ( ( multiplication @ SV1 @ one )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(27,plain,
! [SV2: $i] :
( ( ( multiplication @ one @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(28,plain,
( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= zero )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(29,plain,
! [SV3: ( $i > $o ) > $o] :
( ( ( sup
@ ^ [SY0: $i] :
~ ! [SY1: $i > $o] :
~ ~ ( ~ ( SV3 @ SY1 )
| ( ( sup @ SY1 )
!= SY0 ) ) )
= ( sup
@ ^ [SY2: $i] :
~ ! [SY3: $i > $o] :
~ ~ ( ~ ( SV3 @ SY3 )
| ~ ( SY3 @ SY2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(30,plain,
! [SV4: $i] :
( ( ( sup
@ ^ [SY4: $i] : ( SY4 = SV4 ) )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(31,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( sup
@ ^ [SX2: $i] :
( ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
!= SX1 )
| ( leq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( sup
@ ^ [SX2: $i] :
( ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(32,plain,
! [SV5: $i > $o] :
( ( ! [SY5: $i > $o] :
( ( multiplication @ ( sup @ SV5 ) @ ( sup @ SY5 ) )
= ( sup
@ ^ [SY6: $i] :
~ ! [SY7: $i] :
~ ~ ! [SY8: $i] :
~ ~ ( ~ ~ ( ~ ( SV5 @ SY7 )
| ~ ( SY5 @ SY8 ) )
| ( SY6
!= ( multiplication @ SY7 @ SY8 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(33,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( sup
@ ^ [SX2: $i] :
( ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(34,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( sup
@ ^ [SX2: $i] :
( ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(35,plain,
! [SV6: $i > $o,SV5: $i > $o] :
( ( ( multiplication @ ( sup @ SV5 ) @ ( sup @ SV6 ) )
= ( sup
@ ^ [SY9: $i] :
~ ! [SY10: $i] :
~ ~ ! [SY11: $i] :
~ ~ ( ~ ~ ( ~ ( SV5 @ SY10 )
| ~ ( SV6 @ SY11 ) )
| ( SY9
!= ( multiplication @ SY10 @ SY11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(36,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( sup
@ ^ [SX2: $i] :
( ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
!= SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(37,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( ( sup
@ ^ [SX2: $i] :
( ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(38,plain,
! [SV7: $i] :
( ( ! [SY12: $i] :
( ( ( sup
@ ^ [SY13: $i] :
( ( SY13 = SV7 )
| ( SY13 = SY12 ) ) )
!= SY12 )
| ( leq @ SV7 @ SY12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV8: $i] :
( ( ! [SY14: $i] :
( ~ ( leq @ SV8 @ SY14 )
| ( ( sup
@ ^ [SY15: $i] :
( ( SY15 = SV8 )
| ( SY15 = SY14 ) ) )
= SY14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV9: $i,SV7: $i] :
( ( ( ( sup
@ ^ [SY16: $i] :
( ( SY16 = SV7 )
| ( SY16 = SV9 ) ) )
!= SV9 )
| ( leq @ SV7 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV10: $i,SV8: $i] :
( ( ~ ( leq @ SV8 @ SV10 )
| ( ( sup
@ ^ [SY17: $i] :
( ( SY17 = SV8 )
| ( SY17 = SV10 ) ) )
= SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV9: $i,SV7: $i] :
( ( ( ( sup
@ ^ [SY16: $i] :
( ( SY16 = SV7 )
| ( SY16 = SV9 ) ) )
!= SV9 )
= $true )
| ( ( leq @ SV7 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(43,plain,
! [SV10: $i,SV8: $i] :
( ( ( ~ ( leq @ SV8 @ SV10 ) )
= $true )
| ( ( ( sup
@ ^ [SY17: $i] :
( ( SY17 = SV8 )
| ( SY17 = SV10 ) ) )
= SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(44,plain,
! [SV9: $i,SV7: $i] :
( ( ( ( sup
@ ^ [SY16: $i] :
( ( SY16 = SV7 )
| ( SY16 = SV9 ) ) )
= SV9 )
= $false )
| ( ( leq @ SV7 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV10: $i,SV8: $i] :
( ( ( leq @ SV8 @ SV10 )
= $false )
| ( ( ( sup
@ ^ [SY17: $i] :
( ( SY17 = SV8 )
| ( SY17 = SV10 ) ) )
= SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(46,plain,
! [SV11: $i] :
( ( ( multiplication @ SV11 @ one )
= SV11 )
= $true ),
inference(rename,[status(thm)],[26]) ).
thf(47,plain,
! [SV12: $i] :
( ( ( multiplication @ one @ SV12 )
= SV12 )
= $true ),
inference(rename,[status(thm)],[27]) ).
thf(48,plain,
! [SV12: $i] :
( ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= zero )
= ( ( multiplication @ one @ SV12 )
= SV12 ) )
= $false ),
inference(res,[status(thm)],[28,47]) ).
thf(49,plain,
! [SV11: $i] :
( ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= zero )
= ( ( multiplication @ SV11 @ one )
= SV11 ) )
= $false ),
inference(res,[status(thm)],[28,46]) ).
thf(50,plain,
( ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= zero )
= ( ( sup
@ ^ [SX0: $i] : $false )
= zero ) )
= $false ),
inference(res,[status(thm)],[28,21]) ).
thf(51,plain,
( ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= zero )
= $false )
| ( ( zero
= ( sup
@ ^ [SX0: $i] : $false ) )
= $false ) ),
inference(extuni,[status(esa)],[50]) ).
thf(52,plain,
( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] : $false ) )
= $false ),
inference(extuni,[status(esa)],[50]) ).
thf(53,plain,
( ( zero
= ( multiplication @ ( multiplication @ zero @ ( sup @ sK1_X ) ) @ one ) )
= $false ),
inference(extuni,[status(esa)],[49:[bind(SV11,$thf( multiplication @ zero @ ( sup @ sK1_X ) ))]]) ).
thf(54,plain,
( ( ( sup @ sK1_X )
= one )
= $false ),
inference(extuni,[status(esa)],[49:[bind(SV11,$thf( zero ))]]) ).
thf(55,plain,
( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication @ zero @ one ) )
= $false ),
inference(extuni,[status(esa)],[49:[bind(SV11,$thf( zero ))]]) ).
thf(56,plain,
( ( zero
= ( multiplication @ one @ ( multiplication @ zero @ ( sup @ sK1_X ) ) ) )
= $false ),
inference(extuni,[status(esa)],[48:[bind(SV12,$thf( multiplication @ zero @ ( sup @ sK1_X ) ))]]) ).
thf(57,plain,
( ( ( zero
= ( sup @ sK1_X ) )
= $false )
| ( ( zero = one )
= $false ) ),
inference(extuni,[status(esa)],[48:[bind(SV12,$thf( sup @ sK1_X ))]]) ).
thf(58,plain,
( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication @ one @ zero ) )
= $false ),
inference(extuni,[status(esa)],[48:[bind(SV12,$thf( zero ))]]) ).
thf(59,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ( ( sup @ SX1 )
!= SX0 ) ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ~ ( SX1 @ SX0 ) ) ) )
= $true ),
inference(rename,[status(thm)],[29]) ).
thf(60,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ( ( sup @ SX1 )
!= SX0 ) ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ~ ( SX1 @ SX0 ) ) ) )
= ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= zero ) )
= $false ),
inference(res,[status(thm)],[59,28]) ).
thf(61,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ( ( sup @ SX1 )
!= SX0 ) ) )
= zero )
= $false )
| ( ( ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ~ ( SX1 @ SX0 ) ) )
= ( multiplication @ zero @ ( sup @ sK1_X ) ) )
= $false ) ),
inference(extuni,[status(esa)],[60]) ).
thf(62,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ~ ( SX1 @ SX0 ) ) )
= zero )
= $false )
| ( ( ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ( ( sup @ SX1 )
!= SX0 ) ) )
= ( multiplication @ zero @ ( sup @ sK1_X ) ) )
= $false ) ),
inference(extuni,[status(esa)],[60]) ).
thf(63,plain,
! [SV14: $i] :
( ( ( sup
@ ^ [SX0: $i] : ( SX0 = SV14 ) )
= SV14 )
= $true ),
inference(rename,[status(thm)],[30]) ).
thf(64,plain,
! [SV14: $i] :
( ( ( ( sup
@ ^ [SX0: $i] : ( SX0 = SV14 ) )
= SV14 )
= ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= zero ) )
= $false ),
inference(res,[status(thm)],[63,28]) ).
thf(65,plain,
( ( ( sup
@ ^ [SX0: $i] :
( SX0
= ( multiplication @ zero @ ( sup @ sK1_X ) ) ) )
= zero )
= $false ),
inference(extuni,[status(esa)],[64:[bind(SV14,$thf( multiplication @ zero @ ( sup @ sK1_X ) ))]]) ).
thf(66,plain,
( ( ( sup
@ ^ [SX0: $i] : ( SX0 = zero ) )
= ( multiplication @ zero @ ( sup @ sK1_X ) ) )
= $false ),
inference(extuni,[status(esa)],[64:[bind(SV14,$thf( zero ))]]) ).
thf(67,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ SX1 )
| ~ ( SV15 @ SX2 ) )
| ( SX0
!= ( multiplication @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(rename,[status(thm)],[35]) ).
thf(68,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ SX1 )
| ~ ( SV15 @ SX2 ) )
| ( SX0
!= ( multiplication @ SX1 @ SX2 ) ) ) ) )
= ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= zero ) )
= $false ),
inference(res,[status(thm)],[67,28]) ).
thf(69,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) )
= zero )
= $false )
| ( ( ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ SX1 )
| ~ ( SV15 @ SX2 ) )
| ( SX0
!= ( multiplication @ SX1 @ SX2 ) ) ) )
= ( multiplication @ zero @ ( sup @ sK1_X ) ) )
= $false ) ),
inference(extuni,[status(esa)],[68]) ).
thf(70,plain,
! [SV16: $i > $o] :
( ( ( ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ SX1 )
| ~ ( sK1_X @ SX2 ) )
| ( SX0
!= ( multiplication @ SX1 @ SX2 ) ) ) )
= zero )
= $false )
| ( ( ( sup @ SV16 )
= zero )
= $false ) ),
inference(extuni,[status(esa)],[68:[bind(SV15,$thf( sK1_X ))]]) ).
thf(71,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ SX1 )
| ~ ( SV15 @ SX2 ) )
| ( SX0
!= ( multiplication @ SX1 @ SX2 ) ) ) )
= zero )
= $false )
| ( ( ( sup @ SV15 )
= ( sup @ sK1_X ) )
= $false )
| ( ( ( sup @ SV16 )
= zero )
= $false ) ),
inference(extuni,[status(esa)],[68]) ).
thf(72,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ SX1 )
| ~ ( SV15 @ SX2 ) )
| ( SX0
!= ( multiplication @ SX1 @ SX2 ) ) ) )
= zero )
= $false )
| ( ( ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) )
= ( multiplication @ zero @ ( sup @ sK1_X ) ) )
= $false ) ),
inference(extuni,[status(esa)],[68]) ).
thf(73,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] : $false ) )
= ( ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ SX1 )
| ~ ( SV15 @ SX2 ) )
| ( SX0
!= ( multiplication @ SX1 @ SX2 ) ) ) ) ) )
= $false ),
inference(res,[status(thm)],[52,67]) ).
thf(74,plain,
! [SV14: $i] :
( ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] : $false ) )
= ( ( sup
@ ^ [SX0: $i] : ( SX0 = SV14 ) )
= SV14 ) )
= $false ),
inference(res,[status(thm)],[52,63]) ).
thf(75,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] : $false ) )
= ( ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ( ( sup @ SX1 )
!= SX0 ) ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ~ ( SX1 @ SX0 ) ) ) ) )
= $false ),
inference(res,[status(thm)],[52,59]) ).
thf(76,plain,
! [SV12: $i] :
( ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] : $false ) )
= ( ( multiplication @ one @ SV12 )
= SV12 ) )
= $false ),
inference(res,[status(thm)],[52,47]) ).
thf(77,plain,
! [SV11: $i] :
( ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] : $false ) )
= ( ( multiplication @ SV11 @ one )
= SV11 ) )
= $false ),
inference(res,[status(thm)],[52,46]) ).
thf(78,plain,
( ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] : $false ) )
= ( ( sup
@ ^ [SX0: $i] : $false )
= zero ) )
= $false ),
inference(res,[status(thm)],[52,21]) ).
thf(79,plain,
( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= zero )
= $false ),
inference(extuni,[status(esa)],[78]) ).
thf(80,plain,
( ( ( ( sup
@ ^ [SX0: $i] : $false )
= zero )
= $false )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] : $false ) )
= $false ) ),
inference(extuni,[status(esa)],[78]) ).
thf(81,plain,
( ( ( sup
@ ^ [SX0: $i] : $false )
= ( multiplication @ ( multiplication @ zero @ ( sup @ sK1_X ) ) @ one ) )
= $false ),
inference(extuni,[status(esa)],[77:[bind(SV11,$thf( multiplication @ zero @ ( sup @ sK1_X ) ))]]) ).
thf(82,plain,
( ( ( ( sup
@ ^ [SX0: $i] : $false )
= zero )
= $false )
| ( ( ( sup @ sK1_X )
= one )
= $false ) ),
inference(extuni,[status(esa)],[77:[bind(SV11,$thf( zero ))]]) ).
thf(83,plain,
( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication
@ ( sup
@ ^ [SX0: $i] : $false )
@ one ) )
= $false ),
inference(extuni,[status(esa)],[77:[bind(SV11,$thf( sup @ ^ [SX0: $i] : $false ))]]) ).
thf(84,plain,
( ( ( sup
@ ^ [SX0: $i] : $false )
= ( multiplication @ one @ ( multiplication @ zero @ ( sup @ sK1_X ) ) ) )
= $false ),
inference(extuni,[status(esa)],[76:[bind(SV12,$thf( multiplication @ zero @ ( sup @ sK1_X ) ))]]) ).
thf(85,plain,
( ( $false = $true )
| ( ( sK1_X @ sK4_E )
= $true )
| ( ( zero = one )
= $false ) ),
inference(extuni,[status(esa)],[76:[bind(SV12,$thf( sup @ sK1_X ))]]) ).
thf(87,plain,
( ( ( ( sup
@ ^ [SX0: $i] : $false )
= ( sup @ sK1_X ) )
= $false )
| ( ( zero = one )
= $false ) ),
inference(extuni,[status(esa)],[76:[bind(SV12,$thf( sup @ sK1_X ))]]) ).
thf(88,plain,
( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication @ one
@ ( sup
@ ^ [SX0: $i] : $false ) ) )
= $false ),
inference(extuni,[status(esa)],[76:[bind(SV12,$thf( sup @ ^ [SX0: $i] : $false ))]]) ).
thf(89,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ~ ( SX1 @ SX0 ) ) ) )
= $false )
| ( $false = $true )
| ( ( ~ ! [SY21: $i > $o] :
~ ~ ( ~ ( SV13 @ SY21 )
| ( ( sup @ SY21 )
!= ( sK5_E @ SV13 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[75]) ).
thf(91,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ~ ( SX1 @ SX0 ) ) ) )
= $false )
| ( ( ( sup
@ ^ [SX0: $i] : $false )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ( ( sup @ SX1 )
!= SX0 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[75]) ).
thf(92,plain,
! [SV13: ( $i > $o ) > $o] :
( ( $false = $true )
| ( ( ~ ! [SY22: $i > $o] :
~ ~ ( ~ ( SV13 @ SY22 )
| ~ ( SY22 @ ( sK6_E @ SV13 ) ) ) )
= $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ( ( sup @ SX1 )
!= SX0 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[75]) ).
thf(94,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( ( sup
@ ^ [SX0: $i] : $false )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ~ ( SX1 @ SX0 ) ) ) )
= $false )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ( ( sup @ SX1 )
!= SX0 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[75]) ).
thf(95,plain,
( ( $false = $true )
| ( ( ( sK7_E @ ( multiplication @ zero @ ( sup @ sK1_X ) ) )
= ( multiplication @ zero @ ( sup @ sK1_X ) ) )
= $true ) ),
inference(extuni,[status(esa)],[74:[bind(SV14,$thf( multiplication @ zero @ ( sup @ sK1_X ) ))]]) ).
thf(97,plain,
( ( ( sup
@ ^ [SX0: $i] : $false )
= ( sup
@ ^ [SX0: $i] :
( SX0
= ( multiplication @ zero @ ( sup @ sK1_X ) ) ) ) )
= $false ),
inference(extuni,[status(esa)],[74:[bind(SV14,$thf( multiplication @ zero @ ( sup @ sK1_X ) ))]]) ).
thf(98,plain,
( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
( SX0
= ( sup
@ ^ [SX1: $i] : $false ) ) ) )
= $false ),
inference(extuni,[status(esa)],[74:[bind(SV14,$thf( sup @ ^ [SX0: $i] : $false ))]]) ).
thf(99,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ SX1 )
| ~ ( SV15 @ SX2 ) )
| ( SX0
!= ( multiplication @ SX1 @ SX2 ) ) ) ) )
= $false )
| ( ( ( sup
@ ^ [SX0: $i] : $false )
= ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[73]) ).
thf(100,plain,
! [SV16: $i > $o] :
( ( $false = $true )
| ( ( ~ ! [SY23: $i] :
~ ~ ! [SY24: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ SY23 )
| ~ ( sK1_X @ SY24 ) )
| ( ( sK8_E @ SV16 )
!= ( multiplication @ SY23 @ SY24 ) ) ) )
= $true )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extuni,[status(esa)],[73:[bind(SV15,$thf( sK1_X ))]]) ).
thf(102,plain,
! [SV16: $i > $o] :
( ( ( ( sup
@ ^ [SX0: $i] : $false )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ SX1 )
| ~ ( sK1_X @ SX2 ) )
| ( SX0
!= ( multiplication @ SX1 @ SX2 ) ) ) ) )
= $false )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extuni,[status(esa)],[73:[bind(SV15,$thf( sK1_X ))]]) ).
thf(103,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( $false = $true )
| ( ( ~ ! [SY25: $i] :
~ ~ ! [SY26: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ SY25 )
| ~ ( SV15 @ SY26 ) )
| ( ( sK9_E @ SV15 @ SV16 )
!= ( multiplication @ SY25 @ SY26 ) ) ) )
= $true )
| ( ( ( sup @ sK1_X )
= ( sup @ SV15 ) )
= $false )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extuni,[status(esa)],[73]) ).
thf(105,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ( sup
@ ^ [SX0: $i] : $false )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ SX1 )
| ~ ( SV15 @ SX2 ) )
| ( SX0
!= ( multiplication @ SX1 @ SX2 ) ) ) ) )
= $false )
| ( ( ( sup @ sK1_X )
= ( sup @ SV15 ) )
= $false )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extuni,[status(esa)],[73]) ).
thf(106,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( $false = $true )
| ( ( ~ ! [SY27: $i] :
~ ~ ! [SY28: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ SY27 )
| ~ ( SV15 @ SY28 ) )
| ( ( sK10_E @ SV15 @ SV16 )
!= ( multiplication @ SY27 @ SY28 ) ) ) )
= $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[73]) ).
thf(108,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ( sup
@ ^ [SX0: $i] : $false )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ SX1 )
| ~ ( SV15 @ SX2 ) )
| ( SX0
!= ( multiplication @ SX1 @ SX2 ) ) ) ) )
= $false )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[73]) ).
thf(110,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( ! [SY22: $i > $o] :
~ ~ ( ~ ( SV13 @ SY22 )
| ~ ( SY22 @ ( sK6_E @ SV13 ) ) ) )
= $false )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ( ( sup @ SX1 )
!= SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(112,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( ! [SY21: $i > $o] :
~ ~ ( ~ ( SV13 @ SY21 )
| ( ( sup @ SY21 )
!= ( sK5_E @ SV13 ) ) ) )
= $false )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ~ ( SX1 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(114,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ! [SY27: $i] :
~ ~ ! [SY28: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ SY27 )
| ~ ( SV15 @ SY28 ) )
| ( ( sK10_E @ SV15 @ SV16 )
!= ( multiplication @ SY27 @ SY28 ) ) ) )
= $false )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(116,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ! [SY25: $i] :
~ ~ ! [SY26: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ SY25 )
| ~ ( SV15 @ SY26 ) )
| ( ( sK9_E @ SV15 @ SV16 )
!= ( multiplication @ SY25 @ SY26 ) ) ) )
= $false )
| ( $false = $true )
| ( ( ( sup @ sK1_X )
= ( sup @ SV15 ) )
= $false )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(118,plain,
! [SV16: $i > $o] :
( ( ( ! [SY23: $i] :
~ ~ ! [SY24: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ SY23 )
| ~ ( sK1_X @ SY24 ) )
| ( ( sK8_E @ SV16 )
!= ( multiplication @ SY23 @ SY24 ) ) ) )
= $false )
| ( $false = $true )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(120,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( ~ ~ ( ~ ( SV13 @ ( sK11_SY22 @ SV13 ) )
| ~ ( sK11_SY22 @ SV13 @ ( sK6_E @ SV13 ) ) ) )
= $false )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ( ( sup @ SX1 )
!= SX0 ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[110]) ).
thf(122,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( ~ ~ ( ~ ( SV13 @ ( sK12_SY21 @ SV13 ) )
| ( ( sup @ ( sK12_SY21 @ SV13 ) )
!= ( sK5_E @ SV13 ) ) ) )
= $false )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ~ ( SX1 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[112]) ).
thf(124,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ~ ~ ! [SY30: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ ( sK13_SY27 @ SV15 @ SV16 ) )
| ~ ( SV15 @ SY30 ) )
| ( ( sK10_E @ SV15 @ SV16 )
!= ( multiplication @ ( sK13_SY27 @ SV15 @ SV16 ) @ SY30 ) ) ) )
= $false )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[114]) ).
thf(126,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ~ ~ ! [SY32: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ ( sK14_SY25 @ SV15 @ SV16 ) )
| ~ ( SV15 @ SY32 ) )
| ( ( sK9_E @ SV15 @ SV16 )
!= ( multiplication @ ( sK14_SY25 @ SV15 @ SV16 ) @ SY32 ) ) ) )
= $false )
| ( $false = $true )
| ( ( ( sup @ sK1_X )
= ( sup @ SV15 ) )
= $false )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[116]) ).
thf(128,plain,
! [SV16: $i > $o] :
( ( ( ~ ~ ! [SY34: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ ( sK15_SY23 @ SV16 ) )
| ~ ( sK1_X @ SY34 ) )
| ( ( sK8_E @ SV16 )
!= ( multiplication @ ( sK15_SY23 @ SV16 ) @ SY34 ) ) ) )
= $false )
| ( $false = $true )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[118]) ).
thf(130,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( ~ ( ~ ( SV13 @ ( sK11_SY22 @ SV13 ) )
| ~ ( sK11_SY22 @ SV13 @ ( sK6_E @ SV13 ) ) ) )
= $true )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ( ( sup @ SX1 )
!= SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(132,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( ~ ( ~ ( SV13 @ ( sK12_SY21 @ SV13 ) )
| ( ( sup @ ( sK12_SY21 @ SV13 ) )
!= ( sK5_E @ SV13 ) ) ) )
= $true )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ~ ( SX1 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(134,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ~ ! [SY30: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ ( sK13_SY27 @ SV15 @ SV16 ) )
| ~ ( SV15 @ SY30 ) )
| ( ( sK10_E @ SV15 @ SV16 )
!= ( multiplication @ ( sK13_SY27 @ SV15 @ SV16 ) @ SY30 ) ) ) )
= $true )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(136,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ~ ! [SY32: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ ( sK14_SY25 @ SV15 @ SV16 ) )
| ~ ( SV15 @ SY32 ) )
| ( ( sK9_E @ SV15 @ SV16 )
!= ( multiplication @ ( sK14_SY25 @ SV15 @ SV16 ) @ SY32 ) ) ) )
= $true )
| ( $false = $true )
| ( ( ( sup @ sK1_X )
= ( sup @ SV15 ) )
= $false )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(138,plain,
! [SV16: $i > $o] :
( ( ( ~ ! [SY34: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ ( sK15_SY23 @ SV16 ) )
| ~ ( sK1_X @ SY34 ) )
| ( ( sK8_E @ SV16 )
!= ( multiplication @ ( sK15_SY23 @ SV16 ) @ SY34 ) ) ) )
= $true )
| ( $false = $true )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(140,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( ~ ( SV13 @ ( sK11_SY22 @ SV13 ) )
| ~ ( sK11_SY22 @ SV13 @ ( sK6_E @ SV13 ) ) )
= $false )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ( ( sup @ SX1 )
!= SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(142,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( ~ ( SV13 @ ( sK12_SY21 @ SV13 ) )
| ( ( sup @ ( sK12_SY21 @ SV13 ) )
!= ( sK5_E @ SV13 ) ) )
= $false )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ~ ( SX1 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(144,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ! [SY30: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ ( sK13_SY27 @ SV15 @ SV16 ) )
| ~ ( SV15 @ SY30 ) )
| ( ( sK10_E @ SV15 @ SV16 )
!= ( multiplication @ ( sK13_SY27 @ SV15 @ SV16 ) @ SY30 ) ) ) )
= $false )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(146,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ! [SY32: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ ( sK14_SY25 @ SV15 @ SV16 ) )
| ~ ( SV15 @ SY32 ) )
| ( ( sK9_E @ SV15 @ SV16 )
!= ( multiplication @ ( sK14_SY25 @ SV15 @ SV16 ) @ SY32 ) ) ) )
= $false )
| ( $false = $true )
| ( ( ( sup @ sK1_X )
= ( sup @ SV15 ) )
= $false )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(148,plain,
! [SV16: $i > $o] :
( ( ( ! [SY34: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ ( sK15_SY23 @ SV16 ) )
| ~ ( sK1_X @ SY34 ) )
| ( ( sK8_E @ SV16 )
!= ( multiplication @ ( sK15_SY23 @ SV16 ) @ SY34 ) ) ) )
= $false )
| ( $false = $true )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(150,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( ~ ( SV13 @ ( sK11_SY22 @ SV13 ) ) )
= $false )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ( ( sup @ SX1 )
!= SX0 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(151,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( ~ ( sK11_SY22 @ SV13 @ ( sK6_E @ SV13 ) ) )
= $false )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ( ( sup @ SX1 )
!= SX0 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(153,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( ~ ( SV13 @ ( sK12_SY21 @ SV13 ) ) )
= $false )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ~ ( SX1 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(154,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( ( sup @ ( sK12_SY21 @ SV13 ) )
!= ( sK5_E @ SV13 ) )
= $false )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ~ ( SX1 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(156,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ~ ~ ( ~ ~ ( ~ ( SV16 @ ( sK13_SY27 @ SV15 @ SV16 ) )
| ~ ( SV15 @ ( sK16_SY30 @ SV15 @ SV16 ) ) )
| ( ( sK10_E @ SV15 @ SV16 )
!= ( multiplication @ ( sK13_SY27 @ SV15 @ SV16 ) @ ( sK16_SY30 @ SV15 @ SV16 ) ) ) ) )
= $false )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[144]) ).
thf(158,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ~ ~ ( ~ ~ ( ~ ( SV16 @ ( sK14_SY25 @ SV15 @ SV16 ) )
| ~ ( SV15 @ ( sK17_SY32 @ SV15 @ SV16 ) ) )
| ( ( sK9_E @ SV15 @ SV16 )
!= ( multiplication @ ( sK14_SY25 @ SV15 @ SV16 ) @ ( sK17_SY32 @ SV15 @ SV16 ) ) ) ) )
= $false )
| ( $false = $true )
| ( ( ( sup @ sK1_X )
= ( sup @ SV15 ) )
= $false )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[146]) ).
thf(160,plain,
! [SV16: $i > $o] :
( ( ( ~ ~ ( ~ ~ ( ~ ( SV16 @ ( sK15_SY23 @ SV16 ) )
| ~ ( sK1_X @ ( sK18_SY34 @ SV16 ) ) )
| ( ( sK8_E @ SV16 )
!= ( multiplication @ ( sK15_SY23 @ SV16 ) @ ( sK18_SY34 @ SV16 ) ) ) ) )
= $false )
| ( $false = $true )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[148]) ).
thf(162,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( SV13 @ ( sK11_SY22 @ SV13 ) )
= $true )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ( ( sup @ SX1 )
!= SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(163,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( sK11_SY22 @ SV13 @ ( sK6_E @ SV13 ) )
= $true )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ( ( sup @ SX1 )
!= SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(165,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( SV13 @ ( sK12_SY21 @ SV13 ) )
= $true )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ~ ( SX1 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(166,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( ( sup @ ( sK12_SY21 @ SV13 ) )
= ( sK5_E @ SV13 ) )
= $true )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ~ ( SX1 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(168,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ~ ( ~ ~ ( ~ ( SV16 @ ( sK13_SY27 @ SV15 @ SV16 ) )
| ~ ( SV15 @ ( sK16_SY30 @ SV15 @ SV16 ) ) )
| ( ( sK10_E @ SV15 @ SV16 )
!= ( multiplication @ ( sK13_SY27 @ SV15 @ SV16 ) @ ( sK16_SY30 @ SV15 @ SV16 ) ) ) ) )
= $true )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(170,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ~ ( ~ ~ ( ~ ( SV16 @ ( sK14_SY25 @ SV15 @ SV16 ) )
| ~ ( SV15 @ ( sK17_SY32 @ SV15 @ SV16 ) ) )
| ( ( sK9_E @ SV15 @ SV16 )
!= ( multiplication @ ( sK14_SY25 @ SV15 @ SV16 ) @ ( sK17_SY32 @ SV15 @ SV16 ) ) ) ) )
= $true )
| ( $false = $true )
| ( ( ( sup @ sK1_X )
= ( sup @ SV15 ) )
= $false )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(172,plain,
! [SV16: $i > $o] :
( ( ( ~ ( ~ ~ ( ~ ( SV16 @ ( sK15_SY23 @ SV16 ) )
| ~ ( sK1_X @ ( sK18_SY34 @ SV16 ) ) )
| ( ( sK8_E @ SV16 )
!= ( multiplication @ ( sK15_SY23 @ SV16 ) @ ( sK18_SY34 @ SV16 ) ) ) ) )
= $true )
| ( $false = $true )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(176,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ~ ~ ( ~ ( SV16 @ ( sK13_SY27 @ SV15 @ SV16 ) )
| ~ ( SV15 @ ( sK16_SY30 @ SV15 @ SV16 ) ) )
| ( ( sK10_E @ SV15 @ SV16 )
!= ( multiplication @ ( sK13_SY27 @ SV15 @ SV16 ) @ ( sK16_SY30 @ SV15 @ SV16 ) ) ) )
= $false )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(178,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ~ ~ ( ~ ( SV16 @ ( sK14_SY25 @ SV15 @ SV16 ) )
| ~ ( SV15 @ ( sK17_SY32 @ SV15 @ SV16 ) ) )
| ( ( sK9_E @ SV15 @ SV16 )
!= ( multiplication @ ( sK14_SY25 @ SV15 @ SV16 ) @ ( sK17_SY32 @ SV15 @ SV16 ) ) ) )
= $false )
| ( $false = $true )
| ( ( ( sup @ sK1_X )
= ( sup @ SV15 ) )
= $false )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(180,plain,
! [SV16: $i > $o] :
( ( ( ~ ~ ( ~ ( SV16 @ ( sK15_SY23 @ SV16 ) )
| ~ ( sK1_X @ ( sK18_SY34 @ SV16 ) ) )
| ( ( sK8_E @ SV16 )
!= ( multiplication @ ( sK15_SY23 @ SV16 ) @ ( sK18_SY34 @ SV16 ) ) ) )
= $false )
| ( $false = $true )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(182,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ~ ~ ( ~ ( SV16 @ ( sK13_SY27 @ SV15 @ SV16 ) )
| ~ ( SV15 @ ( sK16_SY30 @ SV15 @ SV16 ) ) ) )
= $false )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(183,plain,
! [SV16: $i > $o,SV15: $i > $o] :
( ( ( ( sK10_E @ SV15 @ SV16 )
!= ( multiplication @ ( sK13_SY27 @ SV15 @ SV16 ) @ ( sK16_SY30 @ SV15 @ SV16 ) ) )
= $false )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(185,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ~ ~ ( ~ ( SV16 @ ( sK14_SY25 @ SV15 @ SV16 ) )
| ~ ( SV15 @ ( sK17_SY32 @ SV15 @ SV16 ) ) ) )
= $false )
| ( $false = $true )
| ( ( ( sup @ sK1_X )
= ( sup @ SV15 ) )
= $false )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(186,plain,
! [SV16: $i > $o,SV15: $i > $o] :
( ( ( ( sK9_E @ SV15 @ SV16 )
!= ( multiplication @ ( sK14_SY25 @ SV15 @ SV16 ) @ ( sK17_SY32 @ SV15 @ SV16 ) ) )
= $false )
| ( $false = $true )
| ( ( ( sup @ sK1_X )
= ( sup @ SV15 ) )
= $false )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(188,plain,
! [SV16: $i > $o] :
( ( ( ~ ~ ( ~ ( SV16 @ ( sK15_SY23 @ SV16 ) )
| ~ ( sK1_X @ ( sK18_SY34 @ SV16 ) ) ) )
= $false )
| ( $false = $true )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(189,plain,
! [SV16: $i > $o] :
( ( ( ( sK8_E @ SV16 )
!= ( multiplication @ ( sK15_SY23 @ SV16 ) @ ( sK18_SY34 @ SV16 ) ) )
= $false )
| ( $false = $true )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(191,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ~ ( ~ ( SV16 @ ( sK13_SY27 @ SV15 @ SV16 ) )
| ~ ( SV15 @ ( sK16_SY30 @ SV15 @ SV16 ) ) ) )
= $true )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(192,plain,
! [SV16: $i > $o,SV15: $i > $o] :
( ( ( ( sK10_E @ SV15 @ SV16 )
= ( multiplication @ ( sK13_SY27 @ SV15 @ SV16 ) @ ( sK16_SY30 @ SV15 @ SV16 ) ) )
= $true )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(194,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ~ ( ~ ( SV16 @ ( sK14_SY25 @ SV15 @ SV16 ) )
| ~ ( SV15 @ ( sK17_SY32 @ SV15 @ SV16 ) ) ) )
= $true )
| ( $false = $true )
| ( ( ( sup @ sK1_X )
= ( sup @ SV15 ) )
= $false )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(195,plain,
! [SV16: $i > $o,SV15: $i > $o] :
( ( ( ( sK9_E @ SV15 @ SV16 )
= ( multiplication @ ( sK14_SY25 @ SV15 @ SV16 ) @ ( sK17_SY32 @ SV15 @ SV16 ) ) )
= $true )
| ( $false = $true )
| ( ( ( sup @ sK1_X )
= ( sup @ SV15 ) )
= $false )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(197,plain,
! [SV16: $i > $o] :
( ( ( ~ ( ~ ( SV16 @ ( sK15_SY23 @ SV16 ) )
| ~ ( sK1_X @ ( sK18_SY34 @ SV16 ) ) ) )
= $true )
| ( $false = $true )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(198,plain,
! [SV16: $i > $o] :
( ( ( ( sK8_E @ SV16 )
= ( multiplication @ ( sK15_SY23 @ SV16 ) @ ( sK18_SY34 @ SV16 ) ) )
= $true )
| ( $false = $true )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(200,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ~ ( SV16 @ ( sK13_SY27 @ SV15 @ SV16 ) )
| ~ ( SV15 @ ( sK16_SY30 @ SV15 @ SV16 ) ) )
= $false )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(202,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ~ ( SV16 @ ( sK14_SY25 @ SV15 @ SV16 ) )
| ~ ( SV15 @ ( sK17_SY32 @ SV15 @ SV16 ) ) )
= $false )
| ( $false = $true )
| ( ( ( sup @ sK1_X )
= ( sup @ SV15 ) )
= $false )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(204,plain,
! [SV16: $i > $o] :
( ( ( ~ ( SV16 @ ( sK15_SY23 @ SV16 ) )
| ~ ( sK1_X @ ( sK18_SY34 @ SV16 ) ) )
= $false )
| ( $false = $true )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(206,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ~ ( SV16 @ ( sK13_SY27 @ SV15 @ SV16 ) ) )
= $false )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(207,plain,
! [SV16: $i > $o,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK16_SY30 @ SV15 @ SV16 ) ) )
= $false )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(209,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ~ ( SV16 @ ( sK14_SY25 @ SV15 @ SV16 ) ) )
= $false )
| ( $false = $true )
| ( ( ( sup @ sK1_X )
= ( sup @ SV15 ) )
= $false )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(210,plain,
! [SV16: $i > $o,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK17_SY32 @ SV15 @ SV16 ) ) )
= $false )
| ( $false = $true )
| ( ( ( sup @ sK1_X )
= ( sup @ SV15 ) )
= $false )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(212,plain,
! [SV16: $i > $o] :
( ( ( ~ ( SV16 @ ( sK15_SY23 @ SV16 ) ) )
= $false )
| ( $false = $true )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[204]) ).
thf(213,plain,
! [SV16: $i > $o] :
( ( ( ~ ( sK1_X @ ( sK18_SY34 @ SV16 ) ) )
= $false )
| ( $false = $true )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[204]) ).
thf(215,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( SV16 @ ( sK13_SY27 @ SV15 @ SV16 ) )
= $true )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(216,plain,
! [SV16: $i > $o,SV15: $i > $o] :
( ( ( SV15 @ ( sK16_SY30 @ SV15 @ SV16 ) )
= $true )
| ( $false = $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(218,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( SV16 @ ( sK14_SY25 @ SV15 @ SV16 ) )
= $true )
| ( $false = $true )
| ( ( ( sup @ sK1_X )
= ( sup @ SV15 ) )
= $false )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(219,plain,
! [SV16: $i > $o,SV15: $i > $o] :
( ( ( SV15 @ ( sK17_SY32 @ SV15 @ SV16 ) )
= $true )
| ( $false = $true )
| ( ( ( sup @ sK1_X )
= ( sup @ SV15 ) )
= $false )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(221,plain,
! [SV16: $i > $o] :
( ( ( SV16 @ ( sK15_SY23 @ SV16 ) )
= $true )
| ( $false = $true )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(222,plain,
! [SV16: $i > $o] :
( ( ( sK1_X @ ( sK18_SY34 @ SV16 ) )
= $true )
| ( $false = $true )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(229,plain,
( ( ( sK1_X @ sK4_E )
= $true )
| ( ( zero = one )
= $false ) ),
inference(sim,[status(thm)],[85]) ).
thf(230,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( SV13 @ ( sK11_SY22 @ SV13 ) )
= $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ( ( sup @ SX1 )
!= SX0 ) ) ) )
= $false ) ),
inference(sim,[status(thm)],[162]) ).
thf(231,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( sK11_SY22 @ SV13 @ ( sK6_E @ SV13 ) )
= $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ( ( sup @ SX1 )
!= SX0 ) ) ) )
= $false ) ),
inference(sim,[status(thm)],[163]) ).
thf(232,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( SV13 @ ( sK12_SY21 @ SV13 ) )
= $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ~ ( SX1 @ SX0 ) ) ) )
= $false ) ),
inference(sim,[status(thm)],[165]) ).
thf(233,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( ( sup @ ( sK12_SY21 @ SV13 ) )
= ( sK5_E @ SV13 ) )
= $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ~ ( SX1 @ SX0 ) ) ) )
= $false ) ),
inference(sim,[status(thm)],[166]) ).
thf(234,plain,
( ( ( sK7_E @ ( multiplication @ zero @ ( sup @ sK1_X ) ) )
= ( multiplication @ zero @ ( sup @ sK1_X ) ) )
= $true ),
inference(sim,[status(thm)],[95]) ).
thf(235,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( SV16 @ ( sK13_SY27 @ SV15 @ SV16 ) )
= $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) ) )
= $false ) ),
inference(sim,[status(thm)],[215]) ).
thf(236,plain,
! [SV16: $i > $o,SV15: $i > $o] :
( ( ( SV15 @ ( sK16_SY30 @ SV15 @ SV16 ) )
= $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) ) )
= $false ) ),
inference(sim,[status(thm)],[216]) ).
thf(237,plain,
! [SV16: $i > $o,SV15: $i > $o] :
( ( ( ( sK10_E @ SV15 @ SV16 )
= ( multiplication @ ( sK13_SY27 @ SV15 @ SV16 ) @ ( sK16_SY30 @ SV15 @ SV16 ) ) )
= $true )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) ) )
= $false ) ),
inference(sim,[status(thm)],[192]) ).
thf(238,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( SV16 @ ( sK14_SY25 @ SV15 @ SV16 ) )
= $true )
| ( ( ( sup @ sK1_X )
= ( sup @ SV15 ) )
= $false )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(sim,[status(thm)],[218]) ).
thf(239,plain,
! [SV16: $i > $o,SV15: $i > $o] :
( ( ( SV15 @ ( sK17_SY32 @ SV15 @ SV16 ) )
= $true )
| ( ( ( sup @ sK1_X )
= ( sup @ SV15 ) )
= $false )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(sim,[status(thm)],[219]) ).
thf(240,plain,
! [SV16: $i > $o,SV15: $i > $o] :
( ( ( ( sK9_E @ SV15 @ SV16 )
= ( multiplication @ ( sK14_SY25 @ SV15 @ SV16 ) @ ( sK17_SY32 @ SV15 @ SV16 ) ) )
= $true )
| ( ( ( sup @ sK1_X )
= ( sup @ SV15 ) )
= $false )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(sim,[status(thm)],[195]) ).
thf(241,plain,
! [SV16: $i > $o] :
( ( ( SV16 @ ( sK15_SY23 @ SV16 ) )
= $true )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(sim,[status(thm)],[221]) ).
thf(242,plain,
! [SV16: $i > $o] :
( ( ( sK1_X @ ( sK18_SY34 @ SV16 ) )
= $true )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(sim,[status(thm)],[222]) ).
thf(243,plain,
! [SV16: $i > $o] :
( ( ( ( sK8_E @ SV16 )
= ( multiplication @ ( sK15_SY23 @ SV16 ) @ ( sK18_SY34 @ SV16 ) ) )
= $true )
| ( ( zero
= ( sup @ SV16 ) )
= $false ) ),
inference(sim,[status(thm)],[198]) ).
thf(244,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( zero
= ( multiplication @ ( multiplication @ zero @ ( sup @ sK1_X ) ) @ one ) )
= ( ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ SX1 )
| ~ ( SV15 @ SX2 ) )
| ( SX0
!= ( multiplication @ SX1 @ SX2 ) ) ) ) ) )
= $false ),
inference(res,[status(thm)],[53,67]) ).
thf(245,plain,
! [SV14: $i] :
( ( ( zero
= ( multiplication @ ( multiplication @ zero @ ( sup @ sK1_X ) ) @ one ) )
= ( ( sup
@ ^ [SX0: $i] : ( SX0 = SV14 ) )
= SV14 ) )
= $false ),
inference(res,[status(thm)],[53,63]) ).
thf(246,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( zero
= ( multiplication @ ( multiplication @ zero @ ( sup @ sK1_X ) ) @ one ) )
= ( ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ( ( sup @ SX1 )
!= SX0 ) ) )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ~ ( SX1 @ SX0 ) ) ) ) )
= $false ),
inference(res,[status(thm)],[53,59]) ).
thf(247,plain,
! [SV12: $i] :
( ( ( zero
= ( multiplication @ ( multiplication @ zero @ ( sup @ sK1_X ) ) @ one ) )
= ( ( multiplication @ one @ SV12 )
= SV12 ) )
= $false ),
inference(res,[status(thm)],[53,47]) ).
thf(248,plain,
! [SV11: $i] :
( ( ( zero
= ( multiplication @ ( multiplication @ zero @ ( sup @ sK1_X ) ) @ one ) )
= ( ( multiplication @ SV11 @ one )
= SV11 ) )
= $false ),
inference(res,[status(thm)],[53,46]) ).
thf(249,plain,
( ( ( zero
= ( multiplication @ ( multiplication @ zero @ ( sup @ sK1_X ) ) @ one ) )
= ( ( sup
@ ^ [SX0: $i] : $false )
= zero ) )
= $false ),
inference(res,[status(thm)],[53,21]) ).
thf(250,plain,
( ( ( multiplication @ ( multiplication @ zero @ ( sup @ sK1_X ) ) @ one )
= ( sup
@ ^ [SX0: $i] : $false ) )
= $false ),
inference(extuni,[status(esa)],[249]) ).
thf(251,plain,
( ( ( ( multiplication @ ( multiplication @ zero @ ( sup @ sK1_X ) ) @ one )
= zero )
= $false )
| ( ( zero
= ( sup
@ ^ [SX0: $i] : $false ) )
= $false ) ),
inference(extuni,[status(esa)],[249]) ).
thf(252,plain,
( ( zero
= ( multiplication @ zero @ ( sup @ sK1_X ) ) )
= $false ),
inference(extuni,[status(esa)],[248:[bind(SV11,$thf( multiplication @ zero @ ( sup @ sK1_X ) ))]]) ).
thf(253,plain,
( ( ( multiplication @ ( multiplication @ zero @ ( sup @ sK1_X ) ) @ one )
= ( multiplication @ zero @ one ) )
= $false ),
inference(extuni,[status(esa)],[248:[bind(SV11,$thf( zero ))]]) ).
thf(254,plain,
( ( zero
= ( multiplication @ ( multiplication @ ( multiplication @ zero @ ( sup @ sK1_X ) ) @ one ) @ one ) )
= $false ),
inference(extuni,[status(esa)],[248:[bind(SV11,$thf( multiplication @ ( multiplication @ zero @ ( sup @ sK1_X ) ) @ one ))]]) ).
thf(255,plain,
( ( ( zero = one )
= $false )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= one )
= $false ) ),
inference(extuni,[status(esa)],[247:[bind(SV12,$thf( one ))]]) ).
thf(256,plain,
( ( ( multiplication @ ( multiplication @ zero @ ( sup @ sK1_X ) ) @ one )
= ( multiplication @ one @ zero ) )
= $false ),
inference(extuni,[status(esa)],[247:[bind(SV12,$thf( zero ))]]) ).
thf(257,plain,
( ( zero
= ( multiplication @ one @ ( multiplication @ ( multiplication @ zero @ ( sup @ sK1_X ) ) @ one ) ) )
= $false ),
inference(extuni,[status(esa)],[247:[bind(SV12,$thf( multiplication @ ( multiplication @ zero @ ( sup @ sK1_X ) ) @ one ))]]) ).
thf(258,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( zero
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ~ ( SX1 @ SX0 ) ) ) )
= $false )
| ( ( ( multiplication @ ( multiplication @ zero @ ( sup @ sK1_X ) ) @ one )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ( ( sup @ SX1 )
!= SX0 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[246]) ).
thf(259,plain,
! [SV13: ( $i > $o ) > $o] :
( ( ( ( multiplication @ ( multiplication @ zero @ ( sup @ sK1_X ) ) @ one )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ~ ( SX1 @ SX0 ) ) ) )
= $false )
| ( ( zero
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i > $o] :
~ ~ ( ~ ( SV13 @ SX1 )
| ( ( sup @ SX1 )
!= SX0 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[246]) ).
thf(260,plain,
( ( ( multiplication @ ( multiplication @ zero @ ( sup @ sK1_X ) ) @ one )
= ( sup
@ ^ [SX0: $i] : ( SX0 = zero ) ) )
= $false ),
inference(extuni,[status(esa)],[245:[bind(SV14,$thf( zero ))]]) ).
thf(261,plain,
( ( zero
= ( sup
@ ^ [SX0: $i] :
( SX0
= ( multiplication @ ( multiplication @ zero @ ( sup @ sK1_X ) ) @ one ) ) ) )
= $false ),
inference(extuni,[status(esa)],[245:[bind(SV14,$thf( multiplication @ ( multiplication @ zero @ ( sup @ sK1_X ) ) @ one ))]]) ).
thf(262,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( zero
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ SX1 )
| ~ ( SV15 @ SX2 ) )
| ( SX0
!= ( multiplication @ SX1 @ SX2 ) ) ) ) )
= $false )
| ( ( one
= ( sup @ SV15 ) )
= $false )
| ( ( ( multiplication @ zero @ ( sup @ sK1_X ) )
= ( sup @ SV16 ) )
= $false ) ),
inference(extuni,[status(esa)],[244]) ).
thf(263,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( zero
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ SX1 )
| ~ ( SV15 @ SX2 ) )
| ( SX0
!= ( multiplication @ SX1 @ SX2 ) ) ) ) )
= $false )
| ( ( ( multiplication @ ( multiplication @ zero @ ( sup @ sK1_X ) ) @ one )
= ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[244]) ).
thf(264,plain,
! [SV15: $i > $o,SV16: $i > $o] :
( ( ( ( multiplication @ ( multiplication @ zero @ ( sup @ sK1_X ) ) @ one )
= ( sup
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( SV16 @ SX1 )
| ~ ( SV15 @ SX2 ) )
| ( SX0
!= ( multiplication @ SX1 @ SX2 ) ) ) ) )
= $false )
| ( ( zero
= ( multiplication @ ( sup @ SV16 ) @ ( sup @ SV15 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[244]) ).
thf(265,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,264,263,262,261,260,259,258,257,256,255,254,253,252,251,250,243,242,241,240,239,238,237,236,235,234,233,232,231,230,229,108,105,102,99,98,97,94,91,88,87,84,83,82,81,80,79,72,71,70,69,67,66,65,63,62,61,59,58,57,56,55,54,53,52,51,47,46,45,44,28]) ).
thf(266,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[265]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : QUA012^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.19 % Computer : n013.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Oct 6 14:00:06 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 180.68/30.50
% 180.68/30.50 No.of.Axioms: 7
% 180.68/30.50
% 180.68/30.50 Length.of.Defs: 1135
% 180.68/30.50
% 180.68/30.50 Contains.Choice.Funs: true
% 180.68/30.50 ..eprover: CPU time limit exceeded, terminating
% 180.68/30.50 eprover: CPU time limit exceeded, terminating
% 180.68/30.50 .....
% 180.68/30.50
% 180.68/30.50 ********************************
% 180.68/30.50 * All subproblems solved! *
% 180.68/30.50 ********************************
% 180.68/30.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,ps:3,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:265,loop_count:10,foatp_calls:3,translation:fof_full)
% 180.68/30.50
% 180.68/30.50 %**** Beginning of derivation protocol ****
% 180.68/30.50 % SZS output start CNFRefutation
% See solution above
% 180.68/30.51
% 180.68/30.51 %**** End of derivation protocol ****
% 180.68/30.51 %**** no. of clauses in derivation: 203 ****
% 180.68/30.51 %**** clause counter: 265 ****
% 180.68/30.51
% 180.68/30.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,ps:3,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:265,loop_count:10,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------