TSTP Solution File: SEU781^2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU781^2 : 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 : n029.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 12:14:42 EDT 2022
% Result : Theorem 0.20s 0.48s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 19
% Syntax : Number of formulae : 95 ( 50 unt; 15 typ; 3 def)
% Number of atoms : 825 ( 176 equ; 0 cnn)
% Maximal formula atoms : 9 ( 10 avg)
% Number of connectives : 2701 ( 446 ~; 318 |; 22 &;1852 @)
% ( 0 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 9 con; 0-5 aty)
% Number of variables : 226 ( 5 ^ 218 !; 3 ?; 226 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_breln,type,
breln: $i > $i > $i > $o ).
thf(tp_breln1,type,
breln1: $i > $i > $o ).
thf(tp_breln1compE,type,
breln1compE: $o ).
thf(tp_breln1compset,type,
breln1compset: $i > $i > $i > $i ).
thf(tp_cartprod,type,
cartprod: $i > $i > $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_kpair,type,
kpair: $i > $i > $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY49,type,
sK2_SY49: $i ).
thf(tp_sK3_SY55,type,
sK3_SY55: $i ).
thf(tp_sK4_SY60,type,
sK4_SY60: $i ).
thf(tp_sK5_SY64,type,
sK5_SY64: $i ).
thf(tp_sK6_SY67,type,
sK6_SY67: $o ).
thf(tp_sK7_Xz,type,
sK7_Xz: $i > $i > $i > $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(breln,definition,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln) ).
thf(breln1,definition,
( breln1
= ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1) ).
thf(breln1compE,definition,
( breln1compE
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
=> ? [Xz: $i] :
( ( in @ Xz @ A )
& ( in @ ( kpair @ Xx @ Xz ) @ R )
& ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compE) ).
thf(1,conjecture,
( breln1compE
=> ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
=> ! [Xphi: $o] :
( ! [Xz: $i] :
( ( in @ Xz @ A )
=> ( ( in @ ( kpair @ Xx @ Xz ) @ R )
=> ( ( in @ ( kpair @ Xz @ Xy ) @ S )
=> Xphi ) ) )
=> Xphi ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compEex) ).
thf(2,negated_conjecture,
( ( breln1compE
=> ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
=> ! [Xphi: $o] :
( ! [Xz: $i] :
( ( in @ Xz @ A )
=> ( ( in @ ( kpair @ Xx @ Xz ) @ R )
=> ( ( in @ ( kpair @ Xz @ Xy ) @ S )
=> Xphi ) ) )
=> Xphi ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY15: $i,SY16: $i] :
( ( subset @ SY16 @ ( cartprod @ SY15 @ SY15 ) )
=> ! [SY21: $i] :
( ( subset @ SY21 @ ( cartprod @ SY15 @ SY15 ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY15 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY15 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ SY15 @ SY16 @ SY21 ) )
=> ? [Xz: $i] :
( ( in @ Xz @ SY15 )
& ( in @ ( kpair @ Xx @ Xz ) @ SY16 )
& ( in @ ( kpair @ Xz @ Xy ) @ SY21 ) ) ) ) ) ) )
=> ! [SY0: $i,SY1: $i] :
( ( subset @ SY1 @ ( cartprod @ SY0 @ SY0 ) )
=> ! [SY6: $i] :
( ( subset @ SY6 @ ( cartprod @ SY0 @ SY0 ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY0 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY0 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ SY0 @ SY1 @ SY6 ) )
=> ! [Xphi: $o] :
( ! [Xz: $i] :
( ( in @ Xz @ SY0 )
=> ( ( in @ ( kpair @ Xx @ Xz ) @ SY1 )
=> ( ( in @ ( kpair @ Xz @ Xy ) @ SY6 )
=> Xphi ) ) )
=> Xphi ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,breln,breln1,breln1compE]) ).
thf(4,plain,
( ( ! [SY15: $i,SY16: $i] :
( ( subset @ SY16 @ ( cartprod @ SY15 @ SY15 ) )
=> ! [SY21: $i] :
( ( subset @ SY21 @ ( cartprod @ SY15 @ SY15 ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY15 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY15 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ SY15 @ SY16 @ SY21 ) )
=> ? [Xz: $i] :
( ( in @ Xz @ SY15 )
& ( in @ ( kpair @ Xx @ Xz ) @ SY16 )
& ( in @ ( kpair @ Xz @ Xy ) @ SY21 ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY0: $i,SY1: $i] :
( ( subset @ SY1 @ ( cartprod @ SY0 @ SY0 ) )
=> ! [SY6: $i] :
( ( subset @ SY6 @ ( cartprod @ SY0 @ SY0 ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY0 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY0 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ SY0 @ SY1 @ SY6 ) )
=> ! [Xphi: $o] :
( ! [Xz: $i] :
( ( in @ Xz @ SY0 )
=> ( ( in @ ( kpair @ Xx @ Xz ) @ SY1 )
=> ( ( in @ ( kpair @ Xz @ Xy ) @ SY6 )
=> Xphi ) ) )
=> Xphi ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [SY0: $i,SY1: $i] :
( ( subset @ SY1 @ ( cartprod @ SY0 @ SY0 ) )
=> ! [SY6: $i] :
( ( subset @ SY6 @ ( cartprod @ SY0 @ SY0 ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY0 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY0 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ SY0 @ SY1 @ SY6 ) )
=> ! [Xphi: $o] :
( ! [Xz: $i] :
( ( in @ Xz @ SY0 )
=> ( ( in @ ( kpair @ Xx @ Xz ) @ SY1 )
=> ( ( in @ ( kpair @ Xz @ Xy ) @ SY6 )
=> Xphi ) ) )
=> Xphi ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ( subset @ sK2_SY49 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
& ( subset @ sK3_SY55 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
& ( in @ sK4_SY60 @ sK1_SY0 )
& ( in @ sK5_SY64 @ sK1_SY0 )
& ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
& ! [SY69: $i] :
( ~ ( in @ SY69 @ sK1_SY0 )
| ~ ( in @ ( kpair @ sK4_SY60 @ SY69 ) @ sK2_SY49 )
| ~ ( in @ ( kpair @ SY69 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 )
& ~ sK6_SY67 )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [SY15: $i,SY16: $i] :
( ~ ( subset @ SY16 @ ( cartprod @ SY15 @ SY15 ) )
| ! [SY21: $i] :
( ~ ( subset @ SY21 @ ( cartprod @ SY15 @ SY15 ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY15 )
| ! [Xy: $i] :
( ~ ( in @ Xy @ SY15 )
| ~ ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ SY15 @ SY16 @ SY21 ) )
| ( ( in @ ( sK7_Xz @ Xy @ Xx @ SY21 @ SY16 @ SY15 ) @ SY15 )
& ( in @ ( kpair @ Xx @ ( sK7_Xz @ Xy @ Xx @ SY21 @ SY16 @ SY15 ) ) @ SY16 )
& ( in @ ( kpair @ ( sK7_Xz @ Xy @ Xx @ SY21 @ SY16 @ SY15 ) @ Xy ) @ SY21 ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(9,plain,
( ( ! [SY15: $i,SY16: $i] :
( ~ ( subset @ SY16 @ ( cartprod @ SY15 @ SY15 ) )
| ! [SY21: $i] :
( ~ ( subset @ SY21 @ ( cartprod @ SY15 @ SY15 ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY15 )
| ! [Xy: $i] :
( ~ ( in @ Xy @ SY15 )
| ~ ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ SY15 @ SY16 @ SY21 ) )
| ( ( in @ ( sK7_Xz @ Xy @ Xx @ SY21 @ SY16 @ SY15 ) @ SY15 )
& ( in @ ( kpair @ Xx @ ( sK7_Xz @ Xy @ Xx @ SY21 @ SY16 @ SY15 ) ) @ SY16 )
& ( in @ ( kpair @ ( sK7_Xz @ Xy @ Xx @ SY21 @ SY16 @ SY15 ) @ Xy ) @ SY21 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(10,plain,
( ( ( subset @ sK2_SY49 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
& ( subset @ sK3_SY55 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
& ( in @ sK4_SY60 @ sK1_SY0 )
& ( in @ sK5_SY64 @ sK1_SY0 )
& ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
& ! [SY69: $i] :
( ~ ( in @ SY69 @ sK1_SY0 )
| ~ ( in @ ( kpair @ sK4_SY60 @ SY69 ) @ sK2_SY49 )
| ~ ( in @ ( kpair @ SY69 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 )
& ~ sK6_SY67 )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ ( cartprod @ SX0 @ SX0 ) )
| ! [SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ ( breln1compset @ SX0 @ SX1 @ SX2 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ ( sK7_Xz @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( in @ ( kpair @ ( sK7_Xz @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,breln,breln1,breln1compE]) ).
thf(12,plain,
( ( ~ ( ~ ( subset @ sK2_SY49 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
| ~ ~ ( ~ ( subset @ sK3_SY55 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
| ~ ~ ( ~ ( in @ sK4_SY60 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ sK5_SY64 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
| ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 )
| ~ ~ sK6_SY67 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,breln,breln1,breln1compE]) ).
thf(13,plain,
! [SV1: $i] :
( ( ! [SY70: $i] :
( ~ ( subset @ SY70 @ ( cartprod @ SV1 @ SV1 ) )
| ! [SY71: $i] :
( ~ ( subset @ SY71 @ ( cartprod @ SV1 @ SV1 ) )
| ! [SY72: $i] :
( ~ ( in @ SY72 @ SV1 )
| ! [SY73: $i] :
( ~ ( in @ SY73 @ SV1 )
| ~ ( in @ ( kpair @ SY72 @ SY73 ) @ ( breln1compset @ SV1 @ SY70 @ SY71 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SY73 @ SY72 @ SY71 @ SY70 @ SV1 ) @ SV1 )
| ~ ( in @ ( kpair @ SY72 @ ( sK7_Xz @ SY73 @ SY72 @ SY71 @ SY70 @ SV1 ) ) @ SY70 ) )
| ~ ( in @ ( kpair @ ( sK7_Xz @ SY73 @ SY72 @ SY71 @ SY70 @ SV1 ) @ SY73 ) @ SY71 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ( subset @ sK2_SY49 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
| ~ ~ ( ~ ( subset @ sK3_SY55 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
| ~ ~ ( ~ ( in @ sK4_SY60 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ sK5_SY64 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
| ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 )
| ~ ~ sK6_SY67 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: $i,SV2: $i] :
( ( ~ ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
| ! [SY74: $i] :
( ~ ( subset @ SY74 @ ( cartprod @ SV1 @ SV1 ) )
| ! [SY75: $i] :
( ~ ( in @ SY75 @ SV1 )
| ! [SY76: $i] :
( ~ ( in @ SY76 @ SV1 )
| ~ ( in @ ( kpair @ SY75 @ SY76 ) @ ( breln1compset @ SV1 @ SV2 @ SY74 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SY76 @ SY75 @ SY74 @ SV2 @ SV1 ) @ SV1 )
| ~ ( in @ ( kpair @ SY75 @ ( sK7_Xz @ SY76 @ SY75 @ SY74 @ SV2 @ SV1 ) ) @ SV2 ) )
| ~ ( in @ ( kpair @ ( sK7_Xz @ SY76 @ SY75 @ SY74 @ SV2 @ SV1 ) @ SY76 ) @ SY74 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( subset @ sK2_SY49 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ~ ( ~ ( subset @ sK3_SY55 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
| ~ ~ ( ~ ( in @ sK4_SY60 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ sK5_SY64 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
| ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 )
| ~ ~ sK6_SY67 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
! [SV1: $i,SV2: $i] :
( ( ( ~ ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) ) )
= $true )
| ( ( ! [SY74: $i] :
( ~ ( subset @ SY74 @ ( cartprod @ SV1 @ SV1 ) )
| ! [SY75: $i] :
( ~ ( in @ SY75 @ SV1 )
| ! [SY76: $i] :
( ~ ( in @ SY76 @ SV1 )
| ~ ( in @ ( kpair @ SY75 @ SY76 ) @ ( breln1compset @ SV1 @ SV2 @ SY74 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SY76 @ SY75 @ SY74 @ SV2 @ SV1 ) @ SV1 )
| ~ ( in @ ( kpair @ SY75 @ ( sK7_Xz @ SY76 @ SY75 @ SY74 @ SV2 @ SV1 ) ) @ SV2 ) )
| ~ ( in @ ( kpair @ ( sK7_Xz @ SY76 @ SY75 @ SY74 @ SV2 @ SV1 ) @ SY76 ) @ SY74 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( subset @ sK2_SY49 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( ~ ( subset @ sK3_SY55 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
| ~ ~ ( ~ ( in @ sK4_SY60 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ sK5_SY64 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
| ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 )
| ~ ~ sK6_SY67 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV1: $i,SV2: $i] :
( ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
= $false )
| ( ( ! [SY74: $i] :
( ~ ( subset @ SY74 @ ( cartprod @ SV1 @ SV1 ) )
| ! [SY75: $i] :
( ~ ( in @ SY75 @ SV1 )
| ! [SY76: $i] :
( ~ ( in @ SY76 @ SV1 )
| ~ ( in @ ( kpair @ SY75 @ SY76 ) @ ( breln1compset @ SV1 @ SV2 @ SY74 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SY76 @ SY75 @ SY74 @ SV2 @ SV1 ) @ SV1 )
| ~ ( in @ ( kpair @ SY75 @ ( sK7_Xz @ SY76 @ SY75 @ SY74 @ SV2 @ SV1 ) ) @ SV2 ) )
| ~ ( in @ ( kpair @ ( sK7_Xz @ SY76 @ SY75 @ SY74 @ SV2 @ SV1 ) @ SY76 ) @ SY74 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ( subset @ sK3_SY55 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
| ~ ~ ( ~ ( in @ sK4_SY60 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ sK5_SY64 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
| ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 )
| ~ ~ sK6_SY67 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
| ! [SY77: $i] :
( ~ ( in @ SY77 @ SV1 )
| ! [SY78: $i] :
( ~ ( in @ SY78 @ SV1 )
| ~ ( in @ ( kpair @ SY77 @ SY78 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SY78 @ SY77 @ SV3 @ SV2 @ SV1 ) @ SV1 )
| ~ ( in @ ( kpair @ SY77 @ ( sK7_Xz @ SY78 @ SY77 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
| ~ ( in @ ( kpair @ ( sK7_Xz @ SY78 @ SY77 @ SV3 @ SV2 @ SV1 ) @ SY78 ) @ SV3 ) ) ) ) )
= $true )
| ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(24,plain,
( ( ~ ( subset @ sK3_SY55 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(25,plain,
( ( ~ ~ ( ~ ( in @ sK4_SY60 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ sK5_SY64 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
| ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 )
| ~ ~ sK6_SY67 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(26,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) ) )
= $true )
| ( ( ! [SY77: $i] :
( ~ ( in @ SY77 @ SV1 )
| ! [SY78: $i] :
( ~ ( in @ SY78 @ SV1 )
| ~ ( in @ ( kpair @ SY77 @ SY78 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SY78 @ SY77 @ SV3 @ SV2 @ SV1 ) @ SV1 )
| ~ ( in @ ( kpair @ SY77 @ ( sK7_Xz @ SY78 @ SY77 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
| ~ ( in @ ( kpair @ ( sK7_Xz @ SY78 @ SY77 @ SV3 @ SV2 @ SV1 ) @ SY78 ) @ SV3 ) ) ) ) )
= $true )
| ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(27,plain,
( ( subset @ sK3_SY55 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(28,plain,
( ( ~ ( ~ ( in @ sK4_SY60 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ sK5_SY64 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
| ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 )
| ~ ~ sK6_SY67 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(29,plain,
! [SV2: $i,SV1: $i,SV3: $i] :
( ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
= $false )
| ( ( ! [SY77: $i] :
( ~ ( in @ SY77 @ SV1 )
| ! [SY78: $i] :
( ~ ( in @ SY78 @ SV1 )
| ~ ( in @ ( kpair @ SY77 @ SY78 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SY78 @ SY77 @ SV3 @ SV2 @ SV1 ) @ SV1 )
| ~ ( in @ ( kpair @ SY77 @ ( sK7_Xz @ SY78 @ SY77 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
| ~ ( in @ ( kpair @ ( sK7_Xz @ SY78 @ SY77 @ SV3 @ SV2 @ SV1 ) @ SY78 ) @ SV3 ) ) ) ) )
= $true )
| ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(30,plain,
( ( ~ ( in @ sK4_SY60 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ sK5_SY64 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
| ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 )
| ~ ~ sK6_SY67 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(31,plain,
! [SV3: $i,SV2: $i,SV1: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ SV1 )
| ! [SY79: $i] :
( ~ ( in @ SY79 @ SV1 )
| ~ ( in @ ( kpair @ SV4 @ SY79 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SY79 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
| ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SY79 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
| ~ ( in @ ( kpair @ ( sK7_Xz @ SY79 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SY79 ) @ SV3 ) ) ) )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
= $false )
| ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(32,plain,
( ( ~ ( in @ sK4_SY60 @ sK1_SY0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(33,plain,
( ( ~ ~ ( ~ ( in @ sK5_SY64 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
| ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 )
| ~ ~ sK6_SY67 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(34,plain,
! [SV3: $i,SV2: $i,SV1: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ SV1 ) )
= $true )
| ( ( ! [SY79: $i] :
( ~ ( in @ SY79 @ SV1 )
| ~ ( in @ ( kpair @ SV4 @ SY79 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SY79 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
| ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SY79 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
| ~ ( in @ ( kpair @ ( sK7_Xz @ SY79 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SY79 ) @ SV3 ) ) ) )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
= $false )
| ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(35,plain,
( ( in @ sK4_SY60 @ sK1_SY0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(36,plain,
( ( ~ ( ~ ( in @ sK5_SY64 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
| ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 )
| ~ ~ sK6_SY67 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(37,plain,
! [SV3: $i,SV2: $i,SV1: $i,SV4: $i] :
( ( ( in @ SV4 @ SV1 )
= $false )
| ( ( ! [SY79: $i] :
( ~ ( in @ SY79 @ SV1 )
| ~ ( in @ ( kpair @ SV4 @ SY79 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SY79 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
| ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SY79 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
| ~ ( in @ ( kpair @ ( sK7_Xz @ SY79 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SY79 ) @ SV3 ) ) ) )
= $true )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
= $false )
| ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(38,plain,
( ( ~ ( in @ sK5_SY64 @ sK1_SY0 )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
| ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 )
| ~ ~ sK6_SY67 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV3: $i,SV2: $i,SV4: $i,SV1: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV1 )
| ~ ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
| ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
| ~ ( in @ ( kpair @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV5 ) @ SV3 ) ) )
= $true )
| ( ( in @ SV4 @ SV1 )
= $false )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
= $false )
| ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(40,plain,
( ( ~ ( in @ sK5_SY64 @ sK1_SY0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(41,plain,
( ( ~ ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
| ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 )
| ~ ~ sK6_SY67 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(42,plain,
! [SV3: $i,SV2: $i,SV4: $i,SV1: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV1 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
| ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
| ~ ( in @ ( kpair @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV5 ) @ SV3 ) ) )
= $true )
| ( ( in @ SV4 @ SV1 )
= $false )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
= $false )
| ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(43,plain,
( ( in @ sK5_SY64 @ sK1_SY0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(44,plain,
( ( ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
| ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 )
| ~ ~ sK6_SY67 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(45,plain,
! [SV3: $i,SV2: $i,SV4: $i,SV1: $i,SV5: $i] :
( ( ( in @ SV5 @ SV1 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
| ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
| ~ ( in @ ( kpair @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV5 ) @ SV3 ) ) )
= $true )
| ( ( in @ SV4 @ SV1 )
= $false )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
= $false )
| ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(46,plain,
( ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
| ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 )
| ~ ~ sK6_SY67 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(47,plain,
! [SV3: $i,SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
( ( ( ~ ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
| ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
| ~ ( in @ ( kpair @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV5 ) @ SV3 ) ) )
= $true )
| ( ( in @ SV5 @ SV1 )
= $false )
| ( ( in @ SV4 @ SV1 )
= $false )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
= $false )
| ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(48,plain,
( ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(49,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
| ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 )
| ~ ~ sK6_SY67 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(50,plain,
! [SV3: $i,SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
( ( ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
| ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
| ~ ( in @ ( kpair @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV5 ) @ SV3 ) ) )
= $true )
| ( ( in @ SV5 @ SV1 )
= $false )
| ( ( in @ SV4 @ SV1 )
= $false )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
= $false )
| ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(51,plain,
( ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(52,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
| ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 )
| ~ ~ sK6_SY67 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(53,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
| ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
| ~ ( in @ ( kpair @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV5 ) @ SV3 ) )
= $false )
| ( ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
= $false )
| ( ( in @ SV5 @ SV1 )
= $false )
| ( ( in @ SV4 @ SV1 )
= $false )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
= $false )
| ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(54,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
| ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 )
| ~ ~ sK6_SY67 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(55,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
| ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) ) )
= $false )
| ( ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
= $false )
| ( ( in @ SV5 @ SV1 )
= $false )
| ( ( in @ SV4 @ SV1 )
= $false )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
= $false )
| ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(56,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV5 ) @ SV3 ) )
= $false )
| ( ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
= $false )
| ( ( in @ SV5 @ SV1 )
= $false )
| ( ( in @ SV4 @ SV1 )
= $false )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
= $false )
| ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(57,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
| ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(58,plain,
( ( ~ ~ sK6_SY67 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(59,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
| ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) ) )
= $true )
| ( ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
= $false )
| ( ( in @ SV5 @ SV1 )
= $false )
| ( ( in @ SV4 @ SV1 )
= $false )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
= $false )
| ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(60,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i] :
( ( ( in @ ( kpair @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV5 ) @ SV3 )
= $true )
| ( ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
= $false )
| ( ( in @ SV5 @ SV1 )
= $false )
| ( ( in @ SV4 @ SV1 )
= $false )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
= $false )
| ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(61,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
| ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(62,plain,
( ( ~ sK6_SY67 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(63,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
| ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
= $false )
| ( ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
= $false )
| ( ( in @ SV5 @ SV1 )
= $false )
| ( ( in @ SV4 @ SV1 )
= $false )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
= $false )
| ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV6: $i] :
( ( ~ ( in @ SV6 @ sK1_SY0 )
| ~ ( in @ ( kpair @ sK4_SY60 @ SV6 ) @ sK2_SY49 )
| ~ ( in @ ( kpair @ SV6 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(65,plain,
sK6_SY67 = $false,
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(66,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 ) )
= $false )
| ( ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
= $false )
| ( ( in @ SV5 @ SV1 )
= $false )
| ( ( in @ SV4 @ SV1 )
= $false )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
= $false )
| ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(67,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV5: $i,SV4: $i] :
( ( ( ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
= $false )
| ( ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
= $false )
| ( ( in @ SV5 @ SV1 )
= $false )
| ( ( in @ SV4 @ SV1 )
= $false )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
= $false )
| ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(68,plain,
! [SV6: $i] :
( ( ( ~ ( in @ SV6 @ sK1_SY0 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ sK4_SY60 @ SV6 ) @ sK2_SY49 )
| ~ ( in @ ( kpair @ SV6 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i] :
( ( ( in @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
= $true )
| ( ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
= $false )
| ( ( in @ SV5 @ SV1 )
= $false )
| ( ( in @ SV4 @ SV1 )
= $false )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
= $false )
| ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(70,plain,
! [SV1: $i,SV2: $i,SV3: $i,SV5: $i,SV4: $i] :
( ( ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 )
= $true )
| ( ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
= $false )
| ( ( in @ SV5 @ SV1 )
= $false )
| ( ( in @ SV4 @ SV1 )
= $false )
| ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
= $false )
| ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(71,plain,
! [SV6: $i] :
( ( ( in @ SV6 @ sK1_SY0 )
= $false )
| ( ( ~ ( in @ ( kpair @ sK4_SY60 @ SV6 ) @ sK2_SY49 )
| ~ ( in @ ( kpair @ SV6 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(72,plain,
! [SV6: $i] :
( ( ( ~ ( in @ ( kpair @ sK4_SY60 @ SV6 ) @ sK2_SY49 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV6 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 )
= $true )
| ( ( in @ SV6 @ sK1_SY0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(73,plain,
! [SV6: $i] :
( ( ( in @ ( kpair @ sK4_SY60 @ SV6 ) @ sK2_SY49 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV6 @ sK5_SY64 ) @ sK3_SY55 )
| sK6_SY67 )
= $true )
| ( ( in @ SV6 @ sK1_SY0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(74,plain,
! [SV6: $i] :
( ( ( ~ ( in @ ( kpair @ SV6 @ sK5_SY64 ) @ sK3_SY55 ) )
= $true )
| ( sK6_SY67 = $true )
| ( ( in @ ( kpair @ sK4_SY60 @ SV6 ) @ sK2_SY49 )
= $false )
| ( ( in @ SV6 @ sK1_SY0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(75,plain,
! [SV6: $i] :
( ( ( in @ ( kpair @ SV6 @ sK5_SY64 ) @ sK3_SY55 )
= $false )
| ( sK6_SY67 = $true )
| ( ( in @ ( kpair @ sK4_SY60 @ SV6 ) @ sK2_SY49 )
= $false )
| ( ( in @ SV6 @ sK1_SY0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(76,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,75,70,69,65,60,51,43,35,27]) ).
thf(77,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU781^2 : TPTP v8.1.0. Released v3.7.0.
% 0.11/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 20 13:52:15 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 0
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 664
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.35 (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).......
% 0.20/0.48
% 0.20/0.48 ********************************
% 0.20/0.48 * All subproblems solved! *
% 0.20/0.48 ********************************
% 0.20/0.48 % 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:76,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.48
% 0.20/0.48 %**** Beginning of derivation protocol ****
% 0.20/0.48 % SZS output start CNFRefutation
% See solution above
% 0.20/0.48
% 0.20/0.48 %**** End of derivation protocol ****
% 0.20/0.48 %**** no. of clauses in derivation: 77 ****
% 0.20/0.48 %**** clause counter: 76 ****
% 0.20/0.48
% 0.20/0.48 % 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:76,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------