%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO555^1 : TPTP v9.3.1. Released v5.2.0.
% 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 : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 11:08:43 AM UTC 2026
% Result : Theorem 1.64s 0.51s
% Output : CNFRefutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 3
% Syntax : Number of formulae : 116 ( 24 unt; 0 typ; 2 def)
% Number of atoms : 1880 ( 972 equ; 0 cnn)
% Maximal formula atoms : 4 ( 16 avg)
% Number of connectives : 2989 (1841 ~; 954 |; 4 &; 190 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 11 con; 0-3 aty)
% Number of variables : 317 ( 232 ^; 85 !; 0 ?; 317 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_eps1,type,
eps1: ( $i > $o ) > $i ).
thf(tp_eps2,type,
eps2: ( $i > $o ) > $i ).
thf(tp_if1,type,
if1: $o > $i > $i > $i ).
thf(tp_if2,type,
if2: $o > $i > $i > $i ).
thf(tp_sK1_SV3,type,
sK1_SV3: $o ).
thf(tp_sK2_SV6,type,
sK2_SV6: $i ).
thf(tp_sK3_SV7,type,
sK3_SV7: $i ).
thf(tp_sK4_E,type,
sK4_E: $o ).
thf(tp_sK5_E,type,
sK5_E: $i ).
thf(tp_sK6_E,type,
sK6_E: $i ).
thf(tp_sK7_E,type,
sK7_E: $i ).
thf(tp_sK8_E,type,
sK8_E: $i ).
thf(tp_sK9_E,type,
sK9_E: $i ).
thf(if1,definition,
( if1
= ( ^ [B: $o,X: $i,Y: $i] :
( eps1
@ ^ [Z: $i] :
( ( B
& ( Z = X ) )
| ( ~ B
& ( Z = Y ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',if1d) ).
thf(if2,definition,
( if2
= ( ^ [B: $o,X: $i,Y: $i] :
( eps2
@ ^ [Z: $i] :
( ( B
& ( Z = X ) )
| ( ~ B
& ( Z = Y ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',if2d) ).
thf(3,conjecture,
if1 = if2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(4,negated_conjecture,
( ( if1 = if2 )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( if1 != if2 )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(10,plain,
( ( if1 != if2 )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(11,plain,
( ( ( ^ [SX0: $o,SX1: $i,SX2: $i] :
( eps1
@ ^ [SX3: $i] :
( ~ ( ~ SX0
| ( SX3 != SX1 ) )
| ~ ( ~ ~ SX0
| ( SX3 != SX2 ) ) ) ) )
!= ( ^ [SX0: $o,SX1: $i,SX2: $i] :
( eps2
@ ^ [SX3: $i] :
( ~ ( ~ SX0
| ( SX3 != SX1 ) )
| ~ ( ~ ~ SX0
| ( SX3 != SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,if1,if2]) ).
thf(14,plain,
( ( ( ^ [SX0: $o,SX1: $i,SX2: $i] :
( eps1
@ ^ [SX3: $i] :
( ~ ( ~ SX0
| ( SX3 != SX1 ) )
| ~ ( ~ ~ SX0
| ( SX3 != SX2 ) ) ) ) )
= ( ^ [SX0: $o,SX1: $i,SX2: $i] :
( eps2
@ ^ [SX3: $i] :
( ~ ( ~ SX0
| ( SX3 != SX1 ) )
| ~ ( ~ ~ SX0
| ( SX3 != SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(17,plain,
( ( ! [SV3: $o] :
( ( ^ [SY2: $i,SY3: $i] :
( eps1
@ ^ [SY4: $i] :
( ~ ( ~ SV3
| ( SY4 != SY2 ) )
| ~ ( ~ ~ SV3
| ( SY4 != SY3 ) ) ) ) )
= ( ^ [SY5: $i,SY6: $i] :
( eps2
@ ^ [SY7: $i] :
( ~ ( ~ SV3
| ( SY7 != SY5 ) )
| ~ ( ~ ~ SV3
| ( SY7 != SY6 ) ) ) ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[14]) ).
thf(18,plain,
( ( ( ^ [SX0: $o,SX1: $i,SX2: $i] :
( eps1
@ ^ [SX3: $i] :
( ~ ( ~ SX0
| ( SX3 != SX1 ) )
| ~ ( ~ ~ SX0
| ( SX3 != SX2 ) ) ) ) )
= ( ^ [SX0: $o,SX1: $i,SX2: $i] :
( eps2
@ ^ [SX3: $i] :
( ~ ( ~ SX0
| ( SX3 != SX1 ) )
| ~ ( ~ ~ SX0
| ( SX3 != SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[14]) ).
thf(21,plain,
( ( ( ^ [SY8: $i,SY9: $i] :
( eps1
@ ^ [SY10: $i] :
( ~ ( ~ sK1_SV3
| ( SY10 != SY8 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY10 != SY9 ) ) ) ) )
= ( ^ [SY11: $i,SY12: $i] :
( eps2
@ ^ [SY13: $i] :
( ~ ( ~ sK1_SV3
| ( SY13 != SY11 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY13 != SY12 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(24,plain,
( ( ! [SV6: $i] :
( ( ^ [SY14: $i] :
( eps1
@ ^ [SY15: $i] :
( ~ ( ~ sK1_SV3
| ( SY15 != SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY15 != SY14 ) ) ) ) )
= ( ^ [SY16: $i] :
( eps2
@ ^ [SY17: $i] :
( ~ ( ~ sK1_SV3
| ( SY17 != SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY17 != SY16 ) ) ) ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( ( ^ [SY8: $i,SY9: $i] :
( eps1
@ ^ [SY10: $i] :
( ~ ( ~ sK1_SV3
| ( SY10 != SY8 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY10 != SY9 ) ) ) ) )
= ( ^ [SY11: $i,SY12: $i] :
( eps2
@ ^ [SY13: $i] :
( ~ ( ~ sK1_SV3
| ( SY13 != SY11 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY13 != SY12 ) ) ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[21]) ).
thf(26,plain,
( ( ( ^ [SY18: $i] :
( eps1
@ ^ [SY19: $i] :
( ~ ( ~ sK1_SV3
| ( SY19 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY19 != SY18 ) ) ) ) )
= ( ^ [SY20: $i] :
( eps2
@ ^ [SY21: $i] :
( ~ ( ~ sK1_SV3
| ( SY21 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY21 != SY20 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[24]) ).
thf(27,plain,
( ( ! [SV7: $i] :
( ( eps1
@ ^ [SY22: $i] :
( ~ ( ~ sK1_SV3
| ( SY22 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY22 != SV7 ) ) ) )
= ( eps2
@ ^ [SY23: $i] :
( ~ ( ~ sK1_SV3
| ( SY23 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY23 != SV7 ) ) ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[26]) ).
thf(28,plain,
( ( ( ^ [SY18: $i] :
( eps1
@ ^ [SY19: $i] :
( ~ ( ~ sK1_SV3
| ( SY19 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY19 != SY18 ) ) ) ) )
= ( ^ [SY20: $i] :
( eps2
@ ^ [SY21: $i] :
( ~ ( ~ sK1_SV3
| ( SY21 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY21 != SY20 ) ) ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[26]) ).
thf(29,plain,
( ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
= ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[27]) ).
thf(30,plain,
( ( ~ ~ ! [SY26: $i] :
~ ( ~ ( ~ sK1_SV3
| ( SY26 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY26 != sK3_SV7 ) ) )
| ~ ( ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ),
inference(choice,[status(thm)],[29]) ).
thf(31,plain,
( ( ~ ~ ! [SY28: $i] :
~ ( ~ ( ~ sK1_SV3
| ( SY28 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY28 != sK3_SV7 ) ) )
| ~ ( ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ),
inference(choice,[status(thm)],[29]) ).
thf(32,plain,
( ( ( ~ ~ ! [SY26: $i] :
~ ( ~ ( ~ sK1_SV3
| ( SY26 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY26 != sK3_SV7 ) ) ) )
= $true )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(33,plain,
( ( ( ~ ~ ! [SY28: $i] :
~ ( ~ ( ~ sK1_SV3
| ( SY28 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY28 != sK3_SV7 ) ) ) )
= $true )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(34,plain,
( ( ( ~ ! [SY26: $i] :
~ ( ~ ( ~ sK1_SV3
| ( SY26 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY26 != sK3_SV7 ) ) ) )
= $false )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(35,plain,
( ( ( ~ ! [SY28: $i] :
~ ( ~ ( ~ sK1_SV3
| ( SY28 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY28 != sK3_SV7 ) ) ) )
= $false )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(36,plain,
( ( ( ! [SY26: $i] :
~ ( ~ ( ~ sK1_SV3
| ( SY26 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY26 != sK3_SV7 ) ) ) )
= $true )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(37,plain,
( ( ( ! [SY28: $i] :
~ ( ~ ( ~ sK1_SV3
| ( SY28 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY28 != sK3_SV7 ) ) ) )
= $true )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(38,plain,
! [SV10: $i] :
( ( ( ~ ( ~ ( ~ sK1_SV3
| ( SV10 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SV10 != sK3_SV7 ) ) ) )
= $true )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ( ~ sK1_SV3
| ( SV11 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SV11 != sK3_SV7 ) ) ) )
= $true )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV10: $i] :
( ( ( ~ ( ~ sK1_SV3
| ( SV10 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SV10 != sK3_SV7 ) ) )
= $false )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV11: $i] :
( ( ( ~ ( ~ sK1_SV3
| ( SV11 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SV11 != sK3_SV7 ) ) )
= $false )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV10: $i] :
( ( ( ~ ( ~ sK1_SV3
| ( SV10 != sK2_SV6 ) ) )
= $false )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(43,plain,
! [SV10: $i] :
( ( ( ~ ( ~ ~ sK1_SV3
| ( SV10 != sK3_SV7 ) ) )
= $false )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(44,plain,
! [SV11: $i] :
( ( ( ~ ( ~ sK1_SV3
| ( SV11 != sK2_SV6 ) ) )
= $false )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(45,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ~ sK1_SV3
| ( SV11 != sK3_SV7 ) ) )
= $false )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(46,plain,
! [SV10: $i] :
( ( ( ~ sK1_SV3
| ( SV10 != sK2_SV6 ) )
= $true )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(47,plain,
! [SV10: $i] :
( ( ( ~ ~ sK1_SV3
| ( SV10 != sK3_SV7 ) )
= $true )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(48,plain,
! [SV11: $i] :
( ( ( ~ sK1_SV3
| ( SV11 != sK2_SV6 ) )
= $true )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(49,plain,
! [SV11: $i] :
( ( ( ~ ~ sK1_SV3
| ( SV11 != sK3_SV7 ) )
= $true )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(50,plain,
! [SV10: $i] :
( ( ( ~ sK1_SV3 ) = $true )
| ( ( SV10 != sK2_SV6 )
= $true )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(51,plain,
! [SV10: $i] :
( ( ( ~ ~ sK1_SV3 )
= $true )
| ( ( SV10 != sK3_SV7 )
= $true )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV11: $i] :
( ( ( ~ sK1_SV3 ) = $true )
| ( ( SV11 != sK2_SV6 )
= $true )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV11: $i] :
( ( ( ~ ~ sK1_SV3 )
= $true )
| ( ( SV11 != sK3_SV7 )
= $true )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV10: $i] :
( ( sK1_SV3 = $false )
| ( ( SV10 != sK2_SV6 )
= $true )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV10: $i] :
( ( ( ~ sK1_SV3 ) = $false )
| ( ( SV10 != sK3_SV7 )
= $true )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(56,plain,
! [SV11: $i] :
( ( sK1_SV3 = $false )
| ( ( SV11 != sK2_SV6 )
= $true )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV11: $i] :
( ( ( ~ sK1_SV3 ) = $false )
| ( ( SV11 != sK3_SV7 )
= $true )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV10: $i] :
( ( ( SV10 = sK2_SV6 )
= $false )
| ( sK1_SV3 = $false )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(59,plain,
! [SV10: $i] :
( ( sK1_SV3 = $true )
| ( ( SV10 != sK3_SV7 )
= $true )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(60,plain,
! [SV11: $i] :
( ( ( SV11 = sK2_SV6 )
= $false )
| ( sK1_SV3 = $false )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(61,plain,
! [SV11: $i] :
( ( sK1_SV3 = $true )
| ( ( SV11 != sK3_SV7 )
= $true )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(62,plain,
! [SV10: $i] :
( ( ( ~ ( ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) ) )
= $true )
| ( ( ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true )
| ( sK1_SV3 = $false )
| ( ( SV10 = sK2_SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV10: $i] :
( ( ( SV10 = sK3_SV7 )
= $false )
| ( sK1_SV3 = $true )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV11: $i] :
( ( ( ~ ( ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) ) )
= $true )
| ( ( ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true )
| ( sK1_SV3 = $false )
| ( ( SV11 = sK2_SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV11: $i] :
( ( ( SV11 = sK3_SV7 )
= $false )
| ( sK1_SV3 = $true )
| ( ( ~ ( ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV10: $i] :
( ( ( ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
= $false )
| ( ( ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true )
| ( sK1_SV3 = $false )
| ( ( SV10 = sK2_SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV10: $i] :
( ( ( ~ ( ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) ) )
= $true )
| ( ( ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true )
| ( sK1_SV3 = $true )
| ( ( SV10 = sK3_SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV11: $i] :
( ( ( ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
= $false )
| ( ( ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true )
| ( sK1_SV3 = $false )
| ( ( SV11 = sK2_SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV11: $i] :
( ( ( ~ ( ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) ) )
= $true )
| ( ( ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true )
| ( sK1_SV3 = $true )
| ( ( SV11 = sK3_SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(71,plain,
! [SV10: $i] :
( ( ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK2_SV6 )
= $false )
| ( ( ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true )
| ( sK1_SV3 = $false )
| ( ( SV10 = sK2_SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(72,plain,
! [SV10: $i] :
( ( ( ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
= $false )
| ( ( ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true )
| ( sK1_SV3 = $true )
| ( ( SV10 = sK3_SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(74,plain,
! [SV11: $i] :
( ( ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK2_SV6 )
= $false )
| ( ( ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true )
| ( sK1_SV3 = $false )
| ( ( SV11 = sK2_SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(75,plain,
! [SV11: $i] :
( ( ( ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK2_SV6 ) )
= $false )
| ( ( ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true )
| ( sK1_SV3 = $true )
| ( ( SV11 = sK3_SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(77,plain,
! [SV10: $i] :
( ( ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( ( ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true )
| ( sK1_SV3 = $false )
| ( ( SV10 = sK2_SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(78,plain,
! [SV10: $i] :
( ( ( ~ sK1_SV3 ) = $false )
| ( ( ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true )
| ( sK1_SV3 = $true )
| ( ( SV10 = sK3_SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(79,plain,
! [SV10: $i] :
( ( ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK2_SV6 )
= $false )
| ( ( ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true )
| ( sK1_SV3 = $true )
| ( ( SV10 = sK3_SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(81,plain,
! [SV11: $i] :
( ( ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( ( ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true )
| ( sK1_SV3 = $false )
| ( ( SV11 = sK2_SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(82,plain,
! [SV11: $i] :
( ( ( ~ sK1_SV3 ) = $false )
| ( ( ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true )
| ( sK1_SV3 = $true )
| ( ( SV11 = sK3_SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(83,plain,
! [SV11: $i] :
( ( ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK2_SV6 )
= $false )
| ( ( ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true )
| ( sK1_SV3 = $true )
| ( ( SV11 = sK3_SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(85,plain,
! [SV10: $i] :
( ( ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) )
= $false )
| ( ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( sK1_SV3 = $false )
| ( ( SV10 = sK2_SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(86,plain,
! [SV10: $i] :
( ( sK1_SV3 = $true )
| ( ( ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true )
| ( sK1_SV3 = $true )
| ( ( SV10 = sK3_SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(87,plain,
! [SV10: $i] :
( ( ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( ( ~ ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true )
| ( sK1_SV3 = $true )
| ( ( SV10 = sK3_SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(89,plain,
! [SV11: $i] :
( ( ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) )
= $false )
| ( ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( sK1_SV3 = $false )
| ( ( SV11 = sK2_SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(90,plain,
! [SV11: $i] :
( ( sK1_SV3 = $true )
| ( ( ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true )
| ( sK1_SV3 = $true )
| ( ( SV11 = sK3_SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(91,plain,
! [SV11: $i] :
( ( ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( ( ~ ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) ) )
= $true )
| ( sK1_SV3 = $true )
| ( ( SV11 = sK3_SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(94,plain,
! [SV10: $i] :
( ( ( ~ ~ sK1_SV3 )
= $false )
| ( ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( sK1_SV3 = $false )
| ( ( SV10 = sK2_SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(95,plain,
! [SV10: $i] :
( ( ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 )
= $false )
| ( ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( sK1_SV3 = $false )
| ( ( SV10 = sK2_SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(96,plain,
! [SV10: $i] :
( ( ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) )
= $false )
| ( sK1_SV3 = $true )
| ( sK1_SV3 = $true )
| ( ( SV10 = sK3_SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(97,plain,
! [SV10: $i] :
( ( ( ~ ~ sK1_SV3
| ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) )
= $false )
| ( ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( sK1_SV3 = $true )
| ( ( SV10 = sK3_SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(100,plain,
! [SV11: $i] :
( ( ( ~ ~ sK1_SV3 )
= $false )
| ( ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( sK1_SV3 = $false )
| ( ( SV11 = sK2_SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(101,plain,
! [SV11: $i] :
( ( ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 )
= $false )
| ( ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( sK1_SV3 = $false )
| ( ( SV11 = sK2_SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(102,plain,
! [SV11: $i] :
( ( ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) )
= $false )
| ( sK1_SV3 = $true )
| ( sK1_SV3 = $true )
| ( ( SV11 = sK3_SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(103,plain,
! [SV11: $i] :
( ( ( ~ ~ sK1_SV3
| ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 ) )
= $false )
| ( ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( sK1_SV3 = $true )
| ( ( SV11 = sK3_SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(106,plain,
! [SV10: $i] :
( ( ( ~ sK1_SV3 ) = $true )
| ( ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( sK1_SV3 = $false )
| ( ( SV10 = sK2_SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(107,plain,
! [SV10: $i] :
( ( ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
= sK3_SV7 )
= $true )
| ( ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( sK1_SV3 = $false )
| ( ( SV10 = sK2_SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(109,plain,
! [SV10: $i] :
( ( ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 )
= $false )
| ( sK1_SV3 = $true )
| ( sK1_SV3 = $true )
| ( ( SV10 = sK3_SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(111,plain,
! [SV10: $i] :
( ( ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
!= sK3_SV7 )
= $false )
| ( ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( sK1_SV3 = $true )
| ( ( SV10 = sK3_SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(114,plain,
! [SV11: $i] :
( ( ( ~ sK1_SV3 ) = $true )
| ( ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( sK1_SV3 = $false )
| ( ( SV11 = sK2_SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(115,plain,
! [SV11: $i] :
( ( ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
= sK3_SV7 )
= $true )
| ( ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( sK1_SV3 = $false )
| ( ( SV11 = sK2_SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(117,plain,
! [SV11: $i] :
( ( ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 )
= $false )
| ( sK1_SV3 = $true )
| ( sK1_SV3 = $true )
| ( ( SV11 = sK3_SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(119,plain,
! [SV11: $i] :
( ( ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
!= sK3_SV7 )
= $false )
| ( ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( sK1_SV3 = $true )
| ( ( SV11 = sK3_SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(121,plain,
! [SV10: $i] :
( ( sK1_SV3 = $false )
| ( ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( sK1_SV3 = $false )
| ( ( SV10 = sK2_SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(123,plain,
! [SV10: $i] :
( ( ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
= sK3_SV7 )
= $true )
| ( sK1_SV3 = $true )
| ( sK1_SV3 = $true )
| ( ( SV10 = sK3_SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(125,plain,
! [SV10: $i] :
( ( ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
= sK3_SV7 )
= $true )
| ( ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( sK1_SV3 = $true )
| ( ( SV10 = sK3_SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(127,plain,
! [SV11: $i] :
( ( sK1_SV3 = $false )
| ( ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( sK1_SV3 = $false )
| ( ( SV11 = sK2_SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(129,plain,
! [SV11: $i] :
( ( ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
= sK3_SV7 )
= $true )
| ( sK1_SV3 = $true )
| ( sK1_SV3 = $true )
| ( ( SV11 = sK3_SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(131,plain,
! [SV11: $i] :
( ( ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
= sK3_SV7 )
= $true )
| ( ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( sK1_SV3 = $true )
| ( ( SV11 = sK3_SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(136,plain,
( ( ( eps1
@ ^ [SY41: $i] :
( ~ ( ~ sK4_E
| ( SY41 != sK5_E ) )
| ~ ( ~ ~ sK4_E
| ( SY41 != sK6_E ) ) ) )
= ( eps2
@ ^ [SY40: $i] :
( ~ ( ~ sK4_E
| ( SY40 != sK5_E ) )
| ~ ( ~ ~ sK4_E
| ( SY40 != sK6_E ) ) ) ) )
= $false ),
inference(extuni,[status(esa)],[18]) ).
thf(137,plain,
( ( ( eps1
@ ^ [SY47: $i] :
( ~ ( ~ sK1_SV3
| ( SY47 != sK7_E ) )
| ~ ( ~ ~ sK1_SV3
| ( SY47 != sK8_E ) ) ) )
= ( eps2
@ ^ [SY46: $i] :
( ~ ( ~ sK1_SV3
| ( SY46 != sK7_E ) )
| ~ ( ~ ~ sK1_SV3
| ( SY46 != sK8_E ) ) ) ) )
= $false ),
inference(extuni,[status(esa)],[25]) ).
thf(138,plain,
( ( ( eps1
@ ^ [SY49: $i] :
( ~ ( ~ sK1_SV3
| ( SY49 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY49 != sK9_E ) ) ) )
= ( eps2
@ ^ [SY48: $i] :
( ~ ( ~ sK1_SV3
| ( SY48 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY48 != sK9_E ) ) ) ) )
= $false ),
inference(extuni,[status(esa)],[28]) ).
thf(141,plain,
( ( sK1_SV3 = $false )
| ( ( ( eps1
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SV3
| ( SX0 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SX0 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( sK1_SV3 = $false ) ),
inference(extuni,[status(esa)],[121:[bind(SV10,$thf( sK2_SV6 ))]]) ).
thf(142,plain,
( ( sK1_SV3 = $false )
| ( ( ( eps1
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SV3
| ( SX0 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SX0 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( ( ( eps1
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SV3
| ( SX0 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SX0 != sK3_SV7 ) ) ) )
= sK3_SV7 )
= $true ) ),
inference(extuni,[status(esa)],[107:[bind(SV10,$thf( sK2_SV6 ))]]) ).
thf(144,plain,
( ( sK1_SV3 = $true )
| ( sK1_SV3 = $true )
| ( ( ( eps1
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SV3
| ( SX0 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SX0 != sK3_SV7 ) ) ) )
= sK3_SV7 )
= $true ) ),
inference(extuni,[status(esa)],[123:[bind(SV10,$thf( sK3_SV7 ))]]) ).
thf(146,plain,
( ( sK1_SV3 = $true )
| ( ( ( eps1
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SV3
| ( SX0 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SX0 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( ( ( eps1
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SV3
| ( SX0 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SX0 != sK3_SV7 ) ) ) )
= sK3_SV7 )
= $true ) ),
inference(extuni,[status(esa)],[125:[bind(SV10,$thf( sK3_SV7 ))]]) ).
thf(149,plain,
( ( sK1_SV3 = $false )
| ( ( ( eps2
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SV3
| ( SX0 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SX0 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( sK1_SV3 = $false ) ),
inference(extuni,[status(esa)],[127:[bind(SV11,$thf( sK2_SV6 ))]]) ).
thf(150,plain,
( ( sK1_SV3 = $false )
| ( ( ( eps2
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SV3
| ( SX0 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SX0 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( ( ( eps2
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SV3
| ( SX0 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SX0 != sK3_SV7 ) ) ) )
= sK3_SV7 )
= $true ) ),
inference(extuni,[status(esa)],[115:[bind(SV11,$thf( sK2_SV6 ))]]) ).
thf(152,plain,
( ( sK1_SV3 = $true )
| ( sK1_SV3 = $true )
| ( ( ( eps2
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SV3
| ( SX0 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SX0 != sK3_SV7 ) ) ) )
= sK3_SV7 )
= $true ) ),
inference(extuni,[status(esa)],[129:[bind(SV11,$thf( sK3_SV7 ))]]) ).
thf(154,plain,
( ( sK1_SV3 = $true )
| ( ( ( eps2
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SV3
| ( SX0 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SX0 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( ( ( eps2
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SV3
| ( SX0 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SX0 != sK3_SV7 ) ) ) )
= sK3_SV7 )
= $true ) ),
inference(extuni,[status(esa)],[131:[bind(SV11,$thf( sK3_SV7 ))]]) ).
thf(155,plain,
! [SV10: $i] :
( ( sK1_SV3 = $false )
| ( ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( ( SV10 = sK2_SV6 )
= $false ) ),
inference(sim,[status(thm)],[121]) ).
thf(156,plain,
! [SV10: $i] :
( ( ( ( eps1
@ ^ [SY24: $i] :
( ~ ( ~ sK1_SV3
| ( SY24 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY24 != sK3_SV7 ) ) ) )
= sK3_SV7 )
= $true )
| ( sK1_SV3 = $true )
| ( ( SV10 = sK3_SV7 )
= $false ) ),
inference(sim,[status(thm)],[123]) ).
thf(157,plain,
! [SV11: $i] :
( ( sK1_SV3 = $false )
| ( ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true )
| ( ( SV11 = sK2_SV6 )
= $false ) ),
inference(sim,[status(thm)],[127]) ).
thf(158,plain,
! [SV11: $i] :
( ( ( ( eps2
@ ^ [SY25: $i] :
( ~ ( ~ sK1_SV3
| ( SY25 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SY25 != sK3_SV7 ) ) ) )
= sK3_SV7 )
= $true )
| ( sK1_SV3 = $true )
| ( ( SV11 = sK3_SV7 )
= $false ) ),
inference(sim,[status(thm)],[129]) ).
thf(159,plain,
( ( sK1_SV3 = $false )
| ( ( ( eps1
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SV3
| ( SX0 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SX0 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true ) ),
inference(sim,[status(thm)],[141]) ).
thf(160,plain,
( ( sK1_SV3 = $true )
| ( ( ( eps1
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SV3
| ( SX0 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SX0 != sK3_SV7 ) ) ) )
= sK3_SV7 )
= $true ) ),
inference(sim,[status(thm)],[144]) ).
thf(161,plain,
( ( sK1_SV3 = $false )
| ( ( ( eps2
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SV3
| ( SX0 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SX0 != sK3_SV7 ) ) ) )
= sK2_SV6 )
= $true ) ),
inference(sim,[status(thm)],[149]) ).
thf(162,plain,
( ( sK1_SV3 = $true )
| ( ( ( eps2
@ ^ [SX0: $i] :
( ~ ( ~ sK1_SV3
| ( SX0 != sK2_SV6 ) )
| ~ ( ~ ~ sK1_SV3
| ( SX0 != sK3_SV7 ) ) ) )
= sK3_SV7 )
= $true ) ),
inference(sim,[status(thm)],[152]) ).
thf(163,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,162,161,160,159,158,157,156,155,154,150,146,142,138,137,136,131,125,115,107,29,28,25]) ).
thf(164,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO555^1 : TPTP v9.3.1. Released v5.2.0.
% 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
% 0.08/0.19 % Computer : n006.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 17:41:52 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.64/0.51
% 1.64/0.51 No.of.Axioms: 2
% 1.64/0.51
% 1.64/0.51 Length.of.Defs: 340
% 1.64/0.51
% 1.64/0.51 Contains.Choice.Funs: true
% 1.64/0.51 .
% 1.64/0.51
% 1.64/0.51 *** Modified list of choice operators: eps1 ***
% 1.64/0.51
% 1.64/0.51 *** Modified list of choice operators: eps2, eps1 ***
% 1.64/0.51 ..
% 1.64/0.51
% 1.64/0.51 ********************************
% 1.64/0.51 * All subproblems solved! *
% 1.64/0.51 ********************************
% 1.64/0.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:163,loop_count:0,foatp_calls:2,translation:fof_full)
% 1.64/0.51
% 1.64/0.51 %**** Beginning of derivation protocol ****
% 1.64/0.51 % SZS output start CNFRefutation
% See solution above
% 1.64/0.51
% 1.64/0.51 %**** End of derivation protocol ****
% 1.64/0.51 %**** no. of clauses in derivation: 114 ****
% 1.64/0.51 %**** clause counter: 163 ****
% 1.64/0.51
% 1.64/0.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:163,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------