TSTP Solution File: SEU614^2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU614^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:13:22 EDT 2022
% Result : Theorem 0.20s 0.43s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 8
% Syntax : Number of formulae : 163 ( 27 unt; 6 typ; 1 def)
% Number of atoms : 1411 ( 407 equ; 0 cnn)
% Maximal formula atoms : 4 ( 8 avg)
% Number of connectives : 2714 ( 628 ~; 738 |; 20 &;1294 @)
% ( 0 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 633 ( 0 ^ 633 !; 0 ?; 633 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY10,type,
sK2_SY10: $i ).
thf(tp_sK3_SY12,type,
sK3_SY12: $i ).
thf(tp_symdiff,type,
symdiff: $i > $i > $i ).
thf(tp_symdiffE,type,
symdiffE: $o ).
thf(symdiffE,definition,
( symdiffE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffE) ).
thf(1,conjecture,
( symdiffE
=> ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(2,negated_conjecture,
( ( symdiffE
=> ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) )
=> ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,symdiffE]) ).
thf(4,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ( in @ sK3_SY12 @ sK1_A )
& ( in @ sK3_SY12 @ sK2_SY10 )
& ( in @ sK3_SY12 @ ( symdiff @ sK1_A @ sK2_SY10 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( symdiff @ A @ B ) )
| ( ( ( in @ Xx @ A )
| ~ ( in @ Xx @ A )
| ! [Xphi: $o] : Xphi )
& ( ( in @ Xx @ A )
| ( in @ Xx @ B )
| ! [Xphi: $o] : Xphi )
& ( ( in @ Xx @ A )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ( ~ ( in @ Xx @ B )
| ~ ( in @ Xx @ A )
| ! [Xphi: $o] : Xphi )
& ( ~ ( in @ Xx @ B )
| ( in @ Xx @ B )
| ! [Xphi: $o] : Xphi )
& ( ~ ( in @ Xx @ B )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ! [Xphi: $o] :
( ~ Xphi
| ~ ( in @ Xx @ A )
| Xphi )
& ! [Xphi: $o] :
( ~ Xphi
| ( in @ Xx @ B )
| Xphi )
& ! [Xphi: $o] :
( ~ Xphi
| ~ Xphi
| Xphi ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(9,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( symdiff @ A @ B ) )
| ( ( ( in @ Xx @ A )
| ~ ( in @ Xx @ A )
| ! [Xphi: $o] : Xphi )
& ( ( in @ Xx @ A )
| ( in @ Xx @ B )
| ! [Xphi: $o] : Xphi )
& ( ( in @ Xx @ A )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ( ~ ( in @ Xx @ B )
| ~ ( in @ Xx @ A )
| ! [Xphi: $o] : Xphi )
& ( ~ ( in @ Xx @ B )
| ( in @ Xx @ B )
| ! [Xphi: $o] : Xphi )
& ( ~ ( in @ Xx @ B )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ! [Xphi: $o] :
( ~ Xphi
| ~ ( in @ Xx @ A )
| Xphi )
& ! [Xphi: $o] :
( ~ Xphi
| ( in @ Xx @ B )
| Xphi )
& ! [Xphi: $o] :
( ~ Xphi
| ~ Xphi
| Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(10,plain,
( ( ( in @ sK3_SY12 @ sK1_A )
& ( in @ sK3_SY12 @ sK2_SY10 )
& ( in @ sK3_SY12 @ ( symdiff @ sK1_A @ sK2_SY10 ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( ~ ( ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SX2 @ SX0 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX1 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SX3: $o] :
( ~ SX3
| ~ ( in @ SX2 @ SX0 )
| SX3 )
| ~ ~ ( ~ ! [SX3: $o] :
( ~ SX3
| ( in @ SX2 @ SX1 )
| SX3 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,symdiffE]) ).
thf(12,plain,
( ( ~ ( ~ ( in @ sK3_SY12 @ sK1_A )
| ~ ~ ( ~ ( in @ sK3_SY12 @ sK2_SY10 )
| ~ ( in @ sK3_SY12 @ ( symdiff @ sK1_A @ sK2_SY10 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,symdiffE]) ).
thf(13,plain,
! [SV1: $i] :
( ( ! [SY13: $i,SY14: $i] :
( ~ ( in @ SY14 @ ( symdiff @ SV1 @ SY13 ) )
| ~ ( ~ ~ ( ~ ( ( in @ SY14 @ SV1 )
| ~ ( in @ SY14 @ SV1 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SY14 @ SV1 )
| ( in @ SY14 @ SY13 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SY14 @ SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SY14 @ SY13 )
| ~ ( in @ SY14 @ SV1 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SY14 @ SY13 )
| ( in @ SY14 @ SY13 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SY14 @ SY13 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY21: $o] :
( ~ SY21
| ~ ( in @ SY14 @ SV1 )
| SY21 )
| ~ ~ ( ~ ! [SX3: $o] :
( ~ SX3
| ( in @ SY14 @ SY13 )
| SX3 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ( in @ sK3_SY12 @ sK1_A )
| ~ ~ ( ~ ( in @ sK3_SY12 @ sK2_SY10 )
| ~ ( in @ sK3_SY12 @ ( symdiff @ sK1_A @ sK2_SY10 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY24: $i] :
( ~ ( in @ SY24 @ ( symdiff @ SV1 @ SV2 ) )
| ~ ( ~ ~ ( ~ ( ( in @ SY24 @ SV1 )
| ~ ( in @ SY24 @ SV1 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SY24 @ SV1 )
| ( in @ SY24 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SY24 @ SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SY24 @ SV2 )
| ~ ( in @ SY24 @ SV1 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SY24 @ SV2 )
| ( in @ SY24 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SY24 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY21: $o] :
( ~ SY21
| ~ ( in @ SY24 @ SV1 )
| SY21 )
| ~ ~ ( ~ ! [SY32: $o] :
( ~ SY32
| ( in @ SY24 @ SV2 )
| SY32 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( in @ sK3_SY12 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ~ ( ~ ( in @ sK3_SY12 @ sK2_SY10 )
| ~ ( in @ sK3_SY12 @ ( symdiff @ sK1_A @ sK2_SY10 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ~ ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
| ~ ( ~ ~ ( ~ ( ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV1 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV3 @ SV1 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV3 @ SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV3 @ SV2 )
| ~ ( in @ SV3 @ SV1 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV3 @ SV2 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV3 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY40: $o] :
( ~ SY40
| ~ ( in @ SV3 @ SV1 )
| SY40 )
| ~ ~ ( ~ ! [SY41: $o] :
( ~ SY41
| ( in @ SV3 @ SV2 )
| SY41 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( in @ sK3_SY12 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( ~ ( in @ sK3_SY12 @ sK2_SY10 )
| ~ ( in @ sK3_SY12 @ ( symdiff @ sK1_A @ sK2_SY10 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV1 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV3 @ SV1 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV3 @ SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV3 @ SV2 )
| ~ ( in @ SV3 @ SV1 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV3 @ SV2 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV3 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY40: $o] :
( ~ SY40
| ~ ( in @ SV3 @ SV1 )
| SY40 )
| ~ ~ ( ~ ! [SY41: $o] :
( ~ SY41
| ( in @ SV3 @ SV2 )
| SY41 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ( in @ sK3_SY12 @ sK2_SY10 )
| ~ ( in @ sK3_SY12 @ ( symdiff @ sK1_A @ sK2_SY10 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV1 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV3 @ SV1 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV3 @ SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV3 @ SV2 )
| ~ ( in @ SV3 @ SV1 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV3 @ SV2 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV3 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY40: $o] :
( ~ SY40
| ~ ( in @ SV3 @ SV1 )
| SY40 )
| ~ ~ ( ~ ! [SY41: $o] :
( ~ SY41
| ( in @ SV3 @ SV2 )
| SY41 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(24,plain,
( ( ~ ( in @ sK3_SY12 @ sK2_SY10 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(25,plain,
( ( ~ ( in @ sK3_SY12 @ ( symdiff @ sK1_A @ sK2_SY10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(26,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV1 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV3 @ SV1 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV3 @ SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV3 @ SV2 )
| ~ ( in @ SV3 @ SV1 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV3 @ SV2 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV3 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY40: $o] :
( ~ SY40
| ~ ( in @ SV3 @ SV1 )
| SY40 )
| ~ ~ ( ~ ! [SY41: $o] :
( ~ SY41
| ( in @ SV3 @ SV2 )
| SY41 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(27,plain,
( ( in @ sK3_SY12 @ sK2_SY10 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(28,plain,
( ( in @ sK3_SY12 @ ( symdiff @ sK1_A @ sK2_SY10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(29,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV1 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV3 @ SV1 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV3 @ SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) ) )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(30,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV3 @ SV2 )
| ~ ( in @ SV3 @ SV1 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV3 @ SV2 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV3 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY40: $o] :
( ~ SY40
| ~ ( in @ SV3 @ SV1 )
| SY40 )
| ~ ~ ( ~ ! [SY41: $o] :
( ~ SY41
| ( in @ SV3 @ SV2 )
| SY41 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(31,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ( ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV1 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV3 @ SV1 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV3 @ SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) ) )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(32,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ SV3 @ SV2 )
| ~ ( in @ SV3 @ SV1 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV3 @ SV2 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV3 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY40: $o] :
( ~ SY40
| ~ ( in @ SV3 @ SV1 )
| SY40 )
| ~ ~ ( ~ ! [SY41: $o] :
( ~ SY41
| ( in @ SV3 @ SV2 )
| SY41 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(33,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV1 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV3 @ SV1 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV3 @ SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ SV3 @ SV2 )
| ~ ( in @ SV3 @ SV1 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV3 @ SV2 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV3 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY40: $o] :
( ~ SY40
| ~ ( in @ SV3 @ SV1 )
| SY40 )
| ~ ~ ( ~ ! [SY41: $o] :
( ~ SY41
| ( in @ SV3 @ SV2 )
| SY41 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV1 )
| ! [SX3: $o] : SX3 ) )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(36,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( ( in @ SV3 @ SV1 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV3 @ SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(37,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ SV3 @ SV2 )
| ~ ( in @ SV3 @ SV1 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV3 @ SV2 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV3 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) ) )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(38,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ! [SY40: $o] :
( ~ SY40
| ~ ( in @ SV3 @ SV1 )
| SY40 )
| ~ ~ ( ~ ! [SY41: $o] :
( ~ SY41
| ( in @ SV3 @ SV2 )
| SY41 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(39,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV1 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(40,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ( ( in @ SV3 @ SV1 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV3 @ SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(41,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV3 @ SV2 )
| ~ ( in @ SV3 @ SV1 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV3 @ SV2 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV3 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) ) )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(42,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ! [SY40: $o] :
( ~ SY40
| ~ ( in @ SV3 @ SV1 )
| SY40 )
| ~ ~ ( ~ ! [SY41: $o] :
( ~ SY41
| ( in @ SV3 @ SV2 )
| SY41 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(43,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ SV1 )
= $true )
| ( ( ~ ( in @ SV3 @ SV1 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ( in @ SV3 @ SV1 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV3 @ SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( ~ ( in @ SV3 @ SV2 )
| ~ ( in @ SV3 @ SV1 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV3 @ SV2 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV3 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ! [SY40: $o] :
( ~ SY40
| ~ ( in @ SV3 @ SV1 )
| SY40 )
| ~ ~ ( ~ ! [SY41: $o] :
( ~ SY41
| ( in @ SV3 @ SV2 )
| SY41 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV1 ) )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ( in @ SV3 @ SV1 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 ) )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(49,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ( in @ SV3 @ SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(50,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( ~ ( in @ SV3 @ SV2 )
| ~ ( in @ SV3 @ SV1 )
| ! [SX3: $o] : SX3 ) )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(51,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ SV3 @ SV2 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV3 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(52,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ! [SY40: $o] :
( ~ SY40
| ~ ( in @ SV3 @ SV1 )
| SY40 ) )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(53,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ! [SY41: $o] :
( ~ SY41
| ( in @ SV3 @ SV2 )
| SY41 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(54,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ SV1 )
= $false )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(55,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ( in @ SV3 @ SV1 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(56,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ( in @ SV3 @ SV1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(57,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 )
| ~ ( in @ SV3 @ SV1 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(58,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV3 @ SV2 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV3 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(59,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ! [SY40: $o] :
( ~ SY40
| ~ ( in @ SV3 @ SV1 )
| SY40 ) )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(60,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( ~ ! [SY41: $o] :
( ~ SY41
| ( in @ SV3 @ SV2 )
| SY41 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(61,plain,
! [SV2: $i,SV1: $i,SV3: $i,SV4: $o] :
( ( SV4 = $true )
| ( ( in @ SV3 @ SV1 )
= $false )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[54]) ).
thf(62,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( $true = $true )
| ( ( in @ SV3 @ SV1 )
= $false )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[54]) ).
thf(63,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( $false = $true )
| ( ( in @ SV3 @ SV1 )
= $false )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[54]) ).
thf(64,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ SV1 )
= $true )
| ( ( ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(65,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ SV1 )
= $true )
| ( ( ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(66,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 ) )
= $true )
| ( ( ~ ( in @ SV3 @ SV1 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(67,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( ~ ( in @ SV3 @ SV2 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV3 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(68,plain,
! [SV2: $i,SV1: $i,SV3: $i,SV5: $o] :
( ( ( ~ SV5
| ~ ( in @ SV3 @ SV1 )
| SV5 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[59]) ).
thf(69,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ $true
| ~ ( in @ SV3 @ SV1 )
| $true )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[59]) ).
thf(70,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ $false
| ~ ( in @ SV3 @ SV1 )
| $false )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[59]) ).
thf(71,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ! [SY41: $o] :
( ~ SY41
| ( in @ SV3 @ SV2 )
| SY41 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(72,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( in @ SV3 @ SV2 )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(73,plain,
! [SV2: $i,SV1: $i,SV3: $i,SV6: $o] :
( ( ( ~ SV6
| SV6 )
= $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[65]) ).
thf(74,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[65]) ).
thf(75,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[65]) ).
thf(76,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( in @ SV3 @ SV2 )
= $false )
| ( ( ~ ( in @ SV3 @ SV1 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(77,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( ~ ( in @ SV3 @ SV2 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 ) )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(78,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( ~ ( in @ SV3 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(79,plain,
! [SV2: $i,SV1: $i,SV3: $i,SV5: $o] :
( ( ( ~ SV5 )
= $true )
| ( ( ~ ( in @ SV3 @ SV1 )
| SV5 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(80,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ $true )
= $true )
| ( ( ~ ( in @ SV3 @ SV1 )
| $true )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(81,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ $false )
= $true )
| ( ( ~ ( in @ SV3 @ SV1 )
| $false )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(82,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ! [SY41: $o] :
( ~ SY41
| ( in @ SV3 @ SV2 )
| SY41 ) )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(83,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(84,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV7: $o] :
( ( SV7 = $true )
| ( ( in @ SV3 @ SV2 )
= $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[72]) ).
thf(85,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( $true = $true )
| ( ( in @ SV3 @ SV2 )
= $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[72]) ).
thf(86,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( $false = $true )
| ( ( in @ SV3 @ SV2 )
= $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[72]) ).
thf(87,plain,
! [SV2: $i,SV1: $i,SV3: $i,SV6: $o] :
( ( ( ~ SV6 )
= $true )
| ( SV6 = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(88,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ $true )
= $true )
| ( $true = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(89,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ $false )
= $true )
| ( $false = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(90,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV1 ) )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(91,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 )
| ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(92,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(93,plain,
! [SV2: $i,SV1: $i,SV3: $i,SV5: $o] :
( ( SV5 = $false )
| ( ( ~ ( in @ SV3 @ SV1 )
| SV5 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(94,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( $true = $false )
| ( ( ~ ( in @ SV3 @ SV1 )
| $true )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(95,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( $false = $false )
| ( ( ~ ( in @ SV3 @ SV1 )
| $false )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(96,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ! [SY41: $o] :
( ~ SY41
| ( in @ SV3 @ SV2 )
| SY41 ) )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(97,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(98,plain,
! [SV2: $i,SV1: $i,SV3: $i,SV6: $o] :
( ( SV6 = $false )
| ( SV6 = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(99,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(100,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(101,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ SV1 )
= $false )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(102,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 ) )
= $true )
| ( ( ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(103,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 ) )
= $true )
| ( ( ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(104,plain,
! [SV2: $i,SV5: $o,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV1 ) )
= $true )
| ( SV5 = $true )
| ( SV5 = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(105,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV1 ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(106,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV1 ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(107,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV8: $o] :
( ( ( ~ SV8
| ( in @ SV3 @ SV2 )
| SV8 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[96]) ).
thf(108,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ $true
| ( in @ SV3 @ SV2 )
| $true )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[96]) ).
thf(109,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ $false
| ( in @ SV3 @ SV2 )
| $false )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[96]) ).
thf(110,plain,
! [SV2: $i,SV1: $i,SV3: $i,SV9: $o] :
( ( ( ~ SV9
| ~ SV9
| SV9 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[97]) ).
thf(111,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ $true
| ~ $true
| $true )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[97]) ).
thf(112,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ $false
| ~ $false
| $false )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[97]) ).
thf(113,plain,
! [SV2: $i,SV1: $i,SV3: $i,SV10: $o] :
( ( SV10 = $true )
| ( ( in @ SV3 @ SV1 )
= $false )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[101]) ).
thf(114,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( $true = $true )
| ( ( in @ SV3 @ SV1 )
= $false )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[101]) ).
thf(115,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( $false = $true )
| ( ( in @ SV3 @ SV1 )
= $false )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[101]) ).
thf(116,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( in @ SV3 @ SV2 )
= $false )
| ( ( ( in @ SV3 @ SV2 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(117,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( in @ SV3 @ SV2 )
= $false )
| ( ( ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(118,plain,
! [SV2: $i,SV5: $o,SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ SV1 )
= $false )
| ( SV5 = $true )
| ( SV5 = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(119,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ SV1 )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(120,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ SV1 )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(121,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV8: $o] :
( ( ( ~ SV8 )
= $true )
| ( ( ( in @ SV3 @ SV2 )
| SV8 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(122,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ $true )
= $true )
| ( ( ( in @ SV3 @ SV2 )
| $true )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(123,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ $false )
= $true )
| ( ( ( in @ SV3 @ SV2 )
| $false )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(124,plain,
! [SV2: $i,SV1: $i,SV3: $i,SV9: $o] :
( ( ( ~ SV9 )
= $true )
| ( ( ~ SV9
| SV9 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(125,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ $true )
= $true )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(126,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ $false )
= $true )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(127,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( in @ SV3 @ SV2 )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(128,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV11: $o] :
( ( ( ~ SV11
| SV11 )
= $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[117]) ).
thf(129,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[117]) ).
thf(130,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[117]) ).
thf(131,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV8: $o] :
( ( SV8 = $false )
| ( ( ( in @ SV3 @ SV2 )
| SV8 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(132,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( $true = $false )
| ( ( ( in @ SV3 @ SV2 )
| $true )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(133,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( $false = $false )
| ( ( ( in @ SV3 @ SV2 )
| $false )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(134,plain,
! [SV2: $i,SV1: $i,SV3: $i,SV9: $o] :
( ( SV9 = $false )
| ( ( ~ SV9
| SV9 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(135,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( $true = $false )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(136,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( $false = $false )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(137,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV12: $o] :
( ( SV12 = $true )
| ( ( in @ SV3 @ SV2 )
= $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[127]) ).
thf(138,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( $true = $true )
| ( ( in @ SV3 @ SV2 )
= $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[127]) ).
thf(139,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( $false = $true )
| ( ( in @ SV3 @ SV2 )
= $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[127]) ).
thf(140,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV11: $o] :
( ( ( ~ SV11 )
= $true )
| ( SV11 = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(141,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ $true )
= $true )
| ( $true = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(142,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ $false )
= $true )
| ( $false = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(143,plain,
! [SV1: $i,SV8: $o,SV2: $i,SV3: $i] :
( ( ( in @ SV3 @ SV2 )
= $true )
| ( SV8 = $true )
| ( SV8 = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(144,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( in @ SV3 @ SV2 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(145,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( in @ SV3 @ SV2 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(146,plain,
! [SV2: $i,SV1: $i,SV3: $i,SV9: $o] :
( ( ( ~ SV9 )
= $true )
| ( SV9 = $true )
| ( SV9 = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(147,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ $true )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(148,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ $false )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(149,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV11: $o] :
( ( SV11 = $false )
| ( SV11 = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(150,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(151,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(152,plain,
! [SV2: $i,SV1: $i,SV3: $i,SV9: $o] :
( ( SV9 = $false )
| ( SV9 = $true )
| ( SV9 = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(153,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(154,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(155,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,154,153,152,151,150,149,145,144,143,139,138,137,120,119,118,115,114,113,100,99,98,86,85,84,63,62,61,28,27]) ).
thf(156,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU614^2 : TPTP v8.1.0. Released v3.7.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 20 13:46:02 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.34
% 0.20/0.34 No.of.Axioms: 0
% 0.20/0.34
% 0.20/0.34 Length.of.Defs: 276
% 0.20/0.34
% 0.20/0.34 Contains.Choice.Funs: false
% 0.20/0.34 (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)..........
% 0.20/0.43
% 0.20/0.43 ********************************
% 0.20/0.43 * All subproblems solved! *
% 0.20/0.43 ********************************
% 0.20/0.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:155,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.45
% 0.20/0.45 %**** Beginning of derivation protocol ****
% 0.20/0.45 % SZS output start CNFRefutation
% See solution above
% 0.20/0.45
% 0.20/0.45 %**** End of derivation protocol ****
% 0.20/0.45 %**** no. of clauses in derivation: 156 ****
% 0.20/0.45 %**** clause counter: 155 ****
% 0.20/0.45
% 0.20/0.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:155,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------