%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU615^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:45:35 AM UTC 2026
% Result : Theorem 0.08s 0.27s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 2
% Syntax : Number of formulae : 142 ( 28 unt; 0 typ; 1 def)
% Number of atoms : 1478 ( 442 equ; 0 cnn)
% Maximal formula atoms : 4 ( 10 avg)
% Number of connectives : 2109 ( 396 ~; 512 |; 0 &;1158 @)
% ( 0 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 437 ( 0 ^; 437 !; 0 ?; 437 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY13,type,
sK2_SY13: $i ).
thf(tp_sK3_SY17,type,
sK3_SY17: $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',symdiffIneg2) ).
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,
( ( ! [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(copy,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,symdiffE]) ).
thf(10,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) )
| ! [SX3: $o] :
( ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| SX3 )
| ~ ( ~ ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| SX3 )
| SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,symdiffE]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: $i] :
( ( ! [SY10: $i,SY11: $i] :
( ~ ( in @ SY11 @ ( symdiff @ SV1 @ SY10 ) )
| ! [SY12: $o] :
( ~ ( ~ ( in @ SY11 @ SV1 )
| ~ ~ ( in @ SY11 @ SY10 )
| SY12 )
| ~ ( ~ ~ ( in @ SY11 @ SV1 )
| ~ ( in @ SY11 @ SY10 )
| SY12 )
| SY12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [SY13: $i,SY14: $i] :
( ~ ~ ( in @ SY14 @ sK1_SX0 )
| ~ ~ ( in @ SY14 @ SY13 )
| ~ ( in @ SY14 @ ( symdiff @ sK1_SX0 @ SY13 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(14,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY15: $i] :
( ~ ( in @ SY15 @ ( symdiff @ SV1 @ SV2 ) )
| ! [SY16: $o] :
( ~ ( ~ ( in @ SY15 @ SV1 )
| ~ ~ ( in @ SY15 @ SV2 )
| SY16 )
| ~ ( ~ ~ ( in @ SY15 @ SV1 )
| ~ ( in @ SY15 @ SV2 )
| SY16 )
| SY16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ! [SY17: $i] :
( ~ ~ ( in @ SY17 @ sK1_SX0 )
| ~ ~ ( in @ SY17 @ sK2_SY13 )
| ~ ( in @ SY17 @ ( symdiff @ sK1_SX0 @ sK2_SY13 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(16,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ~ ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
| ! [SY18: $o] :
( ~ ( ~ ( in @ SV3 @ SV1 )
| ~ ~ ( in @ SV3 @ SV2 )
| SY18 )
| ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| SY18 )
| SY18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ~ ( in @ sK3_SY17 @ sK1_SX0 )
| ~ ~ ( in @ sK3_SY17 @ sK2_SY13 )
| ~ ( in @ sK3_SY17 @ ( symdiff @ sK1_SX0 @ sK2_SY13 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(18,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) ) )
= $true )
| ( ( ! [SY18: $o] :
( ~ ( ~ ( in @ SV3 @ SV1 )
| ~ ~ ( in @ SV3 @ SV2 )
| SY18 )
| ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| SY18 )
| SY18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ~ ( in @ sK3_SY17 @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ~ ( in @ sK3_SY17 @ sK2_SY13 )
| ~ ( in @ sK3_SY17 @ ( symdiff @ sK1_SX0 @ sK2_SY13 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false )
| ( ( ! [SY18: $o] :
( ~ ( ~ ( in @ SV3 @ SV1 )
| ~ ~ ( in @ SV3 @ SV2 )
| SY18 )
| ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| SY18 )
| SY18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ( in @ sK3_SY17 @ sK1_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ~ ( in @ sK3_SY17 @ sK2_SY13 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ( in @ sK3_SY17 @ ( symdiff @ sK1_SX0 @ sK2_SY13 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(25,plain,
! [SV4: $o,SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ( in @ SV3 @ SV1 )
| ~ ~ ( in @ SV3 @ SV2 )
| SV4 )
| ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| SV4 )
| SV4 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ( in @ SV3 @ SV1 )
| ~ ~ ( in @ SV3 @ SV2 )
| $true )
| ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $true )
| $true )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[21]) ).
thf(27,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ( in @ SV3 @ SV1 )
| ~ ~ ( in @ SV3 @ SV2 )
| $false )
| ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $false )
| $false )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[21]) ).
thf(28,plain,
( ( in @ sK3_SY17 @ sK1_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(29,plain,
( ( ~ ( in @ sK3_SY17 @ sK2_SY13 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(30,plain,
( ( in @ sK3_SY17 @ ( symdiff @ sK1_SX0 @ sK2_SY13 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(31,plain,
! [SV4: $o,SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ( in @ SV3 @ SV1 )
| ~ ~ ( in @ SV3 @ SV2 )
| SV4 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| SV4 )
| SV4 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(32,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ( in @ SV3 @ SV1 )
| ~ ~ ( in @ SV3 @ SV2 )
| $true ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $true )
| $true )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(33,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ( in @ SV3 @ SV1 )
| ~ ~ ( in @ SV3 @ SV2 )
| $false ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $false )
| $false )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(34,plain,
( ( in @ sK3_SY17 @ sK2_SY13 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(35,plain,
! [SV4: $o,SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV1 )
| ~ ~ ( in @ SV3 @ SV2 )
| SV4 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| SV4 )
| SV4 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV1 )
| ~ ~ ( in @ SV3 @ SV2 )
| $true )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $true )
| $true )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV1 )
| ~ ~ ( in @ SV3 @ SV2 )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $false )
| $false )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV4: $o,SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV1 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| SV4 )
| SV4 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(39,plain,
! [SV1: $i,SV4: $o,SV2: $i,SV3: $i] :
( ( ( ~ ~ ( in @ SV3 @ SV2 )
| SV4 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| SV4 )
| SV4 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(40,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV1 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $true )
| $true )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(41,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ~ ( in @ SV3 @ SV2 )
| $true )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $true )
| $true )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(42,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV1 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $false )
| $false )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(43,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ~ ( in @ SV3 @ SV2 )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $false )
| $false )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(44,plain,
! [SV4: $o,SV2: $i,SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ SV1 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| SV4 )
| SV4 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(45,plain,
! [SV4: $o,SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ~ ( in @ SV3 @ SV2 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| SV4 )
| SV4 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(46,plain,
! [SV2: $i,SV1: $i,SV3: $i,SV4: $o] :
( ( SV4 = $false )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| SV4 )
| SV4 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(47,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ SV1 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $true )
| $true )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(48,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ~ ( in @ SV3 @ SV2 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $true )
| $true )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(49,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $true )
| $true )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(50,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ SV1 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $false )
| $false )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(51,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ~ ( in @ SV3 @ SV2 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $false )
| $false )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(52,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $false )
| $false )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(53,plain,
! [SV4: $o,SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| SV4 ) )
= $true )
| ( SV4 = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(54,plain,
! [SV4: $o,SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| SV4 )
| SV4 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(55,plain,
! [SV4: $o,SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| SV4 ) )
= $true )
| ( SV4 = $true )
| ( SV4 = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(56,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(57,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $true )
| $true )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(58,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(59,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(60,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $false )
| $false )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(61,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(62,plain,
! [SV4: $o,SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| SV4 )
= $false )
| ( SV4 = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(63,plain,
! [SV4: $o,SV1: $i,SV2: $i,SV3: $i] :
( ( ( in @ SV3 @ SV2 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| SV4 )
| SV4 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(64,plain,
! [SV4: $o,SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| SV4 )
= $false )
| ( SV4 = $true )
| ( SV4 = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(65,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(66,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( in @ SV3 @ SV2 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $true )
| $true )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(67,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(68,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(69,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( in @ SV3 @ SV2 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $false )
| $false )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(70,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(71,plain,
! [SV2: $i,SV4: $o,SV1: $i,SV3: $i] :
( ( ( ~ ~ ( in @ SV3 @ SV1 ) )
= $false )
| ( SV4 = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(72,plain,
! [SV1: $i,SV4: $o,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 )
| SV4 )
= $false )
| ( SV4 = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(73,plain,
! [SV4: $o,SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| SV4 ) )
= $true )
| ( SV4 = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(74,plain,
! [SV2: $i,SV4: $o,SV1: $i,SV3: $i] :
( ( ( ~ ~ ( in @ SV3 @ SV1 ) )
= $false )
| ( SV4 = $true )
| ( SV4 = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(75,plain,
! [SV1: $i,SV4: $o,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 )
| SV4 )
= $false )
| ( SV4 = $true )
| ( SV4 = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(76,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ~ ( in @ SV3 @ SV1 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(77,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(78,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(79,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ~ ( in @ SV3 @ SV1 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(80,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(81,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ~ ( in @ SV3 @ SV1 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(82,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(83,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(84,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ~ ( in @ SV3 @ SV1 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(85,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(86,plain,
! [SV2: $i,SV4: $o,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV1 ) )
= $true )
| ( SV4 = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(87,plain,
! [SV1: $i,SV4: $o,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 ) )
= $false )
| ( SV4 = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(88,plain,
! [SV2: $i,SV1: $i,SV3: $i,SV4: $o] :
( ( SV4 = $false )
| ( SV4 = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(89,plain,
! [SV4: $o,SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| SV4 )
= $false )
| ( SV4 = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(90,plain,
! [SV2: $i,SV4: $o,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV1 ) )
= $true )
| ( SV4 = $true )
| ( SV4 = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(91,plain,
! [SV1: $i,SV4: $o,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 ) )
= $false )
| ( SV4 = $true )
| ( SV4 = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(92,plain,
! [SV2: $i,SV1: $i,SV3: $i,SV4: $o] :
( ( SV4 = $false )
| ( SV4 = $true )
| ( SV4 = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(93,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV1 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(94,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(95,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(96,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(97,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV1 ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(98,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(99,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(100,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV1 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(101,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(102,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(103,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ~ ( in @ SV3 @ SV1 )
| ~ ( in @ SV3 @ SV2 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(104,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV1 ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(105,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(106,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(107,plain,
! [SV2: $i,SV4: $o,SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ SV1 )
= $false )
| ( SV4 = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(108,plain,
! [SV1: $i,SV4: $o,SV2: $i,SV3: $i] :
( ( ( in @ SV3 @ SV2 )
= $true )
| ( SV4 = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(109,plain,
! [SV2: $i,SV4: $o,SV1: $i,SV3: $i] :
( ( ( ~ ~ ( in @ SV3 @ SV1 ) )
= $false )
| ( SV4 = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(110,plain,
! [SV1: $i,SV4: $o,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 )
| SV4 )
= $false )
| ( SV4 = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(111,plain,
! [SV2: $i,SV4: $o,SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ SV1 )
= $false )
| ( SV4 = $true )
| ( SV4 = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(112,plain,
! [SV1: $i,SV4: $o,SV2: $i,SV3: $i] :
( ( ( in @ SV3 @ SV2 )
= $true )
| ( SV4 = $true )
| ( SV4 = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(113,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ SV1 )
= $false )
| ( $true = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(114,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( in @ SV3 @ SV2 )
= $true )
| ( $true = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(115,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ~ ( in @ SV3 @ SV1 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(116,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(117,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)],[97]) ).
thf(118,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( in @ SV3 @ SV2 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(119,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ SV1 )
= $false )
| ( $false = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(120,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( in @ SV3 @ SV2 )
= $true )
| ( $false = $true )
| ( ( in @ SV3 @ SV1 )
= $true )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(121,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ~ ( in @ SV3 @ SV1 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(122,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(123,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)],[104]) ).
thf(124,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( in @ SV3 @ SV2 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(125,plain,
! [SV2: $i,SV4: $o,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV1 ) )
= $true )
| ( SV4 = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(126,plain,
! [SV1: $i,SV4: $o,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 ) )
= $false )
| ( SV4 = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(127,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $o] :
( ( SV4 = $false )
| ( SV4 = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(128,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV1 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(129,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(130,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(131,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV1 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(132,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV2 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(133,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(134,plain,
! [SV2: $i,SV4: $o,SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ SV1 )
= $false )
| ( SV4 = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(135,plain,
! [SV1: $i,SV4: $o,SV2: $i,SV3: $i] :
( ( ( in @ SV3 @ SV2 )
= $true )
| ( SV4 = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(136,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ SV1 )
= $false )
| ( $true = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(137,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( in @ SV3 @ SV2 )
= $true )
| ( $true = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(138,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ SV1 )
= $false )
| ( $false = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(139,plain,
! [SV1: $i,SV2: $i,SV3: $i] :
( ( ( in @ SV3 @ SV2 )
= $true )
| ( $false = $true )
| ( ( in @ SV3 @ SV2 )
= $false )
| ( ( in @ SV3 @ ( symdiff @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(140,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,139,138,137,136,135,134,133,130,127,124,123,120,119,118,117,114,113,112,111,108,107,106,102,99,95,92,88,34,30]) ).
thf(141,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU615^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 15:35:39 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.27
% 0.08/0.27 No.of.Axioms: 0
% 0.08/0.27
% 0.08/0.27 Length.of.Defs: 276
% 0.08/0.27
% 0.08/0.27 Contains.Choice.Funs: false
% 0.08/0.27 ..
% 0.08/0.27
% 0.08/0.27 ********************************
% 0.08/0.27 * All subproblems solved! *
% 0.08/0.27 ********************************
% 0.08/0.27 % 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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:140,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.27
% 0.08/0.27 %**** Beginning of derivation protocol ****
% 0.08/0.27 % SZS output start CNFRefutation
% See solution above
% 0.08/0.27
% 0.08/0.27 %**** End of derivation protocol ****
% 0.08/0.27 %**** no. of clauses in derivation: 141 ****
% 0.08/0.27 %**** clause counter: 140 ****
% 0.08/0.27
% 0.08/0.27 % 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:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:140,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------